Retaining feasibility conditions to solve Time Minimization Transportation Problem using modified Particle Swarm Optimization Algorithm

The Time Minimization Transportation Problems (TMTP) is a critical variant of transportation problem that deal with urgent/earliest supply of goods or services to the destinations. The required source-destination solution pairs have been found with the exact or the analytical methods. However, the dimension increased, the problems become NP Hard and need to be solved using alternative techniques. In this expedition, met heuristic techniques came into force such as Particle Swarm Optimization (PSO) algorithm which has utilized to address a wide range of real life optimization problems (mostly continuous). But PSO has been encapsulated, with different encoding and decoding techniques, to deal with the discrete problems as well. In this paper, the authors propose two modules of amending the negative and the fractional allocations incorporated within the iterations of basic PSO. These modules convert the infeasible solutions that arise because of parameters in PSO, into the feasible ones. The proposed technique has been found to be a good alternative for logistic decisions as compared with existing techniques while tested on different test problems. The extensive search capability of proposed PSO has ascertained in terms of alternate optimal solutions irrespective of the count of allocations (m + n - 1) and independent position of allocated cells within intermediate or global optimal solution. This performance substantiate the scope of Particle Swarm Optimization for discrete combinatorial optimization problems.