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Deep memetic models for combinatorial optimization problems: application to the tool switching problem

Jhon Edgar Amaya, Carlos Cotta, Antonio J. Fernández-Leiva, Pablo García-Sánchez

TL;DR

This paper demonstrates that memetic models can be considered as an efficient alternative to other traditional forms of cooperative algorithms, and shows that deep models are effective to solve a specific combinatorial problem, outperforming metaheuristics proposed in the literature.

Abstract

Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of autonomous basic optimization algorithms that interact among them in a cooperative way in order to deal with a specific optimization problem, aiming to obtain better results than the algorithms that constitute it separately. Going one step beyond this traditional view of cooperative optimization algorithms, this work tackles deep meta-cooperation, namely the use of cooperative optimization algorithms in which some components can in turn be cooperative methods themselves, thus exhibiting a deep algorithmic architecture. The objective of this paper is to demonstrate that such models can be considered as an efficient alternative to other traditional forms of cooperative algorithms. To validate this claim, different structural parameters, such as the communication topology between the agents, or the parameter that influences the depth of the cooperative effort (the depth of meta-cooperation), have been analyzed. To do this, a comparison with the state-of-the-art cooperative methods to solve a specific combinatorial problem, the Tool Switching Problem, has been performed. Results show that deep models are effective to solve this problem, outperforming metaheuristics proposed in the literature.

Deep memetic models for combinatorial optimization problems: application to the tool switching problem

TL;DR

This paper demonstrates that memetic models can be considered as an efficient alternative to other traditional forms of cooperative algorithms, and shows that deep models are effective to solve a specific combinatorial problem, outperforming metaheuristics proposed in the literature.

Abstract

Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of autonomous basic optimization algorithms that interact among them in a cooperative way in order to deal with a specific optimization problem, aiming to obtain better results than the algorithms that constitute it separately. Going one step beyond this traditional view of cooperative optimization algorithms, this work tackles deep meta-cooperation, namely the use of cooperative optimization algorithms in which some components can in turn be cooperative methods themselves, thus exhibiting a deep algorithmic architecture. The objective of this paper is to demonstrate that such models can be considered as an efficient alternative to other traditional forms of cooperative algorithms. To validate this claim, different structural parameters, such as the communication topology between the agents, or the parameter that influences the depth of the cooperative effort (the depth of meta-cooperation), have been analyzed. To do this, a comparison with the state-of-the-art cooperative methods to solve a specific combinatorial problem, the Tool Switching Problem, has been performed. Results show that deep models are effective to solve this problem, outperforming metaheuristics proposed in the literature.

Paper Structure

This paper contains 24 sections, 6 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Cooperative Models
  4. Collaborative approaches
  5. Integrative approaches
  6. The Memetic Perspective: Toward Deep Architectures
  7. The Tool Switching Problem
  8. Formal Representation
  9. Neighborhood Function
  10. Tackling the ToSP
  11. A Framework for Deep Meta-Cooperation
  12. Experiments and Results
  13. Experimental setup
  14. Benchmarking
  15. Metaheuristics
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Different instances of the meta-cooperative model: 0-level ($\Phi^{0}$), 1-level ($\Phi^{1}$), and a 2-level ($\Phi^{2}$), respectively.
  • Figure 2: Rank distribution for 1-level-meta-cooperative algorithms with respect to the best algorithmic approaches to solve the ToSP. In this figure and in subsequent ones, each box comprises the second and third quartiles of the distribution, the median (resp. mean) is marked with a vertical line (resp. circle), whiskers span 1.5 times the inter-quartile range, and outliers are indicated with a plus sign.
  • Figure 3: Rank distribution for 2-level-meta-cooperative models.
  • Figure 4: Rank distribution for 3-level-meta-cooperative models.
  • Figure 5: Rank distribution of each interconnection topology. (a) 1-level (b) 2-level (c) 3-level (d) global for all models