Mine water cooperative optimal scheduling based on improved genetic algorithm

Abstract

This article addresses the issues of unreasonable water scheduling and high costs in coal mine shafts, proposing a hierarchical optimization scheduling strategy. Taking the water quality and quantity of a certain mining area in Inner Mongolia as the research object, it designs the objective function with the highest reuse efficiency and the lowest reuse cost of mine water resources, and establishes the constraint conditions of water quality and quantity for each water-using unit. In response to the problem that traditional genetic algorithms are prone to local optima, an adaptive autobiographical operator is proposed and improved based on Metropolis principle of simulated annealing algorithm. The improved algorithm is applied to the calculation of the scheduling model, and the results show that the recovery cost in the heating season is reduced by 66779.36 CNY/month, a decrease of 10.34%; the recovery cost in the non-heating season is reduced by 61469.28 CNY/month, a decrease of 9.91%. At the same time, the heating season and the non-heating season have reduced by 136.99 h/month and 154.52 h/month respectively, significantly reducing the recovery cost and time.

Highlights

• •A mathematical model for a mine water coordinated scheduling system is established based on the classification of mine water in the mining area and multi-objective water supply rules.
• •An improved genetic simulated annealing algorithm is proposed to optimize the mine scheduling model with complex water constraints and multiple scheduling processes.
• •To address the premature convergence issue of the genetic algorithm, it is combined with simulated annealing. Adaptive improvements are made to the crossover, mutation, and random perturbation processes, enhancing the algorithm's search capability.

1. Introduction

During the coal mining process, groundwater and coal seams undergo a series of physical and chemical reactions, resulting in mine water containing a large amount of acidic substances and organic pollutants. This phenomenon not only leads to the loss of water resources but also has a detrimental impact on the mine environment. In severe cases, groundwater disasters can occur, endangering the safety of personnel and production in coal mines. Therefore, treating mine water during the mining process can not only conserve water resources and protect the water environment but is also of great significance for mine safety. At the same time, the coal production process requires a large amount of water, such as for underground firefighting, coal preparation, and cooling. Currently, mining areas are rationally arranging the reuse of mine water to achieve efficient allocation and utilization of mine water resources. This can not only improve the reuse rate and economic benefits of mine water but is also conducive to the improvement of the ecological environment in the mining area and the sustainable development of the mining area [1].

The treatment of mine water is a complex process composed of multiple processes, and the reuse of mine water also has corresponding differences in water quality requirements due to different functions. Due to environmental restrictions, deep treatment of mine water cannot be achieved underground, but surface water requires deep cleaning. Therefore, in terms of optimizing water resource scheduling in mining areas, a joint scheduling model of surface-underground can be established to achieve coordinated scheduling [2]. In the process of joint scheduling, optimizing the use of mine water, surface water, and groundwater can not only save water resources, protect the mining environment, but also further improve production efficiency and increase mining productivity. Some scholars have proposed a multi-objective economic management model for water resource management, including objective functions and constraints [3]. Some scholars have proposed that different treatment processes should be selected according to the water quality in the mining area to make the water quality of the effluent meet the reuse standard [4].

In the field of mine scheduling, many researchers have made a lot of contributions, including from multiple aspects such as production time, production process, and auxiliary production. Some researchers proposed a new random integer programming framework for underground mining plans, and optimized it with heuristic algorithms to solve the uncertainty and daily variability problems in underground mining plans [5]. Researchers discussed the importance of advanced planning and automation in underground mining plans, with a particular focus on the scheduling problem of mobile production fleets [6]. Some scholars have studied the practical impact of continuous mining systems as an alternative to traditional truck transportation systems in an environment where global energy and labor costs are constantly rising, and have analyzed their optimized scheduling plans [7]. As an auxiliary project in coal mine production, mine water resource scheduling also plays an important role in coal mine production and safety.

At present, most research on water resource optimization scheduling is based on reservoir water use models, and there is less research on mine water resource scheduling. Some scholars have established a regional sewage reuse dynamic programming model, which well combines the water quality requirements of each water unit, water quality control measures, and sewage reuse volume [8]. Researchers have proposed a comprehensive planning method for sewage treatment and reuse projects with cost as the objective function and a series of factors such as technology, society, health, and environment as constraints, providing system planning and related optimal investment and operating cost information [9].

In recent years, more and more researchers have conducted in-depth research on the model construction and problem-solving of mine water optimization configuration. Due to the high nonlinearity, high dimensionality, and uncertainty of mine water resource scheduling, traditional optimization algorithms have limitations, and problems such as “dimensional disaster” are prone to occur when using dynamic programming to solve complex water resource problems [10]. With the emergence of modern intelligent algorithms, new ideas have been proposed to solve the problem of mine water scheduling. Intelligent algorithms have found new applications in solving nonlinear problems and can be tailored to specific instances. Because of its low computational complexity and high computational efficiency, it has achieved good results and is loved by many scholars. Genetic algorithms, particle swarm algorithms, fish swarm algorithms, ant colony algorithms, and a series of intelligent algorithms are gradually being applied to optimal scheduling [11]. Compared with traditional optimization algorithms, these intelligent algorithms are closer to human thinking and easier to understand. While obtaining the solution results of complex optimization problems, some suboptimal solutions can be obtained, which is convenient for planners to study and compare, and improve the convergence speed of optimization variables.

In the field of water resource scheduling, some scholars have used genetic algorithms to establish and solve multi-objective optimal scheduling models [12]. Some researchers have established a multi-objective optimization scheduling model for reservoirs with uncertain runoff and improved the genetic algorithm, applying it to the multi-objective optimization scheduling model [13]. Some scholars use a two-stage method to solve the optimal scheduling model of cascade reservoir groups. In the first stage, the optimization model is simplified by using a random sampling dynamic programming method. In the second stage, the solution of the first stage is used as the initial population, and the genetic algorithm model is used to solve the optimal problem [14]. Some scholars use genetic algorithms to predict ecological water demand and establish an optimal allocation model for multi-source, multi-user water resources [15]. Scholars combine self-organizing mapping with genetic algorithms to make up for the shortcomings of genetic algorithms that are prone to local optima [16]. Some researchers use genetic algorithms with different selection operators to solve the short-term optimal scheduling problem of reservoirs [17]. Some researchers have solved the multi-objective optimization scheduling model of water supply, power generation, and ecology in the lower reaches of the Yellow River based on an improved fast non-inferior sorting genetic algorithm, and obtained the corresponding non-inferior solution set [18]. For the multi-dimensional, multi-objective, and multi-constraint problems of the joint flood control scheduling model of large reservoir groups, some scholars have combined dynamic programming, step-by-step optimization, and particle swarm optimization to solve the scheduling model and achieved good results [19]. Some scholars propose to add an adaptive dynamic control mechanism in the parameter setting of the genetic algorithm and propose an adaptive hierarchical genetic algorithm. The example results show that the calculation efficiency of this method is better than other traditional methods and can achieve better results [20]. Scholars improve the individual machine learning in the genetic algorithm through model training, making it more efficient than the original algorithm [21]. Some researchers have established a multi-objective model for the operation of irrigation canal systems and used a simulated annealing algorithm to solve it [22]. Some scholars have proposed a parallel simulated annealing algorithm, modified the cooling function, and used large neighborhood search technology to enhance local search capabilities [23].

In summary, existing research has primarily focused on the improvement of mine water treatment processes and the intelligent upgrade of a monitoring system. When it comes to scheduling strategies and methods, there is significant research on water usage in reservoirs or irrigation areas, while relatively little research is conducted on mine water scheduling. Additionally, there are challenges such as high recycling costs and slow recycling speeds during the process of mine water treatment. Based on existing research findings, this study models and analyzes the problem of mine water scheduling. Taking into account the actual water quality and quantity balance in a certain mining area in Inner Mongolia, and considering recycling cost and time as the objective functions, a mathematical model for a mine water cooperative scheduling system is proposed. Given the application status of multi-objective optimization algorithms, this study utilizes a genetic algorithm to solve the mine water scheduling model and makes adaptive improvements to traditional genetic algorithms. By combining with the simulated annealing algorithm, which can easily escape local optima, an underground-ground cooperative scheduling system for mine water based on an improved genetic algorithm is proposed.

