In the past decades, various attention has been paid to the global optimization problems. The Monarch Butterfly Optimization (MBO) algorithm is an effective meta-heuristic algorithm for the global optimization problems. However, in the MBO, the diversity of the population is lost in the late iteration. The MBO is easy to trap into the local optima. In this study, an algorithm based on MBO with learning mechanism and topological structure, named LTMBO, is proposed to enhance the ability of exploration and exploitation on the global optimization problems. The learning mechanism is present for the migration operator to increase the speed of the iteration. The topological structure is proposed for the butterfly adjusting operator to improve the diversity of the population. The experimental results demonstrated that the efficiency and significance of the proposed LTMBO algorithm.

A new metaheuristic algorithm, named surrogate-guided algorithm(S-Jaya), is proposed to solve the single objective continuous optimization problems in this paper. A novel mutation strategy for the non-separable single objective continuous optimization problems is introduced to alter the search engine of the Jaya algorithm. The surrogate is embedded to accelerate the convergence of the population and avoid the proposed algorithm falling into the local optimal during the evolutionary process. The suggested S-Jaya algorithm to address the CEC 2017 benchmark problems is effective and validated. On the quality of solution and execution time, the experimental results reveal that the effectiveness of the S-Jaya algorithm is superior compare with the Jaya algorithm and its variants.

Backtracking search algorithm (BSA) has been applied to solve the various optimization problems in recent years. However, BSA is difficult to solve non-separable problems due to its single search mechanism. In this paper, backtracking search algorithm based on knowledge of different populations, named DKBSA, is proposed to solve continuous optimization problems. In DKBSA, sub-population partitioning method is used to enhance the local search ability and alleviate the loss rate of the diversity of population. Afterwards, a mutation strategy with knowledge guidance and rotation invariance, which is based on the current sub-population information and historical information, is designed to improve the convergence speed of the DKBSA. Furthermore, a control parameter of adaptive search factor is embedded in the mutation strategy to balance the exploitation and exploration of the proposed algorithm. Finally, a probabilistic model-based strategy is proposed to generate dominant individuals to further improve the search ability of the proposed algorithm. The experimental results of the state-of-the-art algorithms in the CEC2017 benchmark test suit reveal that the DKBSA is effective for solving non-separable problems.

Water Wave Optimisation algorithm (WWO) is a new swarm-based metaheuristic inspired by shallow wave models for global optimisation. In this paper, an enhanced WWO, which combines with multiple assistant strategies (EWWO), is proposed. First, the random opposition-based learning (ROBL) mechanism is introduced to generate the initial population with high quality. Second, a new modified operation is designed and embedded into propagation operation to balance the global exploration and the local exploitation. Third, the covariance matrix self-adaptation evolution strategy (CMA-ES) is employed by the refraction operation to further strengthen the local exploitation. Furthermore, the diversity of the population is maintained in the evolution process by using a crossover operator. The experiment results based on CEC 2017 benchmarks indicate that the EWWO outperforms the state-of-the-art variant algorithms of the WWO and the standard WWO.

Multi-objective evolutionary algorithms usually utilize fixed evolutionary mechanism and the evolutionary operators are static during the process of algorithm evolution. It is easy to cause a simple population structure, unable to exploit the search space fully and trapped in local optimal solution. In this paper, a novel method named Pareto Archive Evolution Strategy (PAES) with adaptive grid strategy (AGS_PAES) which only makes one mutation to create one new solution and use an “archive” which are called Non-Dominated Archive to store the best solution, is introduced. This procedure is completed by a special approach - adaptive grid method, which decides the criterion of the solution to be archived and the place of the grid location the solution would be stored. The Pareto front obtained by the procedure outperforms the classical Multi-objective Genetic Algorithm (MOGA). Simulation results on the standard benchmark problems show that the proposed adaptive scheme has a better convergence and diversity compared with the second generation classical multi-objective evolutionary algorithms.

NSGA-II is a well known, fast sorting and elite multi-objective genetic algorithm. The local exploitation ability of NSGA-II is relatively limited by the parameters of crossover and mutation. DE has shown powerful search abilities for continuous optimization. In this paper, an enhanced NSGA-II based on differential evolution and L-near distance (DP-NSGA-II/EDA) is proposed. To improve the diversity and convergence of Pareto optimal solutions by NSGA-II algorithm, DP-NSGA-II/EDA produces two populations by different approaches. One is from NSGA-II itself, the other is from differential evolution (DE). Through the competition between two populations, the superior individuals will be selected to construct new offspring population. Meanwhile, a new distance strategy called L-near distance is introduced to NSGA-II to maintain the diversity of the population. To validate the proposed algorithm, it is compared with the original NSGA-II, SPEA2 and MOEA/D-DE through several numerical benchmark problems. Results show the effectiveness of the proposed approach.