Simulated Annealing for Capacitated Vehicle Routing Problem (CVRP)

Application of Simulated Annealing Algorithm in Capacitated Vehicle Routing Problem

The Capacitated Vehicle Routing Problem (CVRP) represents a classic combinatorial optimization challenge, aiming to design optimal delivery routes for a fleet of vehicles with fixed capacities while satisfying customer demands and minimizing total transportation costs. Simulated annealing, as an optimization technique inspired by metal annealing processes, effectively handles the complex search space of such NP-hard problems.

The core challenge lies in balancing the conflict between route length optimization and capacity constraints. Simulated annealing addresses this through temperature parameters and probabilistic acceptance mechanisms for inferior solutions: extensively exploring the solution space during high-temperature phases, then gradually converging to high-quality solutions as temperature decreases. For CVRP-specific implementation, three key components require focused attention:

Solution representation typically employs customer sequence encoding, requiring a split algorithm implementation to partition sequences into feasible routes satisfying capacity constraints Neighborhood operations recommended include 2-opt exchanges and customer relocation strategies, ensuring perturbed solutions maintain capacity feasibility Cooling schedules need customization based on problem scale, typically implementing exponential cooling with multiple reheat cycles

The method's advantage lies in handling complex constraints while maintaining low sensitivity to initial solutions. Practical applications often combine with local search techniques for fine-tuning during later annealing stages. Industrial extensions may incorporate real-world constraints like time windows and multiple vehicle types, requiring more sophisticated energy function design and constraint handling mechanisms in the code implementation.