2. Mine water cooperative scheduling model

The problem of mine water scheduling is a multi-constraint, multi-stage complex mathematical problem. With the gradual expansion of the scale of mine production and construction, the water consumption for mine production and construction is also increasing, and the cost of treating and reusing these water resources is also increasing. This brings many challenges to mine water dispatching. Therefore, how to reduce the cost of reuse and ensure the efficiency of reuse, that is, multi-objective coordinated scheduling has become an urgent problem to be solved [24]. This study will take a certain mining area in Inner Mongolia as the research object, analyze its processing and reuse system, construct a surface-underground coordinated scheduling model, and determine the scheduling strategy.

2.1. Description of mine water cooperative scheduling problem

This study takes a certain mining area in Inner Mongolia as the research object and analyzes its processing and scheduling strategies. In the traditional process of mine water reuse, the proximity principle is adopted, that is, each water supply point is supplied by the nearest water supply point, which can easily lead to confusion in the order of water use and unreasonable water resource calls. In response to the water quality differences of different water supply points and the water quality requirements of water use points, this study proposes a graded treatment water supply rule, which is conducive to achieving the reuse target of mine water [25]. The process of mine water treatment is divided into four stages: underground, surface pretreatment, secondary treatment, and deep treatment. The reuse standard of mine water strictly follows the water quality requirements of each water point. Areas with lower water quality requirements can be reused in the middle stage of the reuse process, while areas with higher water quality requirements need to go through a complex treatment process before reuse.

According to the classification and water quality treatment rules, combined with the actual treatment process, when establishing the scheduling flow chart, the specific water points are determined according to the spatial arrangement. The detailed mine water treatment process and reuse analysis diagram are shown in Fig. 1.

Figure 1.

Analysis diagram of mine water treatment technology and reuse.

In accordance with the classification and quality-based scheduling rules for mine water, the mine water reuse system is compartmentalized into four tanks: clear, middle, high, and reuse tanks.

In the clear water tank, a portion of the mine water is conveyed for underground reuse following sedimentation and filtration processes. The middle water tank receives mine water from the pre-sedimentation tank, primarily for sedimentation, removal of suspended solids, and mitigation of oil pollution. Post-dosing, the reaction and sedimentation predominantly occur within the middle water tank. The water quality post-pretreatment aligns with the requirements for ground dust suppression and fire protection.

The high water tank employs a high-density settling tank and a V-type filter to facilitate secondary sedimentation of suspended solids and oils. This tank is designated as a reuse tank, and the treated water is utilized for coal preparation, heat exchange stations, and boiler water supply.

In the reuse water tank, mine water undergoes softening via ultrafiltration and reverse osmosis devices. At this stage, the water quality requirements are relatively stringent. The treated mine water can cater to the daily needs of the mining area, such as ground cooling water, greening water, potable water, and other ground water uses.

In response to actual demand, the reused water is concentrated in the higher-cost reuse stages, such as in the high water tank and the reuse water tank. Given that the processing stage with a higher level necessitates more time, conflicts in reuse can easily arise when reuse is concentrated within the same timeframe. Consequently, it is imperative to establish a mathematical model of the scheduling system to ascertain the optimal scheduling methodology for the water point.

Taking into account the varying demands for water quality and quantity, this study transforms the scheduling problem into a mathematical problem. That is, considering the reuse cost and effluent quality of each tank, we calculate the water distribution of the four reuse tanks and the impact of the four reuse tanks on each water point. The objective is to achieve system-wide reuse to minimize costs and enhance the efficiency of the system's reuse.

2.2. Reuse cost decision model of mine water cooperative scheduling system

Decision variables form the foundation for establishing a mathematical model of the mine water cooperative scheduling system. The primary optimization objective of this study is the reuse cost of the scheduling system. It is essential to determine the reuse cost decision model of the cooperative scheduling system based on process technology and production standards.

Cost determination of underground pretreatment. The main equipment currently used for underground water production includes sedimentation and filtration devices. The agents used are primarily various chemical reagents, flocculants, and disinfectants. The cost forecast for underground pretreatment is as follows:

$$Y_1=(C_1+D_1)\times S_i$$ (1)

where $Y_1$ represents the cost of underground pretreatment, $C_1$ represents the unit price of water production cost at this stage, $D_1$ represents the unit price of energy consumption cost at this stage, and $S_i$ represents the amount of mine water in underground pretreatment.

The direction of mine water in underground pretreatment includes underground fire water, underground grouting water, underground sprinkling and dust control water, underground cooling water, and underground hydraulic support water. Therefore, the demand for $S_i$ is:

$$S_i=F\times m+G\times V_G+C\times s+L\times t_L+H\times n$$ (2)

where F represents the average water consumption of fire fighting events; m represents the number of fire incidents; G represents the volume of water consumed per unit volume of grouting material; $V_G$ represents the volume of grouting; C represents the water consumption per unit area of sprinkler equipment; s represents the area to be sprayed; L represents the average cooling water consumption, $t_L$ represents the cooling water consumption time; H represents the water consumption required by a single hydraulic support; n indicates the number of hydraulic supports.

Cost determination of ground pretreatment. The main equipment for ground pretreatment currently includes oil sewage treatment devices and high-efficiency cyclones. Pretreatment costs can be estimated as:

$$Y_2=(C_2+D_2)\times S_i$$ (3)

where $Y_2$ represents the cost of ground pretreatment, $C_2$ represents the unit price of water production cost at this stage, $D_2$ represents the unit price of energy consumption cost at this stage, and $S_i$ represents the amount of mine water in ground pretreatment.

The direction of mine water in the ground pretreatment includes ground dust removal water and fire water. The demand of $S_i$ is:

$$S_i=C\times s+F\times m$$ (4)

where C represents the water consumption per unit area of sprinkler equipment; s represents the area to be sprayed; F represents the average water consumption of fire incidents; m is the number of fire incidents.

Cost determination of ground secondary treatment. The main equipment of ground secondary treatment includes high-density settling tank and Vtype filter. Secondary treatment costs can be estimated as:

$$Y_3=(C_3+D_3)\times S_i$$ (5)

where $Y_3$ represents the cost of secondary surface treatment, $C_3$ represents the unit price of water production cost at this stage, $D_3$ represents the unit price of energy consumption cost at this stage, and $S_i$ represents the mine water quantity in secondary surface treatment.

The direction of mine water in the ground secondary treatment includes coal preparation water, heat exchange station water and boiler water. Therefore the predicted $S_i$ quantity is:

$$S_i=X_M\times T_X+H_R\times T_H+G_L\times T_G$$ (6)

where $X_M$ respectively represents water consumption of coal preparation per unit time; $H_R$ represents water consumption per unit time of heat exchange station; $G_L$ stands for boiler water consumption per unit time; $T_X$ represents the time of coal preparation water; $T_H$ is the running time of heat exchange station; $T_G$ represents the operating time of the boiler.

Cost determination of ground deep treatment. The estimated cost for ground deep treatment, which mainly involves the use of ultrafiltration devices and reverse osmosis systems, is

$$Y_4=(C_4+D_4)\times S_i$$ (7)

where $Y_4$ represents the cost of ground depth treatment, $C_4$ represents the unit price of water production cost at this stage, $D_4$ represents the unit price of energy consumption cost at this stage, and $S_i$ represents the amount of mine water in ground deep treatment.

The direction of mine water in the ground deep treatment includes cooling water, greening water, drinking water and other water. The predicted amount of $S_i$ is:

$$S_i=L\times t_L+S_G\times C_G+D_H\times P_H+E$$ (8)

where L represents the average cooling water consumption, $t_L$ represents the cooling water consumption time; $S_G$ represents the green area in the mining area; $C_G$ represents the average water consumption of greening; $D_H$ represents per capita drinking water, $P_H$ represents the number of people in the mining area; E represents other water consumption.

