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This paper appends three proposed heuristic algorithms, viz. Initialization Algorithm, Fraction Repair Algorithm and Negative Repair Algorithm, to Particle Swarm Optimization (PSO) and extends its application to Pure Integer Linear Solid Transportation Problem (STP). The chief contribution of the paper is that the proposed Hybrid Particle Swarm Optimization (HPSO) algorithm discretizes the continuous search space of PSO so that it can operate in the discrete solution space of STP with any of the valid parameter settings. The Initialization Algorithm is developed to generate the sufficient number of random solutions for initiating HPSO with a diverse population of given size. Whereas Fraction Repair and Negative Repair Algorithms are developed to ensure that each successive population obtained with HPSO remains in the solution space of STP. The validity of HPSO is examined and illustrated by solving a numerical problem with certain parameter settings. Further, the HPSO demonstrates its ability to obtain an optimal or near optimal solution along with the alternate optimal solution, if it exists. It searches for the solutions even without adhering to the rigid conditions of traditional methods that every solution of STP must have a fixed number of non-zero decision variables. Moreover, the performance of HPSO is tested with three different parameter settings and compared amongst each other to analyze their significance in solving the problem. The performance of HPSO and the variants of parameters are statistically validated through an extensive experimental design. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic strategy-based quadratic opposition-based learning adaptive variable-speed whale optimization algorithm is proposed. The improved algorithm is used to solve the problems that the whale optimization algorithm's convergence accuracy and convergence speed are insufficient. Firstly, the proposed algorithm is initialized by a method based on chaotic maps and quadratic opposition-based learning strategy to obtain a population with better ergodicity. Secondly, by introducing an adaptive variable speed adjustment factor, each search link unites to form a negative feedback regulation network, thereby effectively balancing the algorithm's exploration ability and exploitation ability. Finally, 20 benchmark test functions and 3 complex constrained engineering optimization problems were used to conduct extensive tests on the improved algorithm. The results show that the improved algorithm has better performance than others in terms of convergence speed and convergence accuracy in a majority of cases, and can effectively jump out of the local optimum. [Display omitted] • Firstly, this paper proposed a quadratic Opposition-Base Learning strategy based on Bernoulli map, and successfully obtained a higher quality initial whale population. • Secondly, this paper proposed a new variable speed adjustment factor and a cooperative convergence factor, and combine them with individual fitness to form a negative feedback adjustment network. Experiments show that the algorithm has good self-adjusting ability. • Finally, the range of some of the original random numbers in whale optimization algorithm has been changed. This adjustment allows the algorithm to have a more variable search range. [ABSTRACT FROM AUTHOR]