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The hop-like problem nature -- unveiling and modelling new features of real-world problems

Michal W. Przewozniczek, Bartosz Frej, Marcin M. Komarnicki

TL;DR

This work tackles how to design and analyze benchmarks that reflect real-world NP-hard optimization features encountered by genetic algorithms. It introduces a hop-based analysis of WP_LFL, a large-scale network-flow problem, and proposes Leading Blocks Problem (LBP), a generalization of Leading Ones that models enabling/disabling block subfunctions and their dependencies. The study shows WP_LFL exhibits step-like, block-wise improvements, and demonstrates that standard linkage-learning approaches struggle without information on block order, motivating new decomposition strategies; it also provides three LBP variants (RestOff, HalfOnHalf, Alter) to explore different disabled-block effects. The results advocate developing structure-aware, hop-aware decomposition techniques to solve LBP and WP_LFL more effectively, with broader implications for hard real-world optimization problems.

Abstract

Benchmarks are essential tools for the optimizer's development. Using them, we can check for what kind of problems a given optimizer is effective or not. Since the objective of the Evolutionary Computation field is to support the tools to solve hard, real-world problems, the benchmarks that resemble their features seem particularly valuable. Therefore, we propose a hop-based analysis of the optimization process. We apply this analysis to the NP-hard, large-scale real-world problem. Its results indicate the existence of some of the features of the well-known Leading Ones problem. To model these features well, we propose the Leading Blocks Problem (LBP), which is more general than Leading Ones and some of the benchmarks inspired by this problem. LBP allows for the assembly of new types of hard optimization problems that are not handled well by the considered state-of-the-art genetic algorithm (GA). Finally, the experiments reveal what kind of mechanisms must be proposed to improve GAs' effectiveness while solving LBP and the considered real-world problem.

The hop-like problem nature -- unveiling and modelling new features of real-world problems

TL;DR

This work tackles how to design and analyze benchmarks that reflect real-world NP-hard optimization features encountered by genetic algorithms. It introduces a hop-based analysis of WP_LFL, a large-scale network-flow problem, and proposes Leading Blocks Problem (LBP), a generalization of Leading Ones that models enabling/disabling block subfunctions and their dependencies. The study shows WP_LFL exhibits step-like, block-wise improvements, and demonstrates that standard linkage-learning approaches struggle without information on block order, motivating new decomposition strategies; it also provides three LBP variants (RestOff, HalfOnHalf, Alter) to explore different disabled-block effects. The results advocate developing structure-aware, hop-aware decomposition techniques to solve LBP and WP_LFL more effectively, with broader implications for hard real-world optimization problems.

Abstract

Benchmarks are essential tools for the optimizer's development. Using them, we can check for what kind of problems a given optimizer is effective or not. Since the objective of the Evolutionary Computation field is to support the tools to solve hard, real-world problems, the benchmarks that resemble their features seem particularly valuable. Therefore, we propose a hop-based analysis of the optimization process. We apply this analysis to the NP-hard, large-scale real-world problem. Its results indicate the existence of some of the features of the well-known Leading Ones problem. To model these features well, we propose the Leading Blocks Problem (LBP), which is more general than Leading Ones and some of the benchmarks inspired by this problem. LBP allows for the assembly of new types of hard optimization problems that are not handled well by the considered state-of-the-art genetic algorithm (GA). Finally, the experiments reveal what kind of mechanisms must be proposed to improve GAs' effectiveness while solving LBP and the considered real-world problem.
Paper Structure (15 sections, 9 equations, 2 figures, 5 tables, 1 algorithm)

This paper contains 15 sections, 9 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Leading Ones problem and its versions
  4. Problem decomposition in state-of-the-art GA-based optimizers
  5. WP_LFL Problem
  6. Problem definition
  7. Problem-dedicated optimizers
  8. Leading Blocks Problem
  9. Motivations and Definition
  10. The Basic Features of Leading Blocks Problem
  11. Considered Leading Blocks Problem Types
  12. Experiments on WP_LFL
  13. Hop-based Analysis of Typical Benchmarks
  14. Experiments on Leading Blocks Problem
  15. Conclusions

Figures (2)

  • Figure 1: HOP-based analysis of the WP_LFL instances
  • Figure 2: Median FFE until finding the optimal solution by LT-GOMEA and LT-GOMEA-DLED in solving various Leading Blocks Problem (using $bimTrap_{10}$) and the concatenation of $bimTrap_{10}$ functions (X axis - problem size)