2.3. Cooperative scheduling system objective function

The objective of water resource scheduling in the mining area is to meet the demand for reused water, while also taking into account the cost-effectiveness and speed of the reuse process as much as possible. This is done to satisfy the long-term demand for water resources in line with sustainable development. For the treatment and reuse costs of mine water, the following relationship can be established:

$$Y=C+D$$ (9)

where Y is the recycling cost of the scheduling system, C is the water production cost, and D is the energy consumption cost. The water production cost mainly includes the cost of pharmaceuticals, water fetching and purifying, and the energy consumption cost includes the cost of scheduling pipes and electricity consumption of pumps, including electricity, maintenance, depreciation and labor costs.

In accordance with the aforementioned principles, this study designates the minimal reuse cost and reuse time of the mine water scheduling system as the objective function. The water quality and quantity at each water point are considered as constraint conditions. The objective function of the model is defined as follows:

$$\min f=\sum _{t=1}^T\sum _{i=1}^I[w_1\frac{(C_{t,i}+D_{t,i})\times S_{t,i}}{Z\times Q_i}+w_2\frac{t_i}{t_{\max }-t_{\min }}]$$ (10)

where T is the total reuse time, I is the number of reuse points, $S_{t,i}$ represents the actual recycling amount of the water point i at time t, $C_{t,i}$ represents the water production cost of the water point i at time t, $CNY/{\text{m}}^3$, $D_{t,i}$ represents the energy consumption cost of the water point i during period t, $CNY/{\text{m}}^3$, $Q_i$ represents the maximum mine water reuse, Z represents the maximum reuse cost of the system, $t_{max}$ represents the maximum reuse time, and $t_{min}$ represents the minimum reuse time, $t_i$ represents the reuse time of the water point i, and the weight coefficients $w_1$ and $w_2$ are 0.6 and 0.4 respectively.

2.4. The constraint

Water balance constraint: The total volume of reclaimed mine water during the treatment process should accurately reflect the amount reclaimed from each underground and surface water source. Considering inevitable evaporation and water losses during treatment, the constraint formula is as follows:

$$Q_i=\sum _{i=1}^I{S}_{t,i}+V$$ (11)

where $Q_i$ represents the total amount of reuse in the mining area, $S_{t,i}$ represents the actual recycling amount of the water point i at time t, and V represents the loss of evaporation and leakage in the water area.

Water points level constraint. Due to the problem of scheduling cost, this paper limits the water level of each water point in the four levels of reuse tanks, according to the actual volume of these tanks. Therefore, in the scheduling process, the water volume in the reuse tank should be judged first, and only when the water level setting range is met can the scheduling be carried out. In any scheduling process, the following constraints should be set as Equation (12):

$$S_{min,t}\le S_{t,i}\le S_{max,t}$$ (12)

where $S_{t,i}$ represents the actual water level of the water point i at time t, $S_{min,t}$ represents the lower limit of the water level change in the water point i at time t, $S_{max,t}$ represents the upper limit of the water level change in the water point i at time t. The non-flood season water level corresponding to the water level in the heating season, and the flood season water level corresponding to the water level in the non-heating season.

Water quality condition constraint. Due to the complex cost of mine water, recycling must be carried out according to the water quality standard. According to the actual production demand, the water quality of each water point should be within a reasonable range, so that the recycling process can be continued. Therefore, in any scheduling process, the following constraints should be set as Equation (13):

$$U_{min,t}\le U_{t,i}\le U_{max,t}$$ (13)

where U represents the water quality of the water point i at time t, $U_{min,t}$ represents the minimum water quality requirement of the water point i at time t, and $U_{max,t}$ represents the maximum water quality requirement of the water point i at time t.

Reuse time constraint. Based on the water quality situation, this paper categorizes the reuse process into four stages: the early-stage reuse point, which completes the reuse process early; the late-stage reuse point, which completes the reuse process late. For instance, the reuse time of underground fire water is shorter than that of ground drinking water. However, there are upper and lower limits. In an ideal state, when all mine water is reused in the clear water tank, the recycling time reaches its minimum; when all mine water is reused in the reuse water tank, the recycling time reaches its maximum. Therefore, this paper imposes constraints on the system's reuse time:

$$t_{\min }\le t\le t_{\max }$$ (14)

where t represents the system reuse time, $t_{min}$ represents the minimum reuse time, and $t_{max}$ represents the maximum reuse time.

By establishing constraint conditions, it is observed that there are three inequality constraints, indicating that the mine water scheduling problem is a nonlinear problem. Typically, the penalty function method is commonly utilized to convert constrained problems into unconstrained problems [26]. The penalty function method involves constructing a sequence of objective functions with penalty effects based on the objective and constraint functions of the problem, thereby transforming the constrained optimization problem into a series of unconstrained optimization problems.

The objective function of this paper is:

$$\min f(x),x\in R$$ (15)

The corresponding constraints are:

$$\left\{\begin{array}{c}{h}_i(x)=0,i\in E=(1,2,\cdots e)\hfill \\ g_i(x)\ge 0,i\in I=(1,2,\cdots l)\hfill \end{array}\right\}$$ (16)

Feasible region D is:

$$D=\{x\in R|h_i(x)=0(i\in E),g_i(x)\ge 0(i\in I)\}$$ (17)

$$\alpha (x)=\sum _i^e{h}_i^2(x)+\sum _{i=1}^l{[\min \{0,g_i(x)\}]}^2$$ (18)

where $\alpha (x)$ represents the penalty function value. Since the optimal objective function in this paper is to find its minimum value, the penalty value is added to form an augmented function relative to the original objective function:

$$\min f(x,\mu )=f(x)+\mu \alpha (x)$$ (19)

where μ is the penalty factor and is a non-negative constant. As long as the value of is large enough, the optimal solution of $minf(x,\mu )$ is close to the optimal solution of the constrained problem, and the constrained problem is transformed into an unconstrained problem.

3. Application of improved genetic algorithm in mine water scheduling system

The scheduling of mine water usage represents a multi-objective optimization problem, with the scheduling system constantly undergoing dynamic changes. The research focus of this paper is on finding an optimal set of solutions within the range of qualified solutions that optimize the global objective function [27]. To achieve this, we introduce the genetic algorithm, a global optimization algorithm, and propose an improved genetic algorithm that combines the adaptive genetic operator with simulated annealing.

3.1. Overview of genetic algorithms

The Genetic Algorithm is predicated on the theory of evolution, emulating the natural selection and evolutionary mechanism of “survival of the fittest” to construct models of artificial systems [28]. It is a potent and widely utilized random search optimization technology, capable of effectively solving many complex problems that traditional methods cannot address [29]. The Genetic Algorithm commences with the concept of a population, which encodes several individuals, each referred to as a chromosome. A group composed of numerous chromosomes is called a population. The genes carried on the chromosomes determine the characteristics of an individual. During the process of evolution, the individual fitness value is set, and individuals are selected in a targeted manner. Selected individuals undergo crossover and mutation operations in genetics to generate a new population composed of a new generation of individuals. Analogous to the evolution of natural organisms, through iterative evolution, the optimal solution of the entire population is obtained [30].

3.2. Solution of mine water cooperative scheduling model based on genetic algorithm

During the operation of the mine water treatment system, mine water reuse is categorized into four levels: clear water tank, middle water tank, high water tank, and reuse water tank. The higher the level, the stricter the water quality requirements. A water reuse point is established at each treatment level to schedule and utilize mine water.

Initially, the mine water demand detected by the mine scheduling system is classified and digitized based on the varying information of water quality and quantity. Subsequently, the digitized mine water demand information is incorporated into the genetic algorithm and set as the initial condition.

Using the iterative method of the genetic algorithm for optimization and computation, each chromosome in the population contains four types of genes that represent different levels of water supply. In each iteration, two individuals undergo crossover and mutation operations with a certain probability to generate new individuals. The final algorithm identifies the optimal population, and the genes expressed by individuals within this population formulate the scheduling scheme of the system. Ultimately, mine water is scheduled to be delivered from four different levels of reuse tanks to the reuse point, aiming to achieve economical treatment and high-efficiency reuse of mine water.

