进化算法求解复杂混合整数规划问题及应用

混合整数规划问题广泛存在于科学和实际工程领域。由于约束条件和整数限制的同时存在，混合整数规划问题的可行域往往被分割为大量的具有不同大小的离散可行块。在使用进化算法求解这类问题时，需要同时考虑如何处理约束条件、整数限制及大量的可行块，这无疑提出了重大挑战。本项目拟对进化算法求解复杂混合整数规划问题展开全面研究，包括：1）挖掘和利用目标函数与约束条件的相关性，设计约束处理技术；2）设计可行块删减技术来减少可行块的数量，降低求解难度；3）设计新的整数限制处理技术，削弱可行块大小对求解带来的影响，进一步提升求解能力；4）将约束处理技术、可行块删减技术、整数限制处理技术与进化算法有机结合，构建新的算法框架；5）设计代理模型辅助的进化算法，并将其应用于求解汽车车身多材料结构匹配设计这类昂贵混合整数规划问题。通过对以上五个方面进行研究，本项目将进一步推动进化算法在复杂混合整数规划问题求解与应用中的发展。

Mixed-integer programming (MIP) problems are frequently encountered in many science and engineering disciplines. Due to the existence of both constraints and integer restrictions, the feasible region of a MIP problem is usually divided into a considerable number of discontinuous feasible parts. When solving a MIP problem by evolutionary algorithms, how to simultaneously deal with constraints, integer restrictions, and a considerable number of feasible parts should be considered. Clearly, it poses a great challenge to current evolutionary algorithms. In this project, we will carry out extensive research on solving complex MIP problems by evolutionary algorithms. Specifically, the following five aspects will be considered: 1) designing constraint-handling techniques by mining and utilizing the correlation between objective function and constraints; 2) designing a technique to delete some inferior feasible parts, with the aim of reducing the number of feasible parts and reducing the difficulty of solving a MIP problem; 3) designing a new integer-restriction-handling technique to reduce the influence of the sizes of different feasible parts and to further improve the ability of the algorithm; 4) developing a new algorithm framework for solving MIP problems by combining constraint-handling technique, feasible-part-deletion technique, and integer-restriction-handling technique with evolutionary algorithms; and 5) constructing a surrogate model-assisted evolutionary algorithm for dealing with automobile body multi-material structure matching design, which is an expensive MIP problem. By researching on the above-mentioned five aspects, this project aims at further promoting the solution and application of complex MIP problems by utilizing evolutionary algorithms.