Constraint handling in evolutionary algorithms

优化问题在科学和工程的所有领域都是丰富的。 解决一个优化问题相当于为一组决策变量选择值，这些值会导致可能的最佳解决方案。 通常，优化问题受到约束，因为决策变量可以采用的值受到限制。 进化算法（EA）是一种优化策略，在许多应用领域中使用越来越多。 它们通过对候选解进行变异和选择来迭代地提高候选解群体的质量。 它们在面对不可微或噪声目标时的鲁棒性，沿着它们可以相对容易地适应于知之甚少的问题，通常使EA成为其他方法不适用或容易失败的选择方法。 在EA中处理约束的许多技术已经被提出并被普遍使用。 然而，对它们各自的能力和缺点的了解是有限的。 最重要的是，自适应变分算子和约束处理技术之间的相互作用知之甚少。 我将通过分析一组精心挑选的测试问题的行为来理解EA的约束优化的缩放特性。 所获得的结果将补充，扩展，并帮助解释今天可用的大型功能测试平台上产生的大量经验知识。 然后，我将使用所获得的见解，开发更有能力的EA约束优化和系统地比较他们的能力与其他直接搜索策略。

Optimisation problems are abundant in all areas of science and engineering. Solving an optimisation problem amounts to choosing values for a set of decision variables that result in the best solution possible. Often, optimisation problems are constrained in that there are restrictions on the values that the decision variables can take on. Evolutionary algorithms (EAs) are optimisation strategies that see increasing use in many areas of application. They iteratively improve the quality of populations of candidate solutions by subjecting them to variation and selection. Their robustness in the face of non-differentiable or noisy objectives, along with the relative ease with which they can be adapted to poorly understood problems, often make EAs the method of choice where other approaches are not applicable or prone to failure. A multitude of techniques for handling constraints in EAs have been proposed and are in common use. However, knowledge with regard to their respective capabilities and shortcomings is limited. Most crucially, the interaction between adaptive variation operators and constraint handling techniques is poorly understood. I will achieve an understanding of scaling properties of EAs for constrained optimisation by analysing their behaviour for sets of carefully selected test problems. The results obtained will complement, extend, and help explain the large body of empirical knowledge generated on large function testbeds that is available today. I will then use the insights gained to develop more capable EAs for constrained optimisation and systematically compare their capabilities with those of other direct search strategies.