Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at tackling one or more difficulty in an optimization problem. For instance, evolutionary algorithms have a niche in handling complexities like discontinuity, non-differentiability, discreteness and non-convexity. However, evolutionary algorithms may get computationally expensive for mathematically well behaved problems with large number of variables for which classical mathematical programming approaches are better suited. In this paper, we demonstrate a decomposition strategy that allows us to synergistically apply two complementary approaches at the same time on a complex optimization problem. Evolutionary algorithms are useful in this context as their flexibility makes pairing with other solution approaches easy. The decomposition idea is a special case of bilevel optimization that separates the difficulties into two levels and assigns different approaches at each level that is better equipped at handling them. We demonstrate the benefits of the proposed decomposition idea on a wide range of test problems.

翻译：实际优化问题可能包含不同类型的困难，若仅依赖特定优化方法往往难以处理。不同优化方法各具优势，擅长应对优化问题中的一种或多种困难。例如，进化算法在处理不连续性、不可微性、离散性和非凸性等复杂特性方面具有独特优势。然而，对于变量规模庞大且数学性质良好的问题，进化算法的计算成本可能过高，而经典数学规划方法更为适用。本文提出一种分解策略，使得两种互补方法能协同应用于复杂优化问题。进化算法在此背景下具有特殊价值，其灵活性便于与其他求解方法结合。该分解思想是双层优化的特例，将问题难度分解至两个层级，并在每个层级分配更擅长处理相应困难的优化方法。我们在多类测试问题上验证了所提分解策略的优越性。