The Problem of Premature Convergence in Engineering Optimization Problems

Optimization is a complex problem in mathematics and engineering applications, which has so far been solved using a variety of approaches based on heuristic methods, methods inspired by nature, methods based on the principles of fuzzy logic, and methods based on rigorous mathematical tools. The most important task is to combine various methods of modeling, optimization, design and management of complex systems within the framework of an integrated approach for a holistic description of the phenomena under study. The objective function of optimization problems combines continuous and discrete variables and various constraints, which indicates its complexity, as well as difficulties in solving such problems. Algorithms that are used in solving optimization problems may suffer from premature convergence when they stop at the optimal solution earlier than required. Based on the problem of premature convergence, a hybrid approach combining a sine–cosine algorithm (SCA) and an artificial bee colony algorithm (ABC) was proposed in the paper. In the proposed algorithm, called the hybrid sine–cosine algorithm (HSCA), both algorithms are executed alternately until the convergence criterion is satisfied.