Offline learning-based competitive swarm optimizer for non-linear fixed-charge transportation problems

Abstract

The fixed-charge transportation (FCT) problem, an extension of the classical transportation problem, holds significance in practical logistics scenarios where fixed charges play a crucial role. Fixed charges categorize it as an NP-hard problem, posing challenges for conventional methods due to their inefficiency, high computational costs, and susceptibility to local optima. This paper introduces an enhanced evolutionary algorithm, offline learning-based competitive swarm optimization (OLCSO), tailored to address the FCT problems efficiently. OLCSO draws inspiration from offline learning, where particles benefit from the experiences of high performers. The algorithm incorporates (i) a ranking-based mechanism where losers learn from peer-to-peer winners based on their ranks, (ii) a two-phase cooperative evolutionary mechanism enhancing searchability and convergence of the algorithm. In the first phase, losers learn from personal best experiences and the shifted center of the population, boosting diversity. In the second phase, losers learn from winners and the center of the population, improving exploitation, (iii) a mutation strategy is embedded to update winner locations in each evolutionary procedure, and (iv) to ensure a feasible solution to FCT problems, the paper also introduces negative and fractional repair mechanisms. OLCSO is applied to solve two sets of FCT problems, linear and non-linear. Experimental results are compared with various heuristic and metaheuristic techniques, commonly used for these problems, using diverse metrics. A comparative analysis of OLCSO’s design elements is also conducted. The results demonstrate OLCSO’s superiority over existing algorithms.