State-of-the-Art Reviews of Meta-Heuristic Algorithms with Their Novel Proposal for Unconstrained Optimization and Applications

• Published in: Archives of computational methods in engineering 2021-08, Vol.28 (5), p.4049-4115
• Main Authors: Parouha, Raghav Prasad, Verma, Pooja
• Format: Article
• Language: English
• Subjects: Algorithms; Convergence; Engineering; Evolutionary computation; Heuristic methods; Mathematical analysis; Mathematical and Computational Engineering; Mutation; Optimization; Original Paper; Particle swarm optimization; Solution space; State-of-the-art reviews; Statistical analysis
• ISSN: 1134-3060; 1886-1784
• DOI: 10.1007/s11831-021-09532-7

A widespread survey of numerous traditional meta-heuristic algorithms has been investigated category wise in this paper. Where, particle swarm optimization (PSO) and differential evolution (DE) is found to be an efficient and powerful optimization algorithm. Therefore, an extensive survey of recent-past PSO and DE variants with their hybrids has been inspected again. After this a novel PSO (called, nPSO) and DE (namely, nDE) with their innovative hybrid (termed as, i h PSODE) is proposed in this paper for unconstrained optimization problems. In nPSO introducing a new linearly decreased inertia weight and gradually decreased and/or increased acceleration coefficient as well a different position update equation (by introducing a non-linear decreasing factor. And in nDE a new mutation strategy and crossover rate are introduced. In view of that, convergence characteristic of nPSO and nDE provides different approximation to the solution space. Further, instead of naïve way proposed hybrid i h PSODE integrating merits of nPSO and nDE. In i h PSODE after initialization and calculation identify best half member and discard rest of members from the population. In current population apply nPSO to maintain exploration and exploitation. Then to enhance local search ability and improve convergence accuracy applies nDE. Hence, proposed i h PSODE has higher probability of avoiding local optima and it is likely to find global optima more quickly due to relating superior capability of the anticipated nPSO and nDE. Performance of the proposed hybrid i h PSODE as well as its anticipated integrating component nPSO and nDE are verified on 23 basic, 30 CEC 2014 and 30 CEC 2017 unconstrained benchmark functions plus 3 real world problems. The several numerical, statistical and graphical as well as comparative analyses over many state-of-the-art algorithms confirm superiority of the proposed algorithms. Finally, based on overall performance i h PSODE is recommended for unconstrained optimization problems in this present study.