TSP-based VRP Solution with Capacity Constraints Using Tabu Search Algorithm

This study presents a computational solution for the Capacity-Constrained Vehicle Routing Problem (CVRP) using the Tabu Search Algorithm. The VRP represents a fundamental logistics optimization challenge requiring determination of optimal routing paths for multiple vehicles serving geographically dispersed customers. Our implementation leverages Tabu Search as a metaheuristic optimization technique, particularly effective for complex combinatorial problems like VRP.

The Tabu Search Algorithm operates through iterative solution refinement, where each iteration generates neighbor solutions by applying specific moves (e.g., 2-opt swaps or customer reassignments). To prevent cyclic behavior and local optima entrapment, the algorithm maintains a short-term memory structure called the Tabu List, which temporarily prohibits recently applied moves. The implementation typically includes aspiration criteria to override tabu status when superior solutions are discovered.

Our methodology integrates capacity constraints directly into the solution evaluation function. Each vehicle route's total demand must not exceed the vehicle's capacity, validated through cumulative load checks during route construction. The objective function combines distance minimization with penalty terms for capacity violations, implemented as: fitness = total_distance + α × overload_penalty. The Tabu Search process explores feasible and marginally infeasible solutions to navigate the constrained search space effectively.

The algorithmic implementation features key components: initial solution generation via savings algorithm, neighborhood structure using customer swap and relocation operators, and adaptive tabu tenure management. Computational experiments demonstrate that this Tabu Search implementation consistently produces high-quality solutions for medium-to-large scale VRP instances with capacity restrictions.

In conclusion, our Tabu Search-based approach for Capacity-Constrained VRP provides a robust framework for logistics optimization. The method's flexibility allows for extensions including time windows and heterogeneous fleets, presenting significant potential for enhancing real-world supply chain operations.