As depicted in Fig. 2, in this study, four reuse tanks of mine water serve as genetic gene segments in the chromosome, corresponding to the gene segments of the genetic algorithm. In the iterative process of the genetic algorithm, the chromosome population undergoes constant crossover and mutation with other chromosomes. The fitness function serves as a reference to induce continuous changes in the entire population. Concurrently, the scheduling amount of mine water also undergoes constant changes. By integrating the fitness function with the objective function, the scheduling process of mine water is continuously optimized during the calculation iteration of the algorithm, ultimately obtaining the optimal scheduling scheme.

Figure 2.

Diagram of mine water scheduling combined with GA.

The choice of the fitness function largely determines the performance of the genetic algorithm, and the complexity of the fitness function also affects the complexity of the algorithm. In the mine water scheduling problem, this article uses the reciprocal of the objective function as the fitness function, and the maximum fitness value as the optimization goal. The fitness function is:

$$fit=\frac{1}{{\sum }_{t=1}^T{\sum }_{i=1}^I[w_1\frac{(C_{t,i}+D_{t,i})\times S_{t,i}}{Z\times Q_i}+w_2\frac{t_i}{t_{\max }-t_{\min }}]}$$ (20)

Genetic operators primarily encompass selection, crossover, and mutation. The fundamental principle of selection is to preserve superior genes within the population, thereby enabling individuals with high fitness values to be more effectively passed on to subsequent generations. This enhances the convergence speed and precision of the algorithm during execution. This study employs a hybrid strategy of elite replacement and roulette selection. It selects the fittest individuals to proceed to the next generation, while the remaining individuals are chosen randomly via roulette selection. This approach can, to some extent, prevent the phenomenon known as ‘premature convergence’.

During the selection operation of the iterative process, retain the top 10% of individuals with the highest fitness value. After the final genetic operation, replace the bottom 10% of individuals with the lowest fitness value in the population. This strategy can swiftly eliminate less fit individuals in the population, accelerating the convergence rate and steering the entire population towards a more favorable direction [31]. The roulette selection method is employed, where selection is based on the proportion of an individual's fitness value in the total population. The probability of an individual being selected, based on the optimal fitness function, is:

$$P_m=\frac{fit(m)}{{\sum }_{m=1}^{M}fit(m)}$$ (21)

During the crossover operation, two individuals from the initial generation exchange information through a specific method to produce two offspring. Initially, a certain crossover probability is established, and then the position of the crossover point in the gene is determined based on this probability. The genes located after the crossover point are the ones exchanged between the two initial individuals, leading to the creation of the second generation. The crossover process distinguishes the genetic algorithm from other optimization algorithms. Exceptional individuals are paired, and certain elements within these individuals are swapped. The crossover algorithm can be represented by the following formula:

$$\left\{\begin{array}{c}{x}_i^{a+1}=\mu ⁎x_i^a+(1-\mu )⁎x_{i+1}^a\hfill \\ x_{i+1}^{a+1}=\mu ⁎x_{i+1}^a+(1-\mu )⁎x_i^a\hfill \end{array}\right\}$$ (22)

where μ is the random number between 0 and 1; $x_i^a$ refers to the generation a of the individual i in the x population; $x_i^{a+1}$ refers to the generation $a+1$ of the individual i in the x population; $x_{i+i}^a$ refers to the generation a of the individual $i+1$ in the x population.

During the mutation process, gene segments from parent chromosomes are exchanged with those from other individuals, resulting in offspring that differ from their parents. The mutation probability is set at $p_m=0.1$. The method of reverse mutation is adopted, with parent individual A set as 010011010101. If the generated mutation points are (4, 6), meaning the 4th and 6th positions of the chromosomal gene undergo mutation, then the 4th to 6th positions of 010011010101 are rearranged in the reverse order of 110. The resulting offspring chromosome, $A_1$, is 010110010101. After the mutation process, the fitness of the offspring and parent chromosomes is calculated. If the offspring is superior, it replaces the parent. If the parent is superior, it is retained and continues to participate in the iterative process.

A good initial population is a prerequisite for the genetic algorithm to converge and obtain the optimal solution. During the calculation process, it is necessary to consider the selection probability, crossover probability, mutation probability, and other key parameters of the algorithm, and to update the size of the genetic operator in real time. However, the genetic algorithm has its disadvantages. It can easily fall into a local optimum, and there may be premature convergence in the later stages of the algorithm. Sometimes, the convergence speed is accelerated, but the optimal solution cannot be found, or the optimal solution is found, but the convergence speed is slow. This creates a contradiction between convergence speed and convergence accuracy, making it difficult to guarantee the computational effectiveness of the algorithm. Based on a review of the current state of genetic algorithm research, it has been found that the probability of crossover mutation largely determines the optimization performance of the algorithm and can enhance the algorithm's performance. Therefore, this paper attempts to improve the crossover mutation probability of the algorithm.

3.3. Adaptive genetic operator

In the genetic algorithm, the crossover operator exhibits a dual nature. It can guide the algorithm towards convergence and attainment of the global optimum. However, when the algorithm falls into a local optimum, it becomes challenging to escape, regardless of the number of crossover and mutation operations applied [32]. Given this phenomenon, it is necessary to employ enhanced crossover and mutation operators for optimization calculations. To solve these problems, an Adaptive genetic algorithm (AGA) is proposed in this paper

Some researchers have proposed an adaptive method for crossover mutation. When the individuals in the population are relatively concentrated, the mutation probability value is increased. Conversely, when the fitness of individuals in the population is relatively dispersed, the mutation probability value is decreased [33]. During the calculation process, the value of the crossover mutation probability is not predetermined. Instead, the crossover mutation probability for each generation of the population is adaptively determined, allowing it to adjust in accordance with the fitness value of each generation of population individuals. The crossover probability for an individual is adjusted based on the individual's current fitness value during the iterative process. The adaptively changing crossover probability can be expressed as follows:

$$P_c=\left\{\begin{array}{cc}\hfill \frac{k_1(f_{\max }-f)}{f_{\max }-f_{\text{avg }}},\hfill & \hfill f>f_{\text{avg }}\hfill \\ \hfill k_2,\hfill & \hfill f\le f_{\text{avg }}\hfill \end{array}\right\}$$ (23)

where $P_c$ represents the crossover probability of the current individual. $f_{avg}$ represents the average fitness value, $f_{max}$ represents the best fitness, f is the larger fitness of the two individuals in the crossover, $k_1$ and $k_2$ are constants, and $k_1$ is less than $k_2$ to ensure that the crossover probability is relatively high when the population fitness tends to be consistent.

When the fitness value is large ($f>f_{avg}$), $P_c$ is small, so that the probability of individuals with large fitness value being destroyed due to crossover is small. When f equals $f_{m}ax$, $P_c$ equals 0, ensuring that the individual with the highest fitness value is preserved. When the fitness value is small ($f\le f_{avg}$), $P_c$ is larger, providing individuals with lower fitness more opportunities to generate new individuals through crossover.

The mutation probability of an individual is adjusted based on the individual's current fitness value during the iterative process. The expression for the adaptively changing mutation probability is as follows:

$$P_m=\left\{\begin{array}{cc}\hfill \frac{k_3(f_{\max }-f)}{f_{\max }-f_{\text{avg }}},\hfill & \hfill f>f_{\text{avg }}\hfill \\ \hfill k_4,\hfill & \hfill f\le f_{\text{avg }}\hfill \end{array}\right\}$$ (24)

where $P_m$ represents the mutation probability of the current individual. $f_{avg}$ is the average fitness value, $f_{max}$ is the maximum fitness, f is the larger fitness of the two individuals with mutation, $k_3$ and $k_4$ are constants, and $k_3$ is less than $k_4$, ensuring that the mutation probability is relatively large when the population fitness tends to be consistent.

