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Seeking and leveraging alternative variable dependency concepts in gray-box-elusive bimodal land-use allocation problems

J. Maciążek, M. W. Przewozniczek, J. Schwaab

TL;DR

The paper addresses a real-world, NP-hard land-use optimization (LUO) problem where standard variable-dependency discovery is impractical due to feasibility repairs. It introduces problem-dedicated variable dependency concepts and three cluster-based crossovers (Simple Region Crossover, Differing Region Crossover, and Individual-based Differing Region Crossover) to enable region-wise mixing in binary LUO representations, integrating them with NSGA-II and MOEA/D. Four initialization schemes (SQ-I, TEL-I, HYB-I, HAL-I) further guide the initial population toward favorable regions of the search space. The results on 14 LUO benchmarks show that the proposed DRC crossover, in particular, substantially improves multi-objective optimization performance, offering a practical approach to leverage spatial dependencies when Walsh-based gray-box methods are inapplicable and pointing to future work on parameterless LUO optimizers and donor-based mixing.

Abstract

Solving land-use allocation problems can help us to deal with some of the most urgent global environmental issues. Since these problems are NP-hard, effective optimizers are needed to handle them. The knowledge about variable dependencies allows for proposing such tools. However, in this work, we consider a real-world multi-objective problem for which standard variable dependency discovery techniques are inapplicable. Therefore, using linkage-based variation operators is unreachable. To address this issue, we propose a definition of problem-dedicated variable dependency. On this base, we propose obtaining masks of dependent variables. Using them, we construct three novel crossover operators. The results concerning real-world test cases show that introducing our propositions into two well-known optimizers (NSGA-II, MOEA/D) dedicated to multi-objective optimization significantly improves their effectiveness.

Seeking and leveraging alternative variable dependency concepts in gray-box-elusive bimodal land-use allocation problems

TL;DR

The paper addresses a real-world, NP-hard land-use optimization (LUO) problem where standard variable-dependency discovery is impractical due to feasibility repairs. It introduces problem-dedicated variable dependency concepts and three cluster-based crossovers (Simple Region Crossover, Differing Region Crossover, and Individual-based Differing Region Crossover) to enable region-wise mixing in binary LUO representations, integrating them with NSGA-II and MOEA/D. Four initialization schemes (SQ-I, TEL-I, HYB-I, HAL-I) further guide the initial population toward favorable regions of the search space. The results on 14 LUO benchmarks show that the proposed DRC crossover, in particular, substantially improves multi-objective optimization performance, offering a practical approach to leverage spatial dependencies when Walsh-based gray-box methods are inapplicable and pointing to future work on parameterless LUO optimizers and donor-based mixing.

Abstract

Solving land-use allocation problems can help us to deal with some of the most urgent global environmental issues. Since these problems are NP-hard, effective optimizers are needed to handle them. The knowledge about variable dependencies allows for proposing such tools. However, in this work, we consider a real-world multi-objective problem for which standard variable dependency discovery techniques are inapplicable. Therefore, using linkage-based variation operators is unreachable. To address this issue, we propose a definition of problem-dedicated variable dependency. On this base, we propose obtaining masks of dependent variables. Using them, we construct three novel crossover operators. The results concerning real-world test cases show that introducing our propositions into two well-known optimizers (NSGA-II, MOEA/D) dedicated to multi-objective optimization significantly improves their effectiveness.

Paper Structure

This paper contains 15 sections, 11 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Land Use Allocation
  4. Multi-objective optimization
  5. Dependency-based optimization leveraging
  6. Land Use Optimization problem
  7. Problem definition and quality measures
  8. Solution encoding and repair mechanisms
  9. Standard operators
  10. Proposed Crossover Operators
  11. Proposed Initialization Procedures
  12. Experiments
  13. Experiment setup
  14. Results
  15. Conclusions

Figures (3)

  • Figure 1: The example of variable mapping, solution encoding and repair for LUO with $R=C=4$, $K=5$, $T=4$, and $U=7$.
  • Figure 2: Clusterization examples employed by proposed crossovers (we consider the same instance as in Fig \ref{['fig:encodingAndRepair']})
  • Figure 3: The influence of the proposed crossover operators (base optimizer, mutation type, crossover results repair operation)