Minimizing a nonlinear function under a fuzzy max-t-norm relational equation constraint

This work studies a nonlinear optimization problem subject to fuzzy relational equations with max-t-norm composition. Since the feasible domain of fuzzy relational equations with more than one minimal solution is non-convex, traditional nonlinear programming methods usually cannot solve them efficiently. This work proposes a genetic algorithm to solve this problem. This algorithm first locates the feasible domain through the maximum solution and the minimal solutions of the fuzzy relational equations, to significantly reduce the search space. The algorithm then executes all genetic operations inside this feasible domain, and thus avoids the need to check the feasibility of each solution generated. Moreover, it uses a local search operation to fine-tune each mutated solution. Experimental results indicate that the proposed algorithm can accelerate the searching speed and find the optimal solution.