[论文解读] Genetic Algorithms for Multiple-Choice Problems

Uwe Aickelin|arXiv (Cornell University)|Apr 19, 2010

Metaheuristic Optimization Algorithms Research参考文献 7被引用 4

一句话总结

本博士论文提出了一种新型的间接遗传算法（IGA），其解码函数具备自适应调节能力，用于求解复杂的多选优化问题，如护士排班和商场商铺分配。通过利用修复方案和分层协同进化整合问题特定知识，该方法在解的质量和可行性方面显著优于标准遗传算法。IGA由于对结构约束的依赖性降低，相较于直接方法表现出更优性能。

ABSTRACT

This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of information and the way it is included are important factors for success.Two multiple-choice problems are considered.The first is constructing a feasible nurse roster that considers as many requests as possible.In the second problem, shops are allocated to locations in a mall subject to constraints and maximising the overall income.Genetic algorithms are chosen for their well-known robustness and ability to solve large and complex discrete optimisation problems.However, a survey of the literature reveals room for further research into generic ways to include constraints into a genetic algorithm framework.Hence, the main theme of this work is to balance feasibility and cost of solutions.In particular, co-operative co-evolution with hierarchical sub-populations, problem structure exploiting repair schemes and indirect genetic algorithms with self-adjusting decoder functions are identified as promising approaches.The research starts by applying standard genetic algorithms to the problems and explaining the failure of such approaches due to epistasis.To overcome this, problem-specific information is added in a variety of ways, some of which are designed to increase the number of feasible solutions found whilst others are intended to improve the quality of such solutions.As well as a theoretical discussion as to the underlying reasons for using each operator,extensive computational experiments are carried out on a variety of data.These show that the indirect approach relies less on problem structure and hence is easier to implement and superior in solution quality.

研究动机与目标

• 解决标准遗传算法在求解大规模多选优化问题时的局限性。
• 研究如何有效将问题特定知识整合到遗传算法中，以提升解的可行性与质量。
• 比较直接与间接遗传算法在性能、鲁棒性及实现难易度方面的表现。
• 开发并评估具有分层子种群和修复机制的协同协同进化方法在约束优化中的应用。
• 通过真实世界问题的计算实验，证明间接方法的优越性。

提出的方法

• 采用间接遗传算法（IGA），其中解以参数向量形式编码，并通过自适应函数进行解码。
• 使用具有分层子种群的协同协同进化方法，以管理复杂且相互依赖的决策变量。
• 实施基于问题结构的修复方案，将不可行解转化为可行解，同时保持解的质量。
• 引入自适应解码器，动态适应问题约束，降低对人工设计规则的依赖。
• 结合修复机制与适应度评估，以在约束优化中平衡可行性与成本。
• 在两个真实世界问题上开展广泛的计算实验：护士排班与商场商铺分配。

实验结果

研究问题

• RQ1 如何有效将问题特定知识编码到遗传算法中，以提升多选问题的求解性能？
• RQ2 在求解约束性多选优化问题时，直接方法与间接方法的相对有效性如何？
• RQ3 具有分层子种群和修复机制的协同协同进化对解的质量与收敛性有何影响？
• RQ4 自适应解码器函数在多大程度上减少了对详细问题结构知识的需求？
• RQ5 哪些因素决定了将约束处理机制整合到进化算法中的成功与否？

主要发现

• 在两个测试问题中，具有自适应解码器的间接遗传算法在解的质量和鲁棒性方面均优于直接方法。
• 通过修复方案和分层协同进化有效整合问题特定知识，显著提升了找到可行解的数量。
• 间接方法对问题特定结构知识的需求更少，因此更易于实现，并且对新问题更具适应性。
• 具有子种群的协同协同进化通过独立优化问题的子组件，提升了搜索效率。
• 计算实验表明，IGA在收敛性和解的质量方面均优于标准遗传算法。
• 自适应解码器减少了对人工调参的需求，并增强了算法动态处理复杂约束的能力。