When the fitness value is large $f>f_{avg}$), $P_m$ is small, reducing the likelihood of individuals with high fitness values being disrupted due to mutation. When f equals $f_{max}$, $P_m$ equals 0, ensuring that the individual with the highest fitness value is preserved. When the fitness value is small ($f\le f_{avg}$), $P_m$ is larger, providing individuals with lower fitness more opportunities to generate new individuals through mutation.

Upon analysis, it has been found that this algorithm also has certain limitations in its operation process. For instance, crossover and mutation operations are easily influenced by coefficients, and the determination of $k_1,k_2,k_3,k_4$ values is subjective and arbitrary, which can easily affect the quality of the population and lead to a local optimum.

When the fitness value of the individual undergoing crossover reaches the maximum value, $P_c$ and $P_m$ will become zero, and the individual will directly enter the next generation and be continuously selected by the roulette operation. This outcome will cause the individuals in the population to grow rapidly and converge prematurely, leading to the problem of local optimality. When the maximum fitness value of the population equals the average fitness value, $f_{max}=f_{avg}$, the denominator in the calculation formula of the crossover probability $P_c$ and $P_m$ becomes 0, which is mathematically incalculable. Moreover, at this time, all individuals in the representative group have the same genetic composition, which is likely to be a local optimal solution, and the algorithm tends to stagnate evolution and cannot obtain a global optimal solution. When $f=f_{avg}$, the values of $P_c$ and $P_m$ cannot be determined, which will also interfere with the crossover process. In light of the above analysis, this paper proposes a new Adaptive Genetic Algorithm (AGA). The formula for the new crossover operator is as follows:

$$P_c=\left\{\begin{array}{cc}\hfill P_{c\max }-\frac{(P_{c\max }-P_{c\min })(f-f_{\text{avg }})}{f_{\max }-f_{\text{avg }}},\hfill & \hfill f>f_{\text{arg }}\hfill \\ \hfill P_{c\max },\hfill & \hfill f\le f_{\text{avg }}\hfill \\ \hfill P_{c\max },\hfill & \hfill f_{\max }=f_{\text{avg }}\hfill \end{array}\right\}$$ (25)

where $f_{max}$ represents the maximum fitness value in the population, $f_{avg}$ represents the average fitness value in the population, f represents the larger fitness value among the parent individuals participating in the crossover, $P_{c_{max}}$ represents the upper limit of the crossover probability, and $P_{c_{min}}$ represents the lower limit of the crossover probability, $0<P_{c_{min}}<P_{c_{max}}<1$.

In the calculation formula of crossover probability, the original coefficients $k_1$ and $k_2$ are replaced by $P_{c_{max}}-P_{c_{min}}$ and $P_{c_{max}}$, which avoids the interference of subjective factors; when $f_{max}=f_{avg}$, the crossover probability takes $P_{c_{max}}$, which avoids the calculation termination caused by the denominator being zero; If the fitness value of the crossover individuals reaches the maximum value, $P_c$ becomes $P_{c_{min}}$, then the crossover probability of the individual is the lowest, avoiding the problem of falling into the local optimum.

Similar to the crossover operator, the new mutation operator is formulated as follows:

$$P_m=\left\{\begin{array}{cc}\hfill P_{m_{max}}-\frac{(P_{m_{max}}-P_{m_{min}})(f-f_{\text{avg }})}{f_{\max }-f_{\text{arg }}},\hfill & \hfill f>f_{\text{arg }}\hfill \\ \hfill P_{m_{max}},\hfill & \hfill f\le f_{\text{arg }}\hfill \\ \hfill P_{m_{max}},\hfill & \hfill f_{\max }=f_{\text{arg }}\hfill \end{array}\right\}$$ (26)

where $f_{max}$ represents the maximum fitness value in the population, $f_{avg}$ represents the average fitness value in the population, f represents the larger fitness value among the parent individuals participating in the mutation, $P_{m_{max}}$ represents the upper limit of the mutation probability, and $P_{m_{min}}$ represents the lower limit of the mutation probability, $0<P_{m_{min}}<P_{m_{max}}<1$.

In the calculation formula of mutation probability, the original coefficients $k_3$ and $k_4$ are replaced by $P_{m_{max}}-P_{m_{min}}$ and $P_{m_{max}}$, which avoids the occurrence of accidental events; when $f_{max}=f_{avg}$, the mutation probability takes $P_{m_{max}}$, which avoids the calculation termination caused by the denominator being zero; If the fitness value of the crossover individuals reaches the maximum value, $P_m$ becomes $P_{m_{min}}$, then the mutation probability of the individual is the lowest, avoiding the problem of falling into the local optimum.

3.4. Improved genetic simulated annealing algorithm

The Genetic Algorithm is a well-established method for solving optimization problems. It offers the benefits of easy implementation and rapid convergence. However, it is prone to premature convergence and often gets trapped in local optima. The Simulated Annealing (SA) algorithm, characterized by its probabilistic jump mechanism, is a random search algorithm that extends the local search algorithm. Theoretically, it can prevent the solution from getting stuck in local optima. When applied to multi-objective optimization problems, the SA algorithm can converge to the global optimal solution [34]. In an effort to enhance the GA and develop a more effective method for mine water scheduling, this paper introduces an improved algorithm that combines the SA algorithm with an adaptive GA, referred to as the Improved Genetic Simulated Annealing (IGSA) algorithm.

SA algorithm emulates the annealing process of solids. The complete process begins by initially heating the solid to a certain temperature, causing the internal molecules to undergo random diffusive motion. The system is then gradually cooled until it reaches a low temperature, at which point the internal molecules of the solid attain a stable state. During annealing, as the temperature decreases, the energy state of the system also decreases. When the temperature is sufficiently low, the system begins to condense and crystallize, reaching its lowest energy state in the crystalline state. This principle enables solutions to continuously escape local optima in the solution space, thereby achieving the global optimal solutions [35].

The general steps of the simulated annealing algorithm are:

(1) Initialize the temperature $T_0$ and randomly generate the initial state $x=x_0$ within the feasible solution space. Compute the objective function value $f(x_0)$.

(2) Generate a new solution $x_1$ based on a state perturbation. Compute the objective function value $f(x_1)$ and the function value difference $\mathrm{\Delta }f=f(x_1)-f(x_0)$.

(3) If $\mathrm{\Delta }f<0$, accept the new solution $x_1$. If $\mathrm{\Delta }f>0$, accept the new solution with a certain probability P.

(4) At the same temperature $T_0$, repeat steps (2) and (3) to perturb the solution for a certain number of iterations.

(5) Define the cooling function and gradually reduce the temperature.

(6) Repeat steps (2) to (5) until a specified convergence criterion is met.

In summary, the SA algorithm selects new solutions with varying probabilities, enabling it to expand the search space, escape local optima, and continue the search transition.

The concept of integrating the GA and the SA algorithm involves using the result of GA's crossover mutation as the initial solution in the SA algorithm. The new solution is then accepted under the Metropolis rule of the SA algorithm, and its corresponding individual is assigned as the initial population of the next generation of the GA. The specific operational steps of the IGSA algorithm proposed in this paper are as follows:

(1) Set the control parameters: population size L, initial temperature $T_0$, cooling coefficient λ, termination temperature $T_e$, and maximum genetic generations (initialized to 0). Set the encoding length and initialize the population to generate a series of chromosomes.

(2) Calculate the fitness value of each individual in the population, sort them in descending order, and compute the average fitness value $f_{avg}$ and the optimal fitness value $f_{max}$ of the population.

(3) Perform selection, crossover, and mutation operations. Introduce the adaptive cross-mutation operators $p_c$ and $p_m$ proposed in this paper to perform cross-mutation operations and generate a new population.

