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A Multi-population Integrated Approach for Capacitated Location Routing

Pengfei He, Jin-Kao Hao, Qinghua Wu

TL;DR

The paper addresses the capacitated location-routing problem by introducing HGAMP, a multi-population integrated framework that jointly optimizes depot configurations and routing. It combines a novel multi-depot edge assembly crossover (mdEAX), a coverage ratio heuristic (CRH) for depot construction, and robust local search with feasibility restoration and mutation, organized into multiple subpopulations by depot configuration. Empirical results on 281 benchmark instances show substantial improvements, including 101 new best-known upper bounds and 84 matches, with particularly strong performance on a large, diverse set. The framework is generalizable to related location-routing problems and the authors provide public code and extensive ablation studies to illustrate the contributions of its components.

Abstract

The capacitated location-routing problem involves determining the depots from a set of candidate capacitated depot locations and finding the required routes from the selected depots to serve a set of customers whereas minimizing a cost function that includes the cost of opening the chosen depots, the fixed utilization cost per vehicle used, and the total cost (distance) of the routes. This paper presents a multi-population integrated framework in which a multi-depot edge assembly crossover generates promising offspring solutions from the perspective of both depot location and route edge assembly. The method includes an effective neighborhood-based local search, a feasibility-restoring procedure and a diversification-oriented mutation. Of particular interest is the multi-population scheme which organizes the population into multiple subpopulations based on depot configurations. Extensive experiments on 281 benchmark instances from the literature show that the algorithm performs remarkably well, by improving 101 best-known results (new upper bounds) and matching 84 best-known results. Additional experiments are presented to gain insight into the role of the key elements of the algorithm.

A Multi-population Integrated Approach for Capacitated Location Routing

TL;DR

The paper addresses the capacitated location-routing problem by introducing HGAMP, a multi-population integrated framework that jointly optimizes depot configurations and routing. It combines a novel multi-depot edge assembly crossover (mdEAX), a coverage ratio heuristic (CRH) for depot construction, and robust local search with feasibility restoration and mutation, organized into multiple subpopulations by depot configuration. Empirical results on 281 benchmark instances show substantial improvements, including 101 new best-known upper bounds and 84 matches, with particularly strong performance on a large, diverse set. The framework is generalizable to related location-routing problems and the authors provide public code and extensive ablation studies to illustrate the contributions of its components.

Abstract

The capacitated location-routing problem involves determining the depots from a set of candidate capacitated depot locations and finding the required routes from the selected depots to serve a set of customers whereas minimizing a cost function that includes the cost of opening the chosen depots, the fixed utilization cost per vehicle used, and the total cost (distance) of the routes. This paper presents a multi-population integrated framework in which a multi-depot edge assembly crossover generates promising offspring solutions from the perspective of both depot location and route edge assembly. The method includes an effective neighborhood-based local search, a feasibility-restoring procedure and a diversification-oriented mutation. Of particular interest is the multi-population scheme which organizes the population into multiple subpopulations based on depot configurations. Extensive experiments on 281 benchmark instances from the literature show that the algorithm performs remarkably well, by improving 101 best-known results (new upper bounds) and matching 84 best-known results. Additional experiments are presented to gain insight into the role of the key elements of the algorithm.
Paper Structure (30 sections, 1 equation, 6 figures, 11 tables, 4 algorithms)

This paper contains 30 sections, 1 equation, 6 figures, 11 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Hierarchical approach
  4. Integrated approach
  5. General approach of HGAMP
  6. Construction engine
  7. Optimization engine
  8. Population initialization
  9. Multi-depot edge assembly crossover
  10. Restore the feasibility of offspring individuals
  11. Mutation
  12. Local search
  13. Population management
  14. Discussion
  15. Experimental Evaluation and Comparisons
  16. ...and 15 more sections

Figures (6)

  • Figure 1: Flow chart of HGAMP for the CLRP.
  • Figure 2: Illustration of the mdEAX crossover for the CLRP
  • Figure 3: CLRP performance comparison over the two classical sets with unknown optima.
  • Figure 4: Performance chart of the CLRP on new set $\mathbb{S}$.
  • Figure 5: Performance chart of the CLRP on set $\mathbb{S}$.
  • ...and 1 more figures