Table 6.

Annotated bibliography

S.No.	Combined methods	Combination type	Hybrid model used	Objective	The performance of proposed method	References
Single objective optimization
1	GA TS	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Incorporate TS to guide GA for better local ptima avoidance	GA-TS provided much better solution accuracy and convergence process than original GA	[72]
2	GAs	Meta-heuristics	Low level co-evolutionaryhomogeneous hybrid model homogeneous hybrid model	Develop an efficient optimization algorithm	It provides better quality results and precise optimal values than HOMER	[73]
3	PSO HS	Meta-heuristic Meta-heuristic	Low level co-evolutionaryheterogeneous hybrid model	Implement HS algorithm to make all the particles of PSO fly inside the variable boundaries and regenerate which fly outside the variables boundary then to check whether they violate the problem-specific constraints and get better solutions	Less computational time compared to PSO The effectiveness to manipulate the new particles fulfilling the problem constrains.	[74]
4	GA Iterative method	Meta-heuristic Exact method	High level relay heterogeneous hybrid model	Reduce computational time by minimizing the number of iterations	Less number of iterations with relatively less consumed time	[75]
5	GA Markov model	Meta-heuristic Exact method	High level relay heterogeneous hybrid model	Minimize the long computational time required by GA	Markov mode-based GA produced high quality solutions It provides less consumed CPU time	[76]
6	SA TS	Meta-heuristic Meta-heuristic	High level Relay heterogeneous hybrid model	SA is not especially fast at finding the optimum in a given solution region	The performance of the proposed algorithm is higher than standard SA and TS	[77]
7	GA ANN	Meta-heuristic Soft computation	High-level Relay heterogeneous hybrid model	Reduce the computational effort required	It provides the optimal size combination under conditions of uncertainty, in a reasonable manner	[78]
8	SA CS HS	Meta-heuristic Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Improve exploration and exploitation capabilities	The combination has showed better performance than other algorithms based on mean and worst values	[79]
9	TLBO DE	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increasing the diversity of the population	This combination has produced high quality solutions	[80]
10	GA Fuzzy logic	Meta-heuristic Soft computation	Low level co-evolutionary heterogeneous hybrid model	Reduce computational time and improve quality results	The proposed algorithm increased the quality of solutions compared to GA	[81]
11	ACOR ILP	Meta-heuristic Soft computation	Low level co-evolutionary heterogeneous hybrid model	Create an effcient optimization algorithm	The method has smaller convergence iterations and consumed time than ABC and GA	[82]
12	PSO SA	Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Enhancing the capability of jumping out of local optimal optima	The proposed combination gives greater cost results in less calculation time than PSO	[83]
13	PSO BB-BC	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Improve the exploration ability of the BB-BC algorithm and avoid local optima entrapment	Low standard deviation relative to PSO and DHS Higher quality results	[84]
14	PSO MCS	Meta-heuristic Exact method	Low level co-evolutionary heterogeneous hybrid model	Increase chance to find the optimal decision variables	It provides excellent solutions quality based on minimizing TAC	[43]
15	GA Exhaustive search	Meta-heuristic Exact method	High level relay heterogeneous hybrid model	Enables GA to avoid probably of trapping into local optima	Proposed method achieved the optimal solution with less number of iterations compared to classical GA	[85]
16	HS CS	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model		HSBCS yields better results than the standard HS	[86]
17	HS SA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Escape from the local optimum	HHSSAA provided better quality results compared to individual HS or individual SA	[87]
18	CS SA IHS	Meta-heuristic Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Balance exploration and exploitation capabilities	Higher convergence accuracy	[88]
19	CS NMA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Employ Nelder-Mead method to reduce the time taken for the search by ACO	The proposed combination improved convergence rate and reduced simulation time	[89]
20	CS HS SA	Meta-heuristic Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Balancd exploration and exploitation capabilities	Better quality results	[90]
21	GA PSO	Meta-heuristic Meta-heuristic	High level co-evolutionary heterogeneous hybrid model	Develop an efficient optimization algorithm	Proposed method achieved search performance	[91]
22	TLBO SSA ED	Meta-heuristic Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Better exploitation of the search space of the search space	Superior quality of solutions	[92]
23	SA IHA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the probability of finding the global solution for a complex optimization problem	Higher optimal solutions accuracy	[93]
24	Jaya TLBO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the search power around the global solution	JLBO provided more promising solutions quality in terms of minimizing TAC than GA	[94]
25	GWO SCA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Improve the accuracy and speed of the GWO method by adding the updating operator of the SCA instead	The new algorithm has produced high quality results than PSO, GWO and GWO	[95]