(4) Apply a simulated annealing operation to the new population. Set the objective function of the problem to be $f(x)$, and calculate its objective function value $f(j)$ for any optimal solution j of the problem. Perturb the current solution j with a random probability.

$$f(x)=\sum _{t=1}^T\sum _{i=1}^I[w_1\frac{(C_{t,i}+D_{t,i})\times S_{t,i}}{Z\times Q_i}+w_2\frac{t_i}{t_{\max }-t_{\min }}]$$ (27)

(5) Utilize the perturbation process to compute the new objective function value $f(k)$, and accept the new solution based on the Metropolis criterion. The probability p is typically defined in accordance with the Metropolis criterion, where K represents the Boltzmann constant and $T_c$ is the current temperature value. The Metropolis criterion formula is then applied.

$$p=\left\{\begin{array}{cc}\hfill 1,\hfill & \hfill f(k)\le f(j)\hfill \\ \hfill \mathrm{esp}(-\frac{f(k)-f(j)}{K{T}_r}),\hfill & \hfill f(k)>f(j)\hfill \end{array}\right\}$$ (28)

(6) Gradually reduce the temperature and evaluate the temperature and the number of iterations. If the number of iterations reaches the predetermined value or the change in the optimal individual fitness is no longer significant, convergence is achieved and a new population is output. If these conditions are not met, the algorithm re-enters the random disturbance process and continues the annealing process.

(7) For the new population, if the termination condition is met, the optimal solution is output. If the termination condition is not met, the algorithm returns to the fitness value calculation stage of the GA, and the GSA algorithm operation is performed again. Fig. 3 illustrates the basic flow of the IGSA algorithm.

Figure 3.

Flow chart of improved genetic simulated annealing.

3.5. Algorithm testing and simulation

To validate the performance of the improved algorithm, this study tested the solution to the mine water scheduling problem using five classical benchmark functions: the Ackley function, the Sphere function, the Rastrigin function, the Booth function, and the Levy Function N. 13 [36].

The Ackley function is a highly nonlinear function characterized by numerous extrema and a global minimum value of $f(x)=0$. During the optimization process, its surface exhibits numerous fluctuations, often resulting in multiple directional gradients. This makes it an ideal candidate for comparing the global search capabilities of various algorithms.

$$f(x)=-a{e}^{(-b\sqrt{\frac{1}{d}{\sum }_{i=1}^d{x}_i^2})}-e^{(\frac{1}{d}{\sum }_{i=1}^d\cos \left(c{x}_i\right))}+a+e$$ (29)

The Sphere function possesses a single extremum, the global minimum. When all independent variables simultaneously achieve a value of 0, the global optimal value of 0 is obtained.

$$f(x)=\sum _{i=1}^D{x}_i^2$$ (30)

The Rastrigin function consists of multiple peaks and high nonlinearity, which utilizes the periodicity of the cosine function to form multiple local optima and additional peaks. Its large number of extrema greatly helps test the optimization capabilities of algorithms.

$$f(x)=\sum _{i=1}^D(x_i^2-10\cos \left(2\pi x_i\right)+10)$$ (31)

The Booth function is a two-dimensional function with an input domain ranging from [-10, 10]. When $x_1=1$, $x_2=3$, the function attains its minimum value of 0.

$$f(x)={(x_1+2x_2-7)}^2+{(2x_1+x_2-5)}^2$$ (32)

The Levy Function N.13, also known as the “Levy function 13”, is a two-dimensional function typically evaluated on the square $x_i\in [\text{-}10,10]$ for all $i=1,2$. When all independent variables are 1, the function achieves its smallest value, which is 0.

$$f(x_1,x_2)={\sin }^2\left(3\pi x_1\right)+{(x_1-1)}^2(1+{\sin }^2\left(3\pi x_2\right))+{(x_2-1)}^2(1+{\sin }^2\left(2\pi x_2\right))$$ (33)

To verify the convergence performance of the improved algorithm, this paper conducted a simulation to analyze the convergence of the comparative test functions. For comparison, the paper selected GA, AGA, IGSA. Each of these algorithms was tested using the aforementioned functions. The simulation aimed to assess the convergence of these algorithms and their respective test functions.

In this study, a total of 200 simulations are performed to demonstrate the superiority of the algorithm through both average and optimal values. The detailed data are presented in Table 1. To visually illustrate convergence, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 are provided. The average value represents the mean of the optimal solutions obtained by various algorithms across 200 independent experiments, while the optimal value represents the minimum value achieved when various algorithms reach convergence in independent experiments.

Table 1.

Function calculation results.

Function	Value	IGSA	GA	AGA
Ackley	optimal value	4.88E-03	1.38E-00	5.40E-02
	average value	1.31E-02	4.63E-01	2.88E-02
Sphere	optimal value	3.84E-08	3.66E-06	5.51E-07
	average value	1.64E-07	1.37E-06	9.54E-07
Restrigin	optimal value	2.09E-06	4.23E-04	3.30E-05
	average value	1.57E-04	2.77E-04	4.87E-04
Booth	optimal value	3.13E-02	7.97E-02	6.82E-02
	average value	5.07E-02	2.74E-01	1.03E-01
Levy Function N. 13	average value	8.95E-06	1.54E-02	1.63E-04
	average value	2.75E-04	2.42E-2	2.20E-03

Figure 4.

Ackley function.

Figure 5.

Sphere function.

Figure 6.

Restrigin function.

Figure 7.

Booth function.

Figure 8.

Levy Function N. 13.

For the Ackley function, as depicted in Fig. 4, the IGSA algorithm requires fewer iterations to reach the optimum, achieving this at approximately the 11th iteration. This is significantly faster than the 36 iterations required by the GA and the 50 iterations required by the AGA. In terms of optimal value, the IGSA initially surpasses AGA during the early stages of evolution. However, as the iterations progress, the IGSA's optimal value becomes the smallest among the three algorithms. This suggests that while AGA exhibits certain convergence characteristics, the IGSA's convergence performance is superior. Regarding the Sphere function, as shown in Fig. 5, the performances of the three algorithms are not significantly different in the initial stage. Even in the early stage, the optimal values of AGA and GA are smaller than that of the IGSA. However, the IGSA reaches the optimal value around the 5th iteration, which is faster than the 48 iterations of GA and the 22 iterations of AGA. Furthermore, the IGSA's optimal value is the smallest, indicating higher convergence accuracy. For the Rastrigin function, as shown in Fig. 6, AGA's optimal value is smaller than the IGSA's at the beginning of the iteration. However, as the iteration progresses, the IGSA reaches the optimal value at approximately the 26th iteration, which is faster than the 46 iterations of GA and the 42 iterations of AGA. The IGSA's optimal value is also the smallest, indicating higher convergence accuracy. From an average perspective, the IGSA is the smallest and the AGA is the largest, suggesting that AGA has certain limitations and may fall into local optima, whereas the IGSA can easily escape local optima and find the optimal solution. For the Booth function, as shown in Fig. 7, the IGSA reaches the optimal value around the 6th iteration, which is faster than the 48 iterations of GA and the 22 iterations of AGA. In terms of both average value and optimal value, the IGSA is the smallest and GA is the largest. For the Levy Function N. 13, as depicted in Fig. 8, the IGSA algorithm reaches the optimum at the 4th iteration. This is significantly faster than the 65 iterations required by GA and the 32 iterations required by AGA. In terms of optimal value, although AGA's optimal value is also small, it does not match the performance of the IGSA.

In summary, the IGSA outperforms both GA and AGA in terms of the number of iterations and convergence accuracy. This indicates an enhancement in both its global and local search performance.

4. Case analysis and discussion

4.1. Application of the improved genetic simulated annealing algorithm in mine water cooperative scheduling system

This study focuses on the water point as the research object and utilizes the four-level reuse tank as the water supply point. By employing the objective function and constraints, the algorithm operates until it calculates an optimal scheduling scheme that satisfies the conditions, at which point it ceases iteration. The final reuse destination of each reuse tank and the corresponding mine water scheduling volume are then determined, providing the optimal solution for mine water scheduling.

To validate the solution of the IGSA algorithm in the cooperative scheduling model of mine water in a certain mining area in Inner Mongolia, this paper combines the water inflow data from the mine's production process. Using Python software, the results of the traditional GA, AGA, and the IGSA are compared, as shown in Fig. 9. As can be seen from Fig. 9, the GA algorithm can reach the optimal value in 23 iterations, while the AGA algorithm converges faster, reaching the optimal state in 19 iterations. In comparison, the IGSA significantly reduces the number of iterations needed to achieve global convergence, requiring only 5 iterations. Moreover, from the perspective of optimal value, the IGSA's optimal value is significantly lower than those of AGA and GA. In summary, the IGSA algorithm demonstrates superior performance in solving the mine water scheduling problem.

