求解约束优化问题的改进自适应μ约束处理技术

Improved adaptive μ-constraint handling technique for solving constrained optimization problems

针对当前的约束处理技术存在易陷入局部最优解、难以满足等式约束和多控制参数的问题,在μ约束处理技术的基础上,以梯度下降法和多目标拥挤距离为理论依据,设计反映种群约束违反度分布信息的ω参数,它可以自适应地调节约束违反度阈值μ的松弛进而有效地解决约束问题.此外,改进了μ阈值比较准则以提高种群的多样性.经对CEC2017的标准约束优化问题(Constraint optimization problems,COP)进行求解,并与其他先进算法相比较,结果表明,改进的μ约束处理技术能够高效地处理含等式约束的COP.

To solve the problems existing in the current constraint handling techniques, where it’s easy to fall into the local optimal solutions, difficult to satisfy the equality constraints and there are also multiple control parameters, the parameterω is designed, based on the gradient descent method and multi-objective crowding-distance theory. In this paper, ω is a reflection of population constraint violation degree distribution information, which can adaptively adjust the relaxation of the constraint violation threshold μ to solve the constrained problem accurately. In addition, the μ threshold comparison criteria have been improved to increase population diversity. After the solutions of the standard constrained optimization problems(COP) of CEC2017, we compare the results with other advanced algorithms. And the comparison shows that the improved μ-constraint handling techniques can deal with complex equation constraints efficiently.