Hybrid Binary SGO-GA for solving MAX-SAT problem

Abstract

The Maximum Satisfiability Problem (MAX-SAT) is a crucial NP-hard optimization problem with applications in artificial intelligence, circuit design, scheduling, and combinatorial optimization. In this work, we provide a unique hybrid strategy that blends Genetic Algorithms (GA) with Social Group Optimization (SGO) algorithm to effectively solve the MAX-SAT problem. The SGO algorithm, inspired by the social behavior of groups, excels in exploring diverse regions of the search space. w used a binary variant of SGO i.e. Binary-SGO which is defined specifically for binary search spaces, while GA leverages evolutionary principles to exploit local optima through selection, crossover, and mutation. By integrating the exploration capabilities of SGO with the exploitation strengths of GA, the hybrid approach strikes an optimal balance between global and local search. Extensive experimental evaluations conducted on standard MAX-SAT benchmarks demonstrate that our hybrid algorithm outperforms several existing state-of-the-art meta-heuristic algorithms. Hybrid BSGO-GA achieved the highest average fitness values, with an average accuracy of 99.7% in Experiment 1, 99.61% in Experiment 2, and 99.21% in Experiment 3 and achieved complete satisfiability in 55 out of 75 cases in Experiment 1, 42 out of 75 cases in Experiment 2, and 7 out of 75 cases in Experiment 3. This approach demonstrates the potential of hybrid metaheuristics in addressing complex optimization problems and offers a robust framework for tackling other NP-hard problems.