High-dimensional optimization has numerous potential applications in both academia and industry. It is a major challenge for optimization algorithms to generate very accurate solutions in high-dimensional search spaces. However, traditional search tools are prone to dimensional catastrophes and local optima, thus failing to provide high-precision results. To solve these problems, a novel hermit crab optimization algorithm (the HCOA) is introduced in this paper. Inspired by the group behaviour of hermit crabs, the HCOA combines the optimal search and historical path search to balance the depth and breadth searches. In the experimental section of the paper, the HCOA competes with 5 well-known metaheuristic algorithms in the CEC2017 benchmark functions, which contain 29 functions, with 23 of these ranking first. The state of work BPSO-CM is also chosen to compare with the HCOA, and the competition shows that the HCOA has a better performance in the 100-dimensional test of the CEC2017 benchmark functions. All the experimental results demonstrate that the HCOA presents highly accurate and robust results for high-dimensional optimization problems.
The offspring selection strategy is the core of evolutionary algorithms, which directly affects the method's accuracy. Normally, to improve the search accuracy in local areas, the population converges quickly around the optimal individual. However, excessive aggregation can narrow the search range of the population, and thus the population may be trapped by local optima. To overcome this problem, a bare-bones particle swarm optimization with crossed memory (BPSO-CM) is proposed in this work. The BPSO-CM contains a multi-memory storage mechanism (MSM) and an elite offspring selection strategy (EOSS). The MSM enables an extra storage space to extend the search ability of the particle swarm and the EOSS enhances the local minimum escaping ability of the particle swarm. The population is endowed with the ability of enhanced global search through the cooperation of the MSM and the EOSS. To verify the performance of the BPSO-CM, the CEC2017 benchmark functions are used in experiments, five population-based methods are selected in the control group. Finally, experimental results proved that the BPSO-CM can present highly accurate results for global optimization problems.
The minimax problem in continuous high-dimensional spaces has been a challenge in optimization. Traditional optimization algorithms cannot balance well between depth search and breadth search in high dimensional search spaces. A new hermit crab optimization algorithm (HCOA) is introduced in this paper to address these problems. Inspired by the population behavior of hermit crabs, the hermit crab optimization algorithm introduces the optimal crab memory and the backtracking search around the memory. Compared with other metaheuristic algorithms, the hermit crab optimization algorithm does not require advanced training or parameter correction and thus can be more quickly employed for different optimization problems. To explore the capabilities of HCOA, the simulation experiment selected CEC2017 as the test function and five well-known optimization algorithms as the control group. Among the 29 benchmark features in the CEC2017, HCAO ranks first in the number of features with 23, and second, third and fifth with two each. Experimental results demonstrate that HCOA present highly accurate and robust results for high-dimensional optimization problems.
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