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Verification of thermo-dynamical genetic algorithm to solve the function optimization problem through diversity measurement — Diversity measurement and its application to selection strategies in genetic algorithms

In this paper, it is experimentally verified that TDGA (Thermo Dynamical Genetic Algorithm) is effective in solving a function optimization problem using Genetic Algorithms, because of its sustainability of population diversity and efficiency of searching for solutions. We experimentally and quantitatively verify the hypothesis that we can improve the ratio of searching for the optimum solution and the accuracy of the solution by maintaining the diversity. In our investigation, we measure the diversity of the population with the entropy defined in TDGA. TDGA is a selection strategy based on the minimum free energy principle in thermodynamics. In applying the principle to GAs, we select individuals to make the average energy <;E> a minimum and the entropy H a maximum. TDGA is compared with immune-GA (immune Genetic Algorithm), simple GA and GA with scaling windows from the viewpoint of sustainability of diversity of population. Immune-GA is an optimization method based on Jerne's idiotype network, which hypothesizes homeostasis of organic immunity system. The effectiveness of these four GA models is verified quantitatively by diversity measurement. In this study, we use BLX-α for localizing and centralizing the search. Each of above four GA models generates individuals by two-point crossover operation, and if the diversity of the generated children falls below the required threshold, BLX-α starts to work. Experimental results by using ten well-known test functions including De Jong's test functions are reported in this paper.