Multi-objective optimization
1	FPA SA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the global search of FPA and prevent the algorithm to be trapped in local optimum solutions	Better results quality than GA Good solution precision than PSO Better performance with less run-time	[96]
2	MOPSO NSGA-II	Meta-heuristic Meta-heuristic	High level relay heterogeneous Hybrid model	Ameliorate quality results	It provides more promising solutions quality in terms of minimizing TC solutions quality in terms of minimizing TC	[97]
3	ACO ABC	Meta-heuristic Meta-heuristic	High level relay heterogeneous hybrid model	Help ACO by produce a good initial solution and determine a good search direction using ABC	ABC-ACO provided better quality results than original ACO	[98]
4	MOL TLBO	Meta-heuristic Meta-heuristic	High level relay heterogeneous hybrid model	Enhance exploration and exploitation capabilities	It provides fast result convergence and lesser chances of local minima It provides better results quality than SGA, PSO, TLBO, ITLBO and MOL	[99]
5	GA PSO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Augment the computational efficiency because PSO can easily fall into a local optimal point prematurely.	The proposed algorithm provided more effective results with lower fitness function value It avoids lack of accuracy of the final solution (premature convergence)	[100]
6	MOEA GA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous Hybrid mode	Reduce computational time and improve results quality	Optimum solution Less computational time	[65]
7	TLBO CSA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous Hybrid model	Improve exploration and exploitation capabilities	New TLBO provided more promising solutions quality (better cost) than GA and PSO	[101]
8	SFLA BAT	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Balanced rade-off between the exploration and exploitation	ShBAT gives best result compared with the GA, SFLA and BAT	[102]
9	MHOD GSA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Balance the exploratory behavior with exploitative behavior	The novel algorithm yields better result in terms of convergence time and losses of the bus compared to both algorithm individually	[103]
10	PSO GWO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Combine the ability of exploitation in PSO with the ability of exploration in GWO for better trade off between the exploration and exploitation in order to avoid high local optima	Hybrid PSO-GWO provided superiority results over the comparative algorithms in terms of reducing the computational time and achieving the best function values for both the single and the multi-objective problems	[104]
11	ABC CS	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the efficiency of ABC	The proposed method provides better performance in than GA, PSO and hybrid GA-PSO	[105]
12	PSO NMA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Improve the convergence rate of the optimal solution and help PSO with best start for faster convergence with global solution	It provides more accurate optimization results compared to PSO and GA	[106]
13	TLBO GWO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the global and local search capability as well as track the optimal answer of TLBO	The suggested algorithm has a better convergence speed in single objective problem solution and also in multi-objective optimization based on Pareto levels and achieving the less loss and more reliability than TLBO and GWO individually	[107]
14	GA GWO	Meta-heuristic Meta-heuristic	Low-level co-evolutionary heterogeneous hybrid model	Increase the exploration capability of GWO	The HGWO algorithm performs better than the PSO algorithm	[108]
15	SFL TLBO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Enhance the exploitation capability of TLBO algorithm	The combination offered higher quality solution compared to TLBO and SFL individually	[109]
16	PSO GSA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Combine the ability for social thinking in PSO with the local search capability of GSA	The hybrid PSOGSA algorithm provides an effective and robust high-quality solution. Hybrid PSOGSA are either better or comparable to those obtained using other techniques reported in the literature	[110]
17	GA PSO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	To avoid falling into the local optimum and to improve the quality of searching global optimum	GA-PSO operated faster and more accurately compared to NSGA-II, E-PSO, DE, and GA	[111]
18	BBO PSO	Meta-heuristic Meta-heuristic	High level co-evolutionary heterogeneous hybrid model	Improve exploration and exploitation capabilities	The proposed algorithm provided better results quality than NSGA-II and MOPSO	[112]
19	AEO SCA	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Reduce the computational time and avoid falling into local optimum	Better quality results and higher convergence accuracy than standard AEO The proposed IAEO has the best performance among PSO, GWO, and SSA	[113]
20	GWO PSO	Meta-heuristic Meta-heuristic	High level relay heterogeneous hybrid model	Reduce the possibilityof falling into a local minimum	Superior quality of solutions	[114]
21	CSO PSO	Meta-heuristic Meta-heuristic	Low level co-evolutionary heterogeneous hybrid model	Increase the exploration capabilities of CSA	Higher convergence accuracy	[115]