Volleyball premier league (VPL) simulating some phenomena of volleyball game has been presented recently. This powerful algorithm uses such racing and interplays between teams within a season. Furthermore, the algorithm imitates the coaching procedure within a game. Therefore, some volleyball metaphors, including substitution, coaching, and learning, are used to find a better solution prepared by the VPL algorithm. However, the learning phase has the largest effect on the performance of the VPL algorithm, in which this phase can lead to making the VPL stuck in optimal local solution. Therefore, this paper proposed a modified VPL using sine cosine algorithm (SCA). In which the SCA operators have been applied in the learning phase to obtain a more accurate solution. So, we have used SCA operators in VPL to grasp their advantages resulting in a more efficient approach for finding the optimal solution of the optimization problem and avoid the limitations of the traditional VPL algorithm. The propounded VPLSCA algorithm is tested on the 25 functions. The results captured by the VPLSCA have been compared with other metaheuristic algorithms such as cuckoo search, social-spider optimization algorithm, ant lion optimizer, grey wolf optimizer, salp swarm algorithm, whale optimization algorithm, moth flame optimization, artificial bee colony, SCA, and VPL. Furthermore, the three typical optimization problems in the field of designing engineering have been solved using the VPLSCA. According to the obtained results, the proposed algorithm shows very reasonable and promising results compared to others.
相似文献Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms.
相似文献