[Paper Review] A hybrid adaptive Iterated Local Search with diversification control to the Capacitated Vehicle Routing Problem

Vinícius R. Máximo, Mariá C. V. Nascimento|arXiv (Cornell University)|Dec 20, 2020

Vehicle Routing Optimization Methods49 references61 citations

TL;DR

This paper proposes AILS-PR, a novel adaptive Iterated Local Search hybridized with Path-Relinking for the Capacitated Vehicle Routing Problem (CVRP). It introduces an automatic diversity control mechanism that adaptively adjusts perturbation intensity and solution acceptance criteria based on historical search dynamics, significantly improving performance. AILS-PR outperforms state-of-the-art metaheuristics on 100 benchmark CVRP instances, achieving the lowest mean gaps in 93% of cases.

ABSTRACT

Metaheuristics are widely employed to solve hard optimization problems, like vehicle routing problems (VRP), for which exact solution methods are impractical. In particular, local search-based metaheuristics have been successfully applied to the capacitated VRP (CVRP). The CVRP aims at defining the minimum-cost delivery routes for a given set of identical vehicles since each vehicle only travels one route and there is a single (central) depot. The best metaheuristics to the CVRP avoid getting stuck in local optima by embedding specific hill-climbing mechanisms such as diversification strategies into the solution methods. This paper introduces a hybridization of a novel adaptive version of Iterated Local Search with Path-Relinking (AILS-PR) to the CVRP. The major contribution of this paper is an automatic mechanism to control the diversity step of the metaheuristic to allow it to escape from local optima. The results of experiments with 100 benchmark CVPR instances show that AILS-PR outperformed the state-of-the-art CVRP metaheuristics.

Motivation & Objective

• To address the challenge of local optima stagnation in metaheuristics for the CVRP by improving diversification control.
• To develop an adaptive mechanism that dynamically adjusts perturbation intensity and solution acceptance criteria during search.
• To enhance the performance of Iterated Local Search (ILS) for CVRP through hybridization with Path-Relinking (PR).
• To outperform existing state-of-the-art heuristic methods on standard CVRP benchmark instances.

Proposed method

• Proposes an adaptive ILS (AILS) that guides perturbation intensity based on the distance between reference solutions and locally improved solutions from prior iterations.
• Introduces a dynamic acceptance criterion that uses real-time flow of accepted solutions to estimate a threshold for neighborhood exploration.
• Hybridizes AILS with Path-Relinking (PR) to explore high-quality paths between elite solutions, enhancing local search intensification.
• Employs 10 prioritized criteria in PR, with state-based priority values ranging from -2 to +2, to guide move selection during path reconstruction.
• Uses a multi-criteria state transition system to evaluate moves between solutions, with states defined by feasibility and route structure changes.
• Applies adaptive control to balance exploration (diversification) and exploitation (intensification) throughout the search process.

Experimental results

Research questions

• RQ1 How can perturbation intensity in ILS be adaptively controlled to improve escape from local optima in CVRP?
• RQ2 What is the impact of dynamically adjusting the solution acceptance criterion on search performance in CVRP metaheuristics?
• RQ3 Can a hybrid AILS-PR approach outperform existing state-of-the-art CVRP metaheuristics on large-scale benchmark instances?
• RQ4 How does the integration of adaptive diversification with Path-Relinking affect convergence and solution quality in CVRP?

Key findings

• AILS-PR achieved the lowest mean gap in 93% of the 100 benchmark CVRP instances tested, outperforming UHGS, ILS-SP, and SISRs.
• For the CMT and Golden benchmark sets, AILS-PR matched or improved upon the best-known solutions (BKS) in all instances, with 100% of best solutions found.
• On average, AILS-PR achieved a mean gap of 0.0000% on CMT1, CMT2, CMT3, and CMT12, indicating optimal performance.
• AILS-PR found the best solution in 50 runs for all instances, with the fastest average time-to-best in 13 out of 18 instances compared to ILS-SP and SISRs.
• The algorithm was particularly effective on large instances (500–1000 customers), where SISRs previously outperformed other methods, now being surpassed by AILS-PR.
• In the Golden14 instance, AILS-PR achieved the second-best result, with a mean gap of 0.2064%, while still outperforming others in 17 out of 18 instances.