Jaya algorithm based new approaches for solving discrete optimization problems

Jaya algorithm is a stochastic population-based heuristic optimization algorithm proposed by Rao (2016) for solving constrained and unconstrained continuous optimization problems. In this study, Jaya algorithm based new approaches have been proposed for solving binary and discrete integer optimization problems. Because of the basic Jaya algorithm proposed for solving continuous optimization problems, it cannot be directly applied to binary optimization problems, because the solution space is discretely structured for this type of optimization problems and the decision variables of the binary optimization problems can be element of set [0,1]. In this context, some modifications have been made in update mechanism of the basic Jaya algorithm, and Jaya algorithm based new approaches have been proposed for solving binary optimization problems. The first proposed approach is JayaX; It is based on Jaya algorithm and the 'exclusive or' (XOR) logic function. The second approach is proposed in order to improve the local search capability of the JayaX algorithm, and it is called JayaX-LSM. JayaX-LSM is based on JayaX algorithm and local search module (LSM). For the performance analysis of the proposed algorithms to solve binary optimization problems, in the experimental phase: Uncapacitated facility location problem (UFLP), CEC 2015 numerical functions and wind turbine placement problem are used. The first experimental analysis is made for UFLP problems. In order to examine and approve the performance of the proposed algorithms, 15 different UFLPs are used in the experiments. The proposed algorithms have been compared with the state-of-art binary optimization algorithms based on PSO, ABC, TSA, DE and GA which have been recently proposed into the literature. According to the experimental results, the proposed algorithms obtained equal or better performance than the compared algorithms in solving UFLP. The second experimental analysis is performed on the CEC 2015 numerical benchmark set consisting of 15 problems. In this analysis, the JayaX-LSM algorithm is compared with the experimental results of the SabDE, BQIGSA, GBABC, BHTPSO-QI, BLDE and SBHS algorithms, and considering the experiments, the JayaX-LSM algorithm obtained competitive or better solutions with the compared algorithms. The last experimental analysis in this section is made for the wind turbine placement problem. Two different grid structures, 10×10 and 20×20 are used in the experiments. According to the experimental results, the JayaX-LSM algorithm get equal or better solutions than GA-based binary methods, BIWO, BPSO-TVAC, EA, NGHS, DGHS and binAAA algorithms used in comparisons. Another proposed method is a Jaya based discrete algorithm called as DJaya for the solution of discrete integer optimization problems. Swap, shift and symmetry transformation operators are being used for discretization process of the update mechanism of basic Jaya. While creating the initial population in DJaya, (N-1) candidate solution is created by random permutation, and one candidate solution is created with the nearest neighbor tour heuristic. Furthermore, 2-opt local search algorithm has been used for improve the quality of solutions in DJaya. In order to examine and confirm the performance of the proposed algorithms, 14 different travelling salesman problems (TSP) are used in the experiments. The proposed algorithm has been compared with the state-of-art optimization algorithms. According to the experimental result, the DJaya algorithm has obtained better or competitive solutions than the compared algorithms for solving the traveling salesman problem.