An Enhanced Ant Colony System for Solving Vehicle Routing Problem with Time Window

Abstract

Vehicle Routing Problem with Time Window (VRPTW), an extension of VRP, is a complex combinatorial problem having many real life applications. It can be described as the problem of minimizing the total route cost while satisfying the capacity and time window constraint. Ant Colony System (ACS) is a meta heuristic that is often applied to solve VRPTW. In this paper an attempt has been made to enhance the already existing ant colony system to solve the problem efficiently. Experimentation with the Solomon data sheet is performed and compared with best known results available in literature.

Modified ant colony optimization with selecting and elimination customer and re-initialization for VRPTW

“…The result from ( 11) is use to select a path that is shorter and has a greater amount of pheromone. After the customer selection of ant process is completed, the fitness of each ant is used to update pheromones and the fitness of the ant is calculated in (12).…”

“…Where ∆τ ij k (t) is the amount of pheromones left by an ant on a route that it is calculated in (12); Q is a consistent value; k representing the k th ant in the colony; Lk is the fitness of ant k; ij(t) denotes the total amount of pheromones that ants use the route between customers i and j have left; m is the amount of ant population;  is the coefficient of evaporation which receives a value between [0-1]. The next step is to repeat this process until the stop condition is reached.…”

A Comprehensive Study of Vehicle Routing Problem With Time Windows Using Ant Colony Optimization Techniques

“…Bansal et al [36] presented an Enhanced ACS for solving VRPTW. To prevent premature convergence and obtain a high-quality solution, the upper and lower bounds were considered for pheromone update.…”