A Multi-Objective Sine Cosine Algorithm Based on a Competitive Mechanism and Its Application in Engineering Design Problems

There are a lot of multi-objective optimization problems (MOPs) in the real world, and many multi-objective evolutionary algorithms (MOEAs) have been presented to solve MOPs. However, obtaining non-dominated solutions that trade off convergence and diversity remains a major challenge for a MOEA. To solve this problem, this paper designs an efficient multi-objective sine cosine algorithm based on a competitive mechanism (CMOSCA). In the CMOSCA, the ranking relies on non-dominated sorting, and the crowding distance rank is utilized to choose the outstanding agents, which are employed to guide the evolution of the SCA. Furthermore, a competitive mechanism stemming from the shift-based density estimation approach is adopted to devise a new position updating operator for creating offspring agents. In each competition, two agents are randomly selected from the outstanding agents, and the winner of the competition is integrated into the position update scheme of the SCA. The performance of our proposed CMOSCA was first verified on three benchmark suites (i.e., DTLZ, WFG, and ZDT) with diversity characteristics and compared with several MOEAs. The experimental results indicated that the CMOSCA can obtain a Pareto-optimal front with better convergence and diversity. Finally, the CMOSCA was applied to deal with several engineering design problems taken from the literature, and the statistical results demonstrated that the CMOSCA is an efficient and effective approach for engineering design problems.

Multi-Level Image Thresholding Based on Modified Spherical Search Optimizer and Fuzzy Entropy

Multi-level thresholding is one of the effective segmentation methods that have been applied in many applications. Traditional methods face challenges in determining the suitable threshold values; therefore, metaheuristic (MH) methods have been adopted to solve these challenges. In general, MH methods had been proposed by simulating natural behaviors of swarm ecosystems, such as birds, animals, and others. The current study proposes an alternative multi-level thresholding method based on a new MH method, a modified spherical search optimizer (SSO). This was performed by using the operators of the sine cosine algorithm (SCA) to enhance the exploitation ability of the SSO. Moreover, Fuzzy entropy is applied as the main fitness function to evaluate the quality of each solution inside the population of the proposed SSOSCA since Fuzzy entropy has established its performance in literature. Several images from the well-known Berkeley dataset were used to test and evaluate the proposed method. The evaluation outcomes approved that SSOSCA showed better performance than several existing methods according to different image segmentation measures.