Figure 9.

Comparison diagram of algorithm solutions.

4.2. Analysis of results

(1) Reuse direction of mine water cooperative scheduling system

In conjunction with the IGSA algorithm proposed in this paper, prior to and following optimization, the amount of water recycled at each of the 14 water points remains unchanged, consistent with meeting their recycling requirements. The distribution of the four reuse tanks to the 14 water points is the only variable that is altered, taking into account the reuse cost and effluent quality. The reuse amount of the four reuse tanks is subsequently redistributed. Table 2 presents the reuse amount of each water point in the mining area.

Table 2.

Reconsumption of each water point before optimization.

Reuse level	Water poin	Position	Heating season water (m3/month)	Non-heating season water (m3/month)
Clear water tank	fire water	underground	13880.00	13880.00
	grouting water	underground	7280.00	7280.00
	sprinkler dust control water	underground	4320.00	8640.00
	cooling water	underground	19800.00	19800.00
	hydraulic support water	underground	4856.00	4856.00
Middle water tank	dust removal water	ground	58130.00	64260.00
	fire water	ground	12680.00	12680.00
High water tank	coal preparation water	ground	29120.00	29120.00
	heat exchange station water	ground	20780.00	35670.00
	boiler water	ground	38460.00	6930.00
Reuse water tank	cooling water	ground	25600.00	20540.00
	greening water	ground	8420.00	8420.00
	drinking water	ground	4620.00	4620.00
	other ground water	ground	14660.00	18670.00

To evaluate the distribution of the proposed IGSA algorithm in solving the mine water scheduling problem, a simulation operation is performed using Python software; with the parameters of the algorithm set as follows: the population size L is 100; the upper bound of the crossover probability $P_{c_{max}}$ is 0.85; the lower bound of the crossover probability $P_{c_{min}}$ is 0.6; the upper bound of the mutation probability $P_{m_{max}}$ is 0.1; the lower bound of the mutation probability $P_{m_{min}}$ is 0.04; the maximum number of iterations is 100; and the initial temperature $T_0$ is 1000.

The optimized reuse destinations of the four levels of reuse tanks are obtained. The clear water tank continues to be responsible for the reuse of five water points, namely, underground fire water, underground grouting water, underground sprinkler dust control water, underground cooling water, and underground hydraulic support water. However, considering the high reuse frequency of clear water tanks and the large amount of equipment used, the amount of water for underground cooling is reduced to minimize costs, while ensuring minimal changes in the amount of water at the reuse point. The total scheduling amount of the middle water tank has increased, and its reuse destinations have expanded from the original ground dust removal and ground fire water to include underground cooling, ground dust removal, ground fire water, ground coal preparation water, and ground heat exchange water. This is attributed to its relatively lower cost, leading to more recycling being allocated to the middle water tank. Simultaneously, the effluent water quality from the middle water tank can meet the requirements for ground coal preparation water and ground heat exchange water, enabling it to supply these as well. The overall scheduling volume of the high water tank has decreased, but the reuse destinations have increased. This is because the cost of the reuse water tank is the highest, and the water quality requirements for ground cooling and greening can be met in the high water tank, leading to the scheduling of the amount of ground cooling and a portion of the greening water to the high water tank. The cost of the reuse water tank is the highest, resulting in a reduction in the water used in the original four places to three places, and a significant reduction in the reused amount of water for greening. The principle of change in the amount of recycling in the heating season and the non-heating season remains the same. The specific reuse destination allocation is depicted in Fig. 10 and Fig. 11. (2) Reuse cost analysis of mine water cooperative scheduling system

Figure 10.

Reuse distribution after optimization in heating season.

Figure 11.

Reuse distribution after optimization in non-heating season.

Firstly, the unit price of recycling cost is analyzed. The reuse cost of the scheduling system encompasses the cost of water production and energy consumption. Given the different treatment processes, the water production costs and energy consumption costs of the four grades of tanks vary. By referring to the production data of the mining area, the scheduling and recycling costs of the tanks for each recycling grade are determined. In the calculation process, the density of mine water is approximated to the density of water, that is, one ton is considered to be approximately 1 cubic meter.

In the underground pretreatment stage, the mine water undergoes deposition and filtration, and is then transported to the clear water tank for underground reuse. The consumption cost is 0.6 CNY/${\text{m}}^3$. In the ground pretreatment stage, the mine water is transported from the underground pre-sedimentation tank to the ground, primarily through the oil pollution treatment device and the high-efficiency cyclone, followed by the dosing process. The cost of water production is 1.3 CNY/${\text{m}}^3$, and the cost of energy consumption is 0.5 CNY/m³.

In the secondary treatment stage, a high-density sedimentation tank and a V-type filter are used to re-precipitate the suspended solids and oil, and the high water tank is designated as a reuse tank. The cost of water production is 1.8 CNY/m³, and the cost of energy consumption is 0.7 CNY/m³. In the deep treatment stage, the mine water is softened with the aid of ultrafiltration and reverse osmosis devices, and a reused water pool is established. The cost of water production is 2.3 CNY/m³, and the cost of energy consumption is 1.3 CNY/m³ [37].

In this paper, water supply rules of classification and water quality treatment are put forward, and mine water is dispatched to each water demand area according to the principle of proximity. This approach considers only the different water quality requirements of different water use points, and does not take into account the cost of different reuse levels. Using the data in Table 2 of this paper as the reused water consumption of each water point in the mining area, the reused amount and reuse cost of each pool before optimization are calculated. The detailed data are presented in Table 3.

Table 3.

Reuse amount and cost of each tank before optimization.

Reuse level	Heating season water	Heating season cost	Non-heating season water	Non-heating season cost
	(m3/month)	(CNY/month)	(m3/month)	(CNY/month)
Clear water tank	50136.00	105286.00	54456.00	114257.60
Middle water tank	70810.00	127458.00	76940.00	138492.00.00
High water tank	88360.00	220900.00	71720.00	179300.00
Reuse water tank	53300.00	191880.00	52250.00	18810.00

According to the formula presented in this paper, the recycling costs for the heating and non-heating seasons are 645523.60 CNY/month and 620249.60 CNY/month, respectively. The calculation results of GA on the scheduling system are detailed below, with comprehensive data shown in Table 4. In terms of recycling cost, during the heating season, the total cost before optimization is 645523.60 CNY/month, and the total cost after optimization is 626569.08 CNY/month, representing a decrease of 2.94%. During the non-heating season, the total cost before optimization is 620249.6 CNY/month, and the total cost after optimization is 597983.75 CNY/month, a decrease of 61469.28 CNY/month, or a reduction of 3.60%.

Table 4.

The recycling amount and cost of each tank after optimization by GA.

Reuse level	Heating season water	Heating season cost	Non-heating season water	Non-heating season cost
	(m3/month)	(CNY/month)	(m3/month)	(CNY/month)
Clear water tank	45234.26	94991.94	48765.25	102407.03
Middle water tank	77615.01	139707.03	85472.35	153850.23
High water tank	101140.10	252850.24	85759.77	214399.42
Reuse water tank	38616.63	139019.88	35368.63	127327.07

The calculation results of GA for the scheduling system are listed below, with the detailed data shown in Table 5. In terms of recycling cost, during the heating season, the total cost before optimization is 645523.60 CNY/month, and the total cost after optimization is 615674.86 CNY/month, a decrease of 4.62%, which is higher than the 2.94% decrease observed with the GA. During the non-heating season, the total cost before optimization is 620249.60 CNY/month, and the total cost after optimization is 587828.92 CNY/month, a decrease of 61469.28 CNY/month, or a reduction of 5.23%, which is higher than the 3.6% decrease observed with the GA.

Table 5.

The recycling amount and cost of each tank after optimization by AGA.

