高效数学启发式算法设计及其应用研究

As a frontier topic in the field of evolutionary computation, matheuristics represent a novel problem solving paradigm, which combines the mechanisms from mathematical programming and heuristic algorithms. Unlike traditional algorithms, matheuristics are able to exploit domain-specific knowledge to guide the problem solving process, and have the capability of solving large-scale real-life problems. However, despite the promising achievements that matheuristics have accomplished, the research framework of matheuristics is still not complete. Based on the comprehensive literature review, we summarize a series of research questions, which are presented as follows. (1) From the algorithmic model perspective: Given a problem instance and a matheuristic, how to decide the suitability of applying the matheuristic to solve the instance. Furthermore, how we should select the most suitable matheuristic, if multiple models are available. (2) From the algorithmic design perspective: How to conduct the parameter setting task automatically, to improve the robustness and the adaptability of matheuristics. (3) From the algorithmic application perspective: How to expand the application scope of matheuristics, to meet the demand of problem solving from industry. Taking the wind farm layout optimization as a case study, we propose a set of practical experiment schemes. Through the project, the performance and the applications of matheuristics could be effectively enhanced.

作为演化计算领域的前沿热点，数学启发式算法结合数学规划方法和启发式算法的优势，形成了一种新的问题求解模式。相比传统算法，数学启发式算法能够充分利用问题相关信息，并具有良好的大规模问题求解能力。然而，虽然取得了令人振奋的成果，数学启发式算法研究体系尚未完备。本项目在归纳现有文献的基础上，凝炼出一系列亟待解决的科学问题，包括（1）算法模型层面：如何预先根据问题特征，判断待求解问题实例是否适合使用数学启发式算法进行求解，以及如何选择合适的问题求解模型；（2）算法求解层面：如何对数学启发式算法中不同模块的参数进行自动化设置，以提升算法健壮性和自适应能力；（3）算法应用层面：如何扩大数学启发式算法的应用范围，以求解传统组合优化问题以外的工业界实际问题。结合已有工作基础，本项目拟定了切实可行的解决思路，并以风电场机组选址问题为案例展开研究。通过本项目，数学启发式算法的性能、适用范围有望得到有效的提升。

作为演化计算领域的前沿热点，数学启发式算法结合数学规划方法和启发式算法的优势，形成了一种新的问题求解模式。相比传统算法，数学启发式算法能够充分利用问题相关信息，并具有良好的大规模问题求解能力。本项目在归纳现有文献的基础上，从算法模型层面、算法求解层面和算法应用层面出发，尝试完善数学启发式算法的框架体系，具体包括（1）算法模型层面：基于元学习，预先根据问题特征，判断待求解问题实例是否适合使用数学启发式算法进行求解；（2）算法求解层面：通过搜索空间平滑、参数自动调制等技术，提升算法健壮性和自适应能力；（3）算法应用层面：将方法推广至更多问题领域，例如软件工程。本课题严格按照课题申请书和计划书要求，分别对3个科学问题进行了深入研究，完成了预定的研究任务。在本课题支持下，在中国科学、PPSN等知名期刊与国际会议发表论文10篇，课题共支持5位博士生和4位硕士生。在课题的支持下，研究团队的科研水平显著提高，在国内外影响力明显提升。