Helper和等价目标：一种有效的约束优化方法
Helper and Equivalent Objectives: An Efficient Approach to Constrained Optimisation
摘要：
在过去的二十年里，许多多目标进化算法被设计用于约束优化。这些算法背后的思想是将约束优化问题转化为没有任何约束的多目标优化问题，然后求解它们。在本文中，我们提出了一个新的多目标约束优化方法，它的工作原理是将一个约束优化问题转化为一个问题的助手和等价的目标。等价目标意味着它的最优解集与约束问题的最优解集相同，而辅助目标则不同。然后，这个多目标优化问题分解成一组子问题，使用加权和的方法。权重是动态调整，使每个子问题最终倾向于一个问题的等效目标。本文从理论上分析了“宽间隙”问题的辅助算法和等价目标算法的计算时间。在“宽间隙”问题中，算法需要指数时间来跨越两个适应度水平（宽间隙）。我们证明了使用辅助目标和等价目标可以缩短跨越“宽间隙”的时间。我们进行了一个案例研究来验证我们的方法。实现了一种具有辅助目标和等价目标的算法。实验结果表明，在IEEE CEC2017基准测试中，与其他8种最先进的进化算法相比，该算法在约束优化中的整体性能排名第一。
英文摘要：
Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation problems without any constraint, and then solve them. In this paper, we propose a new multi-objective method for constrained optimisation, which works by converting a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called ``wide gap''. In a ``wide gap'' problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the ``wide gap''. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms on IEEE CEC2017 benchmarks in constrained optimisation.
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