Reuse level	Heating season water	Heating season cost	Non-heating season water	Non-heating season cost
	(m3/month)	(CNY/month)	(m3/month)	(CNY/month)
Clear water tank	42426.22	89095.05	49465.21	103876.95
Middle water tank	85730.63	154315.14	96954.21	174517.59
High water tank	101592.98	253982.45	75248.42	188121.06
Reuse water tank	32856.18	118282.23	33698.15	121313.32

Upon re-integrating the data, the following lists the calculation results of the IGSA algorithm on the scheduling system, with detailed data shown in Table 6. In terms of recycling cost, during the heating season, the total cost before optimization is 645523.60 CNY/month, and the total cost after optimization is 578744.23 CNY/month, a decrease of 66779.37 CNY/month, or a reduction of 10.34%. During the non-heating season, the total cost before optimization is 620249.60 CNY/month, and the total cost after optimization is 558780.32 CNY/month, a decrease of 61469.28 CNY/month, or a reduction of 9.91%. Compared with traditional recycling and the GA, the calculations by the IGSA algorithm result in a larger reduction in the reuse cost and exhibit superior optimization performance.

Table 6.

The recycling amount and cost of each tank after optimization by IGSA.

Reuse level	Heating season water	Heating season cost	Non-heating season water	Non-heating season cost
	(m3/month)	(CNY/month)	(m3/month)	(CNY/month)
Clear water tank	41336.35	86806.33	49465.21	103876.95
Middle water tank	118730.02	213714.03	122364.53	220256.15
High water tank	82653.47	206633.67	60075.73	150189.33
Reuse water tank	19886.16	71590.20	23460.52	84457.88

(3) Reuse time analysis of mine water cooperative scheduling system

Under the premise of achieving cost savings, this paper employs the IGSA algorithm to calculate and analyze the reuse time. Initially, the mine water reuse rate prior to optimal scheduling is referred to, considering a reuse time of 720 hours per month and taking the four reuse tanks as the research objects. The reuse rate $V_T$ in both the heating and non-heating seasons was calculated.

$$V_T=\frac{G_i}{t_{\max }}$$ (34)

where $V_T$ represents the mine water reuse rate of each grade of reuse tank, $G_i$ represents the mine water reuse amount of each grade of reuse tank, and $t_{max}$ represents the maximum time of mine water reuse. Then put forward the calculation formula of reuse time:

$$t_T=\frac{G_i}{V_T}$$ (35)

where $t_T$ represents the mine water reuse time of each grade of reuse tank. $G_i$ represents the mine water reuse amount of each grade of reuse tank, $V_T$ represents the mine water reuse speed of each grade of reuse tank. Calculation results of reuse speed are shown in Table 7.

Table 7.

Reuse time of mine water before optimization.

Reuse level	Reuse time (h/month)	Heating season recycling speed (m3/h)	Non-heating season recycling speed (m3/h)
Clear water tank	720.00	69.63	75.63
Middle water tank	720.00	98.35	106.86
High water tank	720.00	122.72	99.61
Reuse water tank	720.00	74.03	72.57

In terms of total time, the optimized heating season is 2743.01 hours/month, a decrease of 136.99 hours/month, or a reduction of 4.76%. The optimized non-heating season is 2725.48 hours/month, a decrease of 154.52 hours/month, or a reduction of 5.37%. In terms of average time, the optimized heating season is 685.75 hours/month, a decrease of 34.25 hours/month, or a reduction of 4.76%. The optimized non-heating season is 681.37 hours/month, a decrease of 38.63 hours/month, with a reduction ranging from 4.76% to 5.37%. The specific reuse time is shown in Table 8. In this chapter, the IGSA algorithm is combined with the mine water cooperative scheduling system, using the mine water reuse data of a specific mining area. The mathematical model of the mine water cooperative scheduling system is calculated, and the final result of the mine water cooperative scheduling system is obtained. The reuse destination of mine water was compared and analyzed. The results show that the reuse cost of mine water after the optimized scheduling of the IGSA algorithm is significantly reduced, the recycling speed is significantly improved, and the optimization effect is stronger than that of the traditional GA and AGA.

Table 8.

Reuse time of mine water after optimization.

Reuse level	Heating season recycling speed	Non-heating season recycling speed	Heating season reuse time	Non-heating season reuse time
	(m3/h)	(m3/h)	(h/month)	(h/month)
Clear water tank	69.63	75.63	593.63	654.01
Middle water tank	98.3472	106.8611	1207.2533	1145.08
High water tank	122.72	99.61	673.50	603.10
Reuse water tank	74.03	72.57	268.63	323.28

5. Conclusions

Drawing on the hydrogeological data of a mining area in Inner Mongolia, this paper, in conjunction with the current treatment process and reuse status, proposes a graded and qualitative water supply rule. It constructs a mathematical model of the cooperative scheduling system for mine water at both underground and surface levels. The model is simulated and calculated using an IGSA algorithm. The superiority of the algorithm is validated through comparisons of test functions and analyses of the simulation results of the objective functions. This paper primarily accomplishes two aspects of research content:

(1) This paper conducts a comprehensive investigation of the geographical location, well field overview, hydrological conditions, and other information pertaining to the Narinhe No. 2 mine. It systematically analyzes the underground and surface water consumption and water quality requirements, formulates the treatment process and water supply rules for mine water classification and quality classification, and establishes the objective function based on reuse cost and reuse time. Taking the water quality and water quantity at the mine water point as the constraint conditions, it constructs a mathematical model of the mine water cooperative dispatching system, thereby setting up a theoretical framework for the application of the algorithm.

(2) Considering the strengths and weaknesses of the genetic algorithm and simulated annealing algorithm, and addressing the issue of premature convergence in the traditional genetic algorithm, this paper adapts its operators and integrates it with the simulated annealing algorithm to propose an IGSA algorithm. The rationality and feasibility of the model and algorithm are verified through comparisons of test functions. Finally, the IGSA algorithm is used to calculate the mathematical model proposed in this paper. The results show that the system reuse cost in the heating season is reduced by 66779.37 CNY/month, a decrease of 10.34%; and the system reuse cost in the non-heating season is reduced by 61469.28 CNY/month, a decrease of 9.91%. The system recycling time in the heating season can be reduced by 136.99 hours/month, and the system recycling time in the non-heating season can be reduced by 154.52 hours/month, thereby achieving the goal of reducing the recycling cost and improving the recycling speed.

Looking forward, the research in this paper opens up several possible ways for the future mine resource optimization scheduling. On this basis, the following aspects can be studied.

(i) Enhanced scheduling scheme: This paper primarily focuses on the mine water treatment process of a specific mining area, while acknowledging variations in the mine water treatment processes across different mining areas. In future studies, the methods and strategies proposed in this paper can be utilized to enhance and tailor the process and model according to the specific requirements of each mining area, thereby improving water resource utilization rates.

(ii) Innovative optimization methods: The optimization algorithm proposed in this paper has a good effect on the model proposed in this paper, and more novel meta-heuristic algorithms can be considered for different target models.

(iii) Real-time monitoring and control: This study revolves around rescheduling and distributing completed data. Future research should consider real-time monitoring of water resources in mining areas, enabling dynamic operational scheduling to enhance resource reuse efficiency and reduce associated costs.

(iv) Anti-interference capability: Given the significant disturbances encountered within coal mines, future investigations can focus on developing robust scheduling strategies that ensure production safety during equipment failures or faults occurring within the mining area.

Ethics declarations

Review and approval by an ethics committee was not needed for this study the purpose of this study is to promote the development of coal mine underground water treatment field and improve the effect of related technologies and applications. In the course of the research, we strictly adhered to academic ethics and norms and did not involve any violation of moral or ethical standards.

CRediT authorship contribution statement

Yang Liu: Writing – original draft, Validation, Resources, Methodology, Investigation. Zihang Zhang: Writing – review & editing, Software, Data curation. Dongxu Zhu: Visualization, Validation. Lei Bo: Writing – review & editing, Supervision. Shangqing Yang: Software. Yuangan Yue: Methodology. Yiying Wang: Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

All data generated or analysed during this study are included in this article.