Game Theory and Social Interaction for Selection and Crossover Pressure Control in Genetic Algorithms: An Empirical Analysis to Real-Valued Constrained Optimization

Abstract

Game Theory (GT) formalizes dispute scenarios between two or more players where each one makes a move following their strategy profiles. The following paper introduces the integration of GT to selection and crossover steps of Genetic Algorithms as an evolutionary model of the representation of population in a similar way to human social evolution. Two ideas are proposed to be incorporated into the GA. First, the Genetic Algorithm with Social Interaction (GASI), a family of GAs that uses GT in selection phase to increase the diversification of the solutions. Second, the (Game-Based Crossover) GBX and GBX2 crossover operators, competition-based tournament selection methods that employ social dispute to generate more diverse offspring. Performance and robustness of the new approaches were assessed by ten continuous and constrained engineering design optimization problems and compared against variants of the canonical GA, as well as well-known heuristics from the literature. Results indicate significant performance relevance in most instances compared to other algorithms and highlight the benefits of combining GT and GA.

Dynamic Interconnection Approach With BLX-Based Search Applied to Multi-Swarm Optimizer: An Empirical Analysis to Real Constrained Optimization

“…GBX2 27 ), previously published by the present authors [29]. The use of Social Interaction has been associated with good results for constrained optimization [29].…”

“…For the variant particles and its directedbased crossover, the addition of a game-based crossover scheme (i.e. GBX2 27 ), previously published by the present authors [29]. The use of Social Interaction has been associated with good results for constrained optimization [29].…”

“…The problem features four constraints describing the minimal deflection, shearing tension, surge frequency and external diameter limits [85], [86]. More details about the ten COPs used for benchmark, including their mathematical functions, can be found in the authors' previous work: Lisboa et al [29]. 21 Regarding the minimum and maximum limits para for the acceleration coefficients (i.e.…”

“…The main reason why the BLX crossover was selected as the foundation for the proposed method (V1/V2) is the fact that BLX is a simple -yet efficient -approach, which presented good results in previous experiments when applied to constrained optimization problems (COPs) [29]. It is important to emphasize that, as in FC-CPMSO, the use of V1/V2 had a low impact on computational complexity.…”

Algoritmo Genético Aplicado à Geração Automática de Casos de Teste

“…Como proposta, será implementada duas variac ¸ões de AGs e será realizada uma análise comparativa entre os algoritmos. O primeiro AG será conforme o padrão originalmente proposto por John Holland [Holland 1975] e segundo AG será hibiridizado com Interac ¸ão Social por meio da Teoria dos Jogos (TJ), visando expandir os estudos propostos em [Pereira et al 2020].…”