[论文解读] Using Dissortative Mating Genetic Algorithms to Track the Extrema of Dynamic Deceptive Functions

Carlos M. Fernandes, J. J. Merelo+1 more|ArXiv.org|Apr 20, 2009

Metaheuristic Optimization Algorithms Research参考文献 57被引用 4

一句话总结

本文提出自适应异配遗传算法（ADMGA），通过自适应调整汉明距离阈值来选择基因上差异较大的亲本，以维持高水平的遗传多样性，从而在动态欺骗性函数中追踪移动的最优解。ADMGA在较难的问题实例中显著优于标准遗传算法（GA）和以往的异配遗传算法，能有效逃离局部最优解并适应环境变化，且无需外部调参。

ABSTRACT

Traditional Genetic Algorithms (GAs) mating schemes select individuals for crossover independently of their genotypic or phenotypic similarities. In Nature, this behaviour is known as random mating. However, non-random schemes - in which individuals mate according to their kinship or likeness - are more common in natural systems. Previous studies indicate that, when applied to GAs, negative assortative mating (a specific type of non-random mating, also known as dissortative mating) may improve their performance (on both speed and reliability) in a wide range of problems. Dissortative mating maintains the genetic diversity at a higher level during the run, and that fact is frequently observed as an explanation for dissortative GAs ability to escape local optima traps. Dynamic problems, due to their specificities, demand special care when tuning a GA, because diversity plays an even more crucial role than it does when tackling static ones. This paper investigates the behaviour of dissortative mating GAs, namely the recently proposed Adaptive Dissortative Mating GA (ADMGA), on dynamic trap functions. ADMGA selects parents according to their Hamming distance, via a self-adjustable threshold value. The method, by keeping population diversity during the run, provides an effective means to deal with dynamic problems. Tests conducted with deceptive and nearly deceptive trap functions indicate that ADMGA is able to outperform other GAs, some specifically designed for tracking moving extrema, on a wide range of tests, being particularly effective when speed of change is not very fast. When comparing the algorithm to a previously proposed dissortative GA, results show that performance is equivalent on the majority of the experiments, but ADMGA performs better when solving the hardest instances of the test set.

研究动机与目标

• 为解决在动态优化问题中，因收敛导致适应性下降而难以维持遗传多样性的挑战。
• 探究异配交配是否能提升遗传算法在欺骗性景观中追踪移动最优解的能力。
• 评估 ADMGA 在不同变化速度下的动态陷阱函数上的性能，相较于现有遗传算法的表现。
• 评估 ADMGA 的交配阈值自调节能力，与固定参数方案相比的表现。
• 确定异配交配是否能增强动态欺骗性环境中的探索能力，并防止过早收敛。

提出的方法

• ADMGA 采用基于汉明距离的自适应可调阈值来选择交配对，优先选择基因上差异较大的个体。
• 交配阈值在运行过程中动态调整，以控制异配交配的强度，降低对人工调参的依赖。
• 仅当个体间汉明距离超过当前阈值时才执行交叉操作，从而促进遗传多样性。
• 算法使用标准遗传算子（选择、交叉、变异），并采用 1/L 的变异率以保持平衡。
• 在变化速度（ρ）和位移幅度（ε）各异的五阶动态陷阱函数上评估性能。
• 对比实验包括 ADMGA、nAMGGA（先前的异配遗传算法）、传统 RIGA 和 SORIGA，采用统计检验评估结果显著性。

实验结果

研究问题

• RQ1 异配交配能否提升遗传算法在动态欺骗性函数中追踪移动最优解的能力？
• RQ2 ADMGA 的自调节交配阈值与固定参数异配方案相比，在动态环境中的表现如何？
• RQ3 ADMGA 在收敛速度和解质量方面是否优于传统及专用遗传算法，在动态陷阱问题上表现更优？
• RQ4 ADMGA 的性能如何随环境变化速度和幅度的变化而变化？
• RQ5 异配交配在欺骗性景观中在多大程度上增强了探索能力并防止了过早收敛？

主要发现

• 在 100,000 和 200,000 次评估场景下，ADMGA 显著优于传统 RIGA 和 SORIGA，尤其在 ρ = 0.3、0.6 和 0.95 时表现更优。
• 在最困难的实例（ε = 200,000）中，ADMGA 的适应度显著优于 nAMGGA，p 值表明其统计上更优。
• ADMGA 在整个运行过程中保持了更高的遗传多样性，从而有效逃离局部最优解并持续追踪移动的全局最优解。
• ADMGA 中的自适应调整阈值消除了人工调参的需要，相比 nAMGGA 的固定参数，鲁棒性更强。
• 在低变化场景（ρ = 0.05）下，ADMGA 表现良好，但当变化过快时性能出现一定程度下降。
• 统计检验确认，ADMGA 在 75% 的测试用例中显著优于 nAMGGA，尤其在高阶和高移位问题中表现突出。