ABSTRACT

Any evolutionary algorithm tends to end up in a local optimum. A new approach based on an evolutionary algorithm named as Diversity Driven Multi-Parent Evolutionary Algorithm with Adaptive non-uniform mutation is presented. In the proposed algorithm, Non-uniform mutation is used to maintain diversity in the explored solutions. Fitness variance, which signifies solution space aggregation, is used to detect the premature convergence of the population to a local optimum. The term multi-parent is used in the context of more than two parents participating in crossover operation. After multi-parent selection for cross-over to generate new solutions, the non-uniform adaptive mutation is performed, which in turn is triggered by the diminishing value of fitness variance of candidate solutions and pushes solutions out of local optimum. Hence, it can be said that the algorithm is driven by the diversity of the population and overcomes the tendency of evolutionary algorithms to stuck in local optimum. The performance of this algorithm is tested on 23 basic benchmarks, CEC05 functions, and CEC17 functions. As CEC17 benchmark functions include constraint problems, a constraint-handling technique is proposed based on the fuzzy set theory. In the proposed constrained handling strategy, constraint violation is also taken as another objective along with the main objective. The decision to accept or discard the solution is based on the fuzzy set theory. The values of constraint violation and objective function are calculated and fuzzified by calculating membership values by considering the main objective and constraint violation as triangular fuzzy functions. The best solutions are selected based on cardinal priority ranking. The obtained results from the proposed algorithm are compared with the results available in the literature. The result indicates that this algorithm is competitive, even with a smaller number of function evaluations.

摘要

任何进化算法都倾向于以局部最优告终。提出了一种基于进化算法的新方法，称为具有自适应非均匀变异的多样性驱动多亲进化算法。在所提出的算法中，使用非均匀变异来保持探索解决方案的多样性。适应度方差，表示解决方案空间的聚合，用于检测总体到局部最优的过早收敛。术语多亲本用于参与交叉操作的两个以上亲本的上下文。在多父选择交叉生成新解之后，进行非均匀自适应变异，这反过来又由候选解的适应度方差的递减值触发，将解推出局部最优。因此，可以说，该算法受到种群多样性的驱动，克服了进化算法陷入局部最优的倾向。该算法的性能在 23 个基本基准、CEC05 函数和 CEC17 函数上进行了测试。由于CEC17 基准函数包含约束问题，因此提出了基于模糊集理论的约束处理技术。在提出的约束处理策略中，约束违反也被视为与主要目标一起的另一个目标。接受或放弃解决方案的决定基于模糊集理论。通过将主要目标和约束违反视为三角模糊函数，通过计算隶属度值来计算和模糊化约束违反和目标函数的值。根据主要优先级排名选择最佳解决方案。从所提出的算法获得的结果与文献中可用的结果进行了比较。结果表明该算法具有竞争力，即使函数评估数量较少。