MBHGA: A Matrix-Based Hybrid Genetic Algorithm for Solving an Agent-Based Model of Controlled Trade Interactions

The article discusses the development and study of a new matrix-based hybrid genetic algorithm (MBHGA) for solving an agent-based model of firms’ behavior with controlled trade interactions. The proposed model employs symmetric strategies optimized using the MBHGA algorithm. This algorithm combines evolutionary search with real-coded crossover and matrix binary-coded crossover as genetic operators, creating a hybrid approach. The aim of the designed system is to assist decision-makers in selecting optimal strategies for their firms in situations where some companies impose restrictions on interactions. As demonstrated by the results of optimization experiments, the MBHGA algorithm significantly outperformed other methods, such as RCGA, PSO, GWO, SPEA2, and NSGA-II, in terms of both accuracy (measured by deviations from reference values) and the quality of the Pareto front approximation (measured by LHV, IGD, and CPF) when solving an agent-based model of firms’ behavior. As demonstrated in this study, the performance of MBHGA significantly depends on the size of the model (i.e., the number of agents), and it can be enhanced by parallelizing the evolutionary search process, including matrix crossover operations for decision variables. Optimization experiments using a genetic algorithm were conducted to maximize utility functions for agent companies under trade restrictions. The results showed that trade restrictions have a negative impact on the utility function values in both single- and multi-objective optimization, for selected countries and for all countries’ firms. However, an optimization-based approach using the MBHGA algorithm can help minimize the negative consequences of trade restrictions by providing the ability to find nondominated solutions and the best possible trade-offs.