Improved evolutionary optimization from genetically adaptive multimethod search -- Vrugt and Robinson 104 (3): 708 Data Supplement - HTML Page - index.htslp -- Proceedings of the National Academy of Sciences

Vrugt and Robinson 1010.1073/pnas.0610471104

Supporting Information

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SI Figure 4
SI Text
SI Table 2
SI Movie 1
SI Movie 2

SI Figure 4

Fig. 4. Flowchart of the AMALGAM optimization method outlined in this paper. The method implements the concepts of multimethod search and adaptive offspring creation to find a well-distributed set of Pareto solutions. The method is entirely generic and can accommodate any combination and number of reproductive operators to create the offspring population.

SI Movie 1

Movie 1. Evolution of the best non-dominated fronts generated with the individual NSGA-II ('▢' - red), PSO ('o' - cyan), AMS ('+' - black) and DE ('.' - green) algorithms and the AMALGAM method ('x' - blue) for test problem ZDT4. Each transition between two slides stands for a hundred function evaluations. The dark line depicts the location of the true Pareto-optimal front, whereas the colored bar charts at the right hand side depict AMALGAM's evolution of the number of offspring points generated with the individual algorithms. The results illustrate the utility of individual search algorithms during different stages of the optimization, and demonstrate that competition between individual algorithms and adaptive offspring creation dramatically improves the efficiency of evolutionary search.

SI Movie 2

Movie 2. Similar to Movie 1, for the Rotational Test Problem (ROT).

Table 2. Description of multiobjective test problems used in this study

Problem	n	Parameter Ranges	Objective Functions	Characteristics
ZDT1	30	[0,1]		Convex
ZDT2	30	[0,1]		Nonconvex
ZDT3	30	[0,1]		Convex, disconnected
ZDT4	10			Nonconvex
ZDT6	10	[0,1]		Nonconvex, nonuniformly spaced
SCH	1	[-10³,10³]		Convex
SCH2	1	[-10³,10³]		Convex, disconnected
FON	3	[-4,4]		Nonconvex
KUR	3	[-5,5]		Nonconvex, disconnected
ROT	10	[-0.3,0.3]		Rotated, correlated

Abbreviations for the functions: ZDT1 - ZDT4 and ZDT6, Zitzler et al. (1); SCH and SCH2, Schaffer (2); FON, Fonseca and Fleming (3); KUR, Kursawe (4); and ROT, Deb et al. (5).

1. Zitzler, E., Deb, K. & Thiele, L. (2000) Evol. Comp. 8, 173 - 195.

2. Schaffer, J.D. (1987) Proc. First Inter. Conf. on Genetic Algorithms (Hillsdale, NJ).

3. Fonseca, C.M. & Fleming, P.J. (1993) Proc. Fifth Inter. Conf. on Genetic Algorithms (San Mateo, CA).

4. Kursawe, F. (1990) Parallel problem solving from nature

(Springer-Verlag, Berlin, 1990).

5. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002) IEEE Trans. Evol.Comp

. 6, 182 - 197.