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Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial

Begoña González1, Daniel A Rossit2, Máximo Méndez1

  • 1Universidad de Las Palmas de Gran Canaria (ULPGC), Instituto Universitario SIANI, Spain.

Mathematical Biosciences and Engineering : MBE
|March 28, 2022
PubMed
Summary

Overlapping solutions hinder Multi-Objective Evolutionary Algorithms (MOEAs). A new hybrid MOEA using Objective Space Division (OSD) improves population diversity and performance on multi-objective problems like the Knapsack Problem.

Keywords:
bi-objective knapsack problemmulti-objective combinatorial optimization problemsmulti-objective evolutionary algorithmsobjective space divisionoverlapping solutions

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Area of Science:

  • Operations Research
  • Computer Science
  • Artificial Intelligence

Background:

  • Overlapping solutions, where multiple decision solutions map to a single objective solution, degrade the exploration capabilities and population diversity of Multi-Objective Evolutionary Algorithms (MOEAs).
  • This issue is particularly pronounced in multi-objective combinatorial problems with fewer objectives.
  • Existing MOEAs struggle to maintain diversity when faced with overlapping solutions.

Purpose of the Study:

  • To introduce a novel hybrid MOEA designed to effectively handle overlapping solutions.
  • To enhance the diversity of non-dominated solutions in the population.
  • To evaluate the proposed algorithm's performance on a benchmark Operations Research problem.

Main Methods:

  • A hybrid MOEA, termed NSGA-II/OSD, is proposed, integrating the NSGA-II algorithm with an Objective Space Division (OSD) strategy.
  • The OSD strategy divides the objective space into regions using the nadir solution and applies distinct optimization strategies within each region to classify solutions into non-dominated fronts.
  • The algorithm is tested on the 0-1 Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives, comparing its performance against NSGA-II, MOEA/D, and Global WASF-GA.

Main Results:

  • The NSGA-II/OSD algorithm demonstrates significantly enhanced diversity in the approximate front of non-dominated solutions.
  • Performance analysis includes metrics such as the number of overlapping solutions, solution repairs, hypervolume, attainment surfaces, and approximation to the true Pareto front.
  • The proposed method shows very good performance compared to established algorithms like NSGA-II, MOEA/D, and Global WASF-GA on the 0-1 MOKP.

Conclusions:

  • The NSGA-II/OSD algorithm effectively addresses the challenge of overlapping solutions in MOEAs.
  • Objective Space Division is a viable strategy for improving population diversity and solution quality in multi-objective optimization.
  • The proposed hybrid approach offers a promising advancement for tackling complex multi-objective combinatorial problems.