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.

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The Multi-Swarm approach allows the use of multiple configurations between two or more populations of particles, where each one can present different approaches (e.g. lbest, gbest, Unified, Guaranteed-Convergence) directed towards improving the optimization process. This article presents a proposal for local/global stochastic interconnection applied to the context of the Multi-Swarm algorithm, as well as for incrementing a local search method for refining previously obtained solutions. Two proposals are introduced for this new Multi-Swarm PSO (MSO). The first one is the inclusion of "counterpart particles", which establishes a sub-topology between inter-swarm particles, accessed by migration and evaluability rules. The other involves using customized crossover operators and is based on the BLX scheme (Blend Crossover) with direction information used as a reference for establish a subspace search around the particles. Performance and robustness of the new approaches were assessed by ten constrained engineering design optimization problems (COPs), as is compared to other solutions already published in the scientific literature. Results indicate significant performance improvements for all 10 COPs when compared to concurrent-based MSOs. By making available new references from other swarms, the counterpart particles approach tends to improve the optimization process in the search space, while an intermediate layer of local search based on a modified directed BLX crossover should provide an extra search around the particle, and thus, refining previously obtained solutions.

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