This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm.

本文讨论了一个以最大阿基米德双极模糊关系方程组为约束的非线性优化问题。证明了与最大阿基米德双极模糊关系方程解集结构有关的一些结果。利用这些结果，提出了一种遗传算法来解决获得最优解或收敛解的问题。该算法的有效性也与文献中发现的其他方法进行了比较。以往的方法需要将问题转化为0-1混合整数优化问题，可以通过一些非线性优化求解器来解决，因此，计算量可能会随着问题的规模而增加。开发了一些测试问题来评估所提出算法的性能。