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A biased random-key genetic algorithm with variable mutants to solve a vehicle routing problem

Paola Festa, Francesca Guerriero, Mauricio G. C. Resende, Edoardo Scalzo

TL;DR

This work introduces BRKGA-VM, a biased random-key genetic algorithm with a variable mutant population, to solve the Vehicle Routing Problem with Occasional Drivers and Time Windows ($VRPODTW$). A dedicated decoder, a permutation-based path-relinking procedure, and a restart strategy with a Variable Neighborhood Descent (VM+L) are integrated to improve solution quality and convergence speed. Computational experiments across multiple instance classes show that BRKGA-VM generally outperforms the prior MP BRKGA variant and often matches or exceeds exact methods on smaller instances, with VM+L delivering stronger results on random-type instances. The findings support the viability of variable mutation and local search hybrids for complex logistics planning problems involving company and occasional drivers in last-mile delivery scenarios.

Abstract

The paper explores the Biased Random-Key Genetic Algorithm (BRKGA) in the domain of logistics and vehicle routing. Specifically, the application of the algorithm is contextualized within the framework of the Vehicle Routing Problem with Occasional Drivers and Time Window (VRPODTW) that represents a critical challenge in contemporary delivery systems. Within this context, BRKGA emerges as an innovative solution approach to optimize routing plans, balancing cost-efficiency with operational constraints. This research introduces a new BRKGA, characterized by a variable mutant population which can vary from generation to generation, named BRKGA-VM. This novel variant was tested to solve a VRPODTW. For this purpose, an innovative specific decoder procedure was proposed and implemented. Furthermore, a hybridization of the algorithm with a Variable Neighborhood Descent (VND) algorithm has also been considered, showing an improvement of problem-solving capabilities. Computational results show a better performances in term of effectiveness over a previous version of BRKGA, denoted as MP. The improved performance of BRKGA-VM is evident from its ability to optimize solutions across a wide range of scenarios, with significant improvements observed for each type of instance considered. The analysis also reveals that VM achieves preset goals more quickly compared to MP, thanks to the increased variability induced in the mutant population which facilitates the exploration of new regions of the solution space. Furthermore, the integration of VND has shown an additional positive impact on the quality of the solutions found.

A biased random-key genetic algorithm with variable mutants to solve a vehicle routing problem

TL;DR

This work introduces BRKGA-VM, a biased random-key genetic algorithm with a variable mutant population, to solve the Vehicle Routing Problem with Occasional Drivers and Time Windows (). A dedicated decoder, a permutation-based path-relinking procedure, and a restart strategy with a Variable Neighborhood Descent (VM+L) are integrated to improve solution quality and convergence speed. Computational experiments across multiple instance classes show that BRKGA-VM generally outperforms the prior MP BRKGA variant and often matches or exceeds exact methods on smaller instances, with VM+L delivering stronger results on random-type instances. The findings support the viability of variable mutation and local search hybrids for complex logistics planning problems involving company and occasional drivers in last-mile delivery scenarios.

Abstract

The paper explores the Biased Random-Key Genetic Algorithm (BRKGA) in the domain of logistics and vehicle routing. Specifically, the application of the algorithm is contextualized within the framework of the Vehicle Routing Problem with Occasional Drivers and Time Window (VRPODTW) that represents a critical challenge in contemporary delivery systems. Within this context, BRKGA emerges as an innovative solution approach to optimize routing plans, balancing cost-efficiency with operational constraints. This research introduces a new BRKGA, characterized by a variable mutant population which can vary from generation to generation, named BRKGA-VM. This novel variant was tested to solve a VRPODTW. For this purpose, an innovative specific decoder procedure was proposed and implemented. Furthermore, a hybridization of the algorithm with a Variable Neighborhood Descent (VND) algorithm has also been considered, showing an improvement of problem-solving capabilities. Computational results show a better performances in term of effectiveness over a previous version of BRKGA, denoted as MP. The improved performance of BRKGA-VM is evident from its ability to optimize solutions across a wide range of scenarios, with significant improvements observed for each type of instance considered. The analysis also reveals that VM achieves preset goals more quickly compared to MP, thanks to the increased variability induced in the mutant population which facilitates the exploration of new regions of the solution space. Furthermore, the integration of VND has shown an additional positive impact on the quality of the solutions found.
Paper Structure (14 sections, 4 equations, 9 figures, 12 tables, 3 algorithms)

This paper contains 14 sections, 4 equations, 9 figures, 12 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. State of the Art
  3. The VRPODTW Description
  4. The Solution Approaches
  5. The Biased Random-Key Genetic Algorithm with Variable Mutants
  6. The Decoder
  7. A Permutation-based Path-relinking
  8. Restart Strategy and Variable Neighborhood Descent
  9. Computational Study
  10. Instances and Parameter Setting
  11. Experimental Results
  12. Experiments on Test Class
  13. Experiments on Small, Medium and Large Classes
  14. Conclusions

Figures (9)

  • Figure 1: Graphical representation of an optimal solution in a scenario specifically designed to highlight the importance of the random component in the decoder. Note that each occasional driver has a capacity of 3, while each customer has a demand of 1. The optimal solution, with a cost of 7.8, was identified by both CPLEX and BRKGA using the random component of the decoder.
  • Figure 2: Graphic representation of the solution provided by BRKGA without the random component in the same scenario as Figure \ref{['fig:prDel_1']}. The cost of the identified solution is 19.2.
  • Figure 3: Diagram of both metaheuristics considered to solve the VRPODTW.
  • Figure 4: Run time distribution for analyzing of the restart parameter $h$: Small class
  • Figure 5: Run time distribution for analyzing of the restart parameter $h$: Medium class
  • ...and 4 more figures