A Comparison of Several Algorithms and Representations for Single Objective Optimization

In this paper we perform two experiments. In the first experiment we analyze the convergence ability to using different base for encoding solutions. For this purpose we use the bases 2 to 16. We apply the same algorithm (with the same basic parameters) for all considered bases of representation and for all considered test functions. The algorithm is an (1+1) ES. In the second experiment we will perform a comparison between three algorithms which use different bases for solution representation. Each of these algorithms uses a dynamic representation of the solutions in the sense that the representation is not fixed and is changed during the search process. The difference between these algorithms consists in the technique adopted for changing the base over which the solution is represented. These algorithms are: Adaptive Representation Evolutionary Algorithms (AREA) [1], Dynamic Representation Evolution Strategy (DRES) and Seasonal Model Evolution Strategy (SMES) [2]. AREA change the alphabet if the number of successive harmful mutations for an individual exceeds a prescribed threshold. In DRES algorithm the base is changed at the end of each generation with a fixed probability. In SMES algorithm the base in which solution is encoded is changed after a fixed (specified) number of generations. Test functions used in these experiments are are well known benchmarking problems ([3]): Ackley’s function (f1), Griewangk’s function (f2), Michalewicz function (f3), Rosenbrock’s function (f4), Rastrigin’s function(f5) and Schwefel’s function (f6). The essential role of these experiments is to show that using only one base for solution encoding (without change it during the search process) there are cases when the optimum cannot be found. Changing the representation base provides a new way of searching through the solution space. The second experiment show us which technique used for changing the base is suitable. The number of space dimension was set to 30 for each test function. Each algorithm is run 100 times for each test function in each experiment and with any considered parameters. In first experiment for test functions f1, f2 and f4 the best results are obtained using binary encoding. For test functions f3, f5 and f6 the best result is obtained by encoding solutions in the base 4.