electromagnetism-like algorithms for the fuzzy fixed charge transportation problem

in this paper, we consider the fuzzy fixed-charge transportation problem (ffctp). both of fixed and transportation cost are fuzzy numbers. contrary to previous works, electromagnetism-like algorithms (em) is firstly proposed in this research area to solve the problem. three types of em; original em, revised em, and hybrid em are firstly employed for the given problem. the latter is being firstly developed and proposed in this paper. another contribution is to present a novel, simple and cost-efficient representation method, named string representation. it is employed for the problem and can be used in any extended transportation problems. it is also adaptable for both discrete and continues combinatorial optimization problems. the employed operators and parameters are calibrated, according to the full factorial and taguchi experimental design. besides, different problem sizes are considered at random to study the impacts of the rise in the problem size on the performance of the algorithms.