Particle Swarm Optimization (PSO) has emulated the social behaviour of some animals such as a flock of birds and a school of fish, searching for food. This communicative sociality when modelled as computational procedure has solved a wide range of complex problems. Over the years, PSO has undergone transformations and numerous variants have come up. In this paper, PSO has been hybridized with two new algorithms to solve the fixed charge transportation problem to minimize the transportation cost (variable and fixed) of delivering goods while satisfying supply/demand constraints. The method considers the reduction of objective function defined by Balinski, Adlakha et al., Yousefi et al. and is incorporated within the PSO. An independent approach of solving the problem on the basis of variable cost initially followed by addition of fixed cost has also been explored. It was observed that proposed PSO works best without reducing the objective function. The simulation results reveal a substantial gain of the proposed method in terms of its efficiency and effectiveness examined on different test problems. To validate the claims, the proposed PSO has also been compared with the solutions attained by other existing methods (either exact or heuristics).

粒子群优化 (PSO) 模拟了一些动物的社会行为，例如一群鸟类和一群鱼寻找食物。当建模为计算程序时，这种交流社会性已经解决了广泛的复杂问题。多年来，PSO 经历了转型，并出现了许多变体。在本文中，PSO 已与两种新算法混合以解决固定费用运输问题，以在满足供需约束的同时最小化交付货物的运输成本（可变和固定）。该方法考虑了由 Balinski、Adlakha 等人、Yousefi 等人定义的目标函数的约简。并被纳入 PSO。还探索了一种独立的方法来解决这个问题，首先是可变成本，然后是固定成本的增加。据观察，提议的 PSO 在不减少目标函数的情况下效果最好。仿真结果表明，所提出的方法在对不同测试问题的效率和有效性方面取得了实质性的进步。为了验证这些主张，还将提出的 PSO 与其他现有方法（精确或启发式）获得的解决方案进行了比较。