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求解带约束优化问题的混合式多策略萤火虫算法

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目前多目标优化算法主要针对如何处理多个目标之间的冲突,对于如何处理约束考虑较少,鉴于此,提出一种求解带约束优化问题的混合式多策略萤火虫算法(HMSFA-PC).首先,提出一种改进的动态罚函数策略对约束优化问题进行预处理,将其转换为非约束优化问题;其次,对萤火虫算法本身进行改进,采用Lévy flights搜索机制有效地增大搜索范围;接着,引入随机扩张因子改进算法吸引模型,使种群突破束缚,有效避免早熟收敛,提出自适应维度重组机制,根据不同迭代时期选择差异性较大的个体进行信息交互、相互学习.为检验算法处理无约束优化问题的性能,将其在基准测试函数上与部分典型算法进行比较;为检验算法处理约束优化问题的性能,将其在实际约束测试问题中与一些顶尖约束求解算法进行比较.结果表明,HMSFA-PC在处理无约束优化问题时具有收敛速度快、收敛精度高等优势,并且在动态罚函数的协作下求解实际约束优化问题时仍具有良好的优化性能.
Hybrid multi-strategy firefly algorithm for solving optimization problems with constraints
We propose a hybrid multi-strategy firefly algorithm(HMSFA-PC)for solving constrained optimization problems.Firstly,an improved dynamic penalty function strategy is proposed to preprocess the constrained optimization problem so as to convert it into an unconstrained optimization problem.Secondly,the firefly algorithm itself is improved:the Lévy flights search mechanism is adopted to effectively increase the search range;a random expansion factor is introduced to improve the attraction model of the algorithm so that the population breaks through the constraint,effectively avoiding premature convergence and maintaining the population convergence;an adaptive dimensional reorganization mechanism is proposed to maintain the population convergence.The adaptive dimensional reorganization mechanism is proposed to select individuals with greater variability according to different iteration periods to interact with information and learn from each other,effectively improving the diversity of the population.To test the performance of the algorithm in dealing with unconstrained optimization problems,it is compared with some typical algorithms on the benchmark test function;to test the performance of the algorithm to deal with constrained optimization problems,it is compared with some top constraint solving algorithms on actual constraint test problems.The results show that the HMSFA-PC has the advantages of fast convergence and high convergence accuracy when dealing with unconstrained optimization problems,and still has good optimization performance when solving real constrained optimization problems with the collaboration of dynamic penalty functions.

firefly algorithmconstrained multi-objective optimizationdynamic penalty function methodLévy flightsstochastic expansion factoradaptive dimensional reorganization

吕莉、潘宁康、肖人彬、王晖、谭德坤

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南昌工程学院信息工程学院,南昌 330099

华中科技大学人工智能与自动化学院,武汉 430074

萤火虫算法 约束多目标优化 动态罚函数法 Lévy flights 随机扩张因子 自适应维度重组

科技创新2030-"新一代人工智能"重大项目国家自然科学基金项目

2018AAA010120062066030

2024

10.13195/j.kzyjc.2023.0051

控制与决策
东北大学

控制与决策

CSTPCD北大核心
影响因子：1.227
ISSN：1001-0920
年,卷(期)：2024.39(8)