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Many real-life problems can be formulated as numerical optimization problems. Such problems pose a challenge for researchers when designing efficient techniques that are capable of finding the desired solution without suffering from premature convergence. This paper proposes a novel evolutionary algorithm that blends the exploitative and explorative merits of two main evolutionary algorithms, namely the Stochastic Fractal Search (SFS) and a Differential Evolution (DE) variant. This amalgam has an effective interaction and cooperation of an ensemble of diverse strategies to derive a single framework called Iterative Cyclic Tri-strategy with adaptive Differential Stochastic Fractal Evolutionary Algorithm (Ic3-aDSF-EA). The component algorithms cooperate and compete to enhance the quality of the generated solutions and complement each other. The iterative cycles in the proposed algorithm consist of three consecutive phases. The main idea behind the cyclic nature of Ic3-aDSF-EA is to gradually emphasize the work of the best-performing algorithm without ignoring the effects of the other inferior algorithm during the search process. The cooperation of component algorithms takes place at the end of each cycle for information sharing and the quality of solutions for the next cycle. The algorithm's performance is evaluated on 43 problems from three different benchmark suites. The paper also investigates the application to a set of real-life problems. The overall results show that the proposed Ic3-aDSF-EA has a propitious performance and a reliable scalability behavior compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• A many objective evolutionary algorithm based on decomposition and moth search is proposed. • Random and adaptive weights is used to break the limitation of uniform distribution weights. • Mutual evaluation value is used to evaluate the optimal individual in the neighborhood. • Improving scale factor α in MSA is to improve the performance of the proposed algorithm. Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs. [ABSTRACT FROM AUTHOR]