Constraint handling in evolutionary algorithms

优化问题在科学和工程的各个领域都很常见。解决优化问题相当于为一组决策变量选择值，从而产生可能的最佳解决方案。通常，优化问题是受约束的，因为决策变量可以采用的值有限制。 进化算法(EA)是一种优化策略，在许多应用领域得到了越来越多的应用。它们通过对候选解进行变异和选择来迭代地提高候选解的群体质量。它们在面对不可区分或有噪音的目标时的稳健性，以及它们可以相对容易地适应理解较少的问题，往往使环境评估成为其他方法不适用或容易失败的选择方法。 已经提出了许多用于处理EA中的约束的技术，并且这些技术是常用的。然而，关于它们各自的能力和缺点的知识是有限的。最关键的是，人们对自适应变异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EA对一组精心选择的测试问题的行为，来了解EA在约束优化中的缩放特性。所获得的结果将补充、扩展和帮助解释今天在大型功能试验台上产生的大量经验知识。然后，我将使用所获得的见解来开发更有能力的EA来进行受限优化，并系统地将它们的能力与其他直接搜索策略的能力进行比较。

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.