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44 pages, 3468 KiB

Open AccessArticle

Challenging the Limits of Binarization: A New Scheme Selection Policy Using Reinforcement Learning Techniques for Binary Combinatorial Problem Solving

by Marcelo Becerra-Rozas, Broderick Crawford, Ricardo Soto, El-Ghazali Talbi and Jose M. Gómez-Pulido

Biomimetics 2024, 9(2), 89; https://doi.org/10.3390/biomimetics9020089 - 1 Feb 2024

Viewed by 1701

Abstract

In this study, we introduce an innovative policy in the field of reinforcement learning, specifically designed as an action selection mechanism, and applied herein as a selector for binarization schemes. These schemes enable continuous metaheuristics to be applied to binary problems, thereby paving new paths in combinatorial optimization. To evaluate its efficacy, we implemented this policy within our BSS framework, which integrates a variety of reinforcement learning and metaheuristic techniques. Upon resolving 45 instances of the Set Covering Problem, our results demonstrate that reinforcement learning can play a crucial role in enhancing the binarization techniques employed. This policy not only significantly outperformed traditional methods in terms of precision and efficiency, but also proved to be extensible and adaptable to other techniques and similar problems. The approach proposed in this article is capable of significantly surpassing traditional methods in precision and efficiency, which could have important implications for a wide range of real-world applications. This study underscores the philosophy behind our approach: utilizing reinforcement learning not as an end in itself, but as a powerful tool for solving binary combinatorial problems, emphasizing its practical applicability and potential to transform the way we address complex challenges across various fields. Full article

(This article belongs to the Special Issue Nature-Inspired Computer Algorithms: 2nd Edition)

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24 pages, 1412 KiB

Open AccessArticle

Learning to Optimise a Swarm of UAVs

by Gabriel Duflo, Grégoire Danoy, El-Ghazali Talbi and Pascal Bouvry

Appl. Sci. 2022, 12(19), 9587; https://doi.org/10.3390/app12199587 - 24 Sep 2022

Cited by 2 | Viewed by 7241

Abstract

The use of Unmanned Aerial Vehicles (UAVs) has shown a drastic increase in interest in the past few years. Current applications mainly depend on single UAV operations, which face critical limitations such as mission range or resilience. Using several autonomous UAVs as a swarm is a promising approach to overcome these. However, designing an efficient swarm is a challenging task, since its global behaviour emerges solely from local decisions and interactions. These properties make classical multirobot design techniques not applicable, while evolutionary swarm robotics is typically limited to a single use case. This work, thus, proposes an automated swarming algorithm design approach, and more precisely, a generative hyper-heuristic relying on multi-objective reinforcement learning, that permits us to obtain not only efficient but also reusable swarming behaviours. Experimental results on a three-objective variant of the Coverage of a Connected UAV Swarm problem demonstrate that it not only permits one to generate swarming heuristics that outperform the state-of-the-art in terms of coverage by a swarm of UAVs but also provides high stability. Indeed, it is empirically demonstrated that the model trained on a certain class of instances generates heuristics and is capable of performing well on instances with a different size or swarm density. Full article

(This article belongs to the Special Issue Artificial Intelligence within Robot Swarms)

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26 pages, 7639 KiB

Open AccessArticle

Deep Gaussian Process for the Approximation of a Quadratic Eigenvalue Problem: Application to Friction-Induced Vibration

by Jeremy Sadet, Franck Massa, Thierry Tison, El-Ghazali Talbi and Isabelle Turpin

Vibration 2022, 5(2), 344-369; https://doi.org/10.3390/vibration5020020 - 10 Jun 2022

Cited by 3 | Viewed by 2738

Abstract

Despite numerous works over the past two decades, friction-induced vibrations, especially braking noises, are a major issue for transportation manufacturers as well as for the scientific community. To study these fugitive phenomena, the engineers need numerical methods to efficiently predict the mode coupling instabilities in a multiparametric context. The objective of this paper is to approximate the unstable frequencies and the associated damping rates extracted from a complex eigenvalue analysis under variability. To achieve this, a deep Gaussian process is considered to fit the non-linear and non-stationary evolutions of the real and imaginary parts of complex eigenvalues. The current challenge is to build an efficient surrogate modelling, considering a small training set. A discussion about the sample distribution density effect, the training set size and the kernel function choice is proposed. The results are compared to those of a Gaussian process and a deep neural network. A focus is made on several deceptive predictions of surrogate models, although the better settings were well chosen in theory. Finally, the deep Gaussian process is investigated in a multiparametric analysis to identify the best number of hidden layers and neurons, allowing a precise approximation of the behaviours of complex eigensolutions. Full article

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39 pages, 670 KiB

Open AccessArticle

Matheuristics and Column Generation for a Basic Technician Routing Problem

by Nicolas Dupin, Rémi Parize and El-Ghazali Talbi

Algorithms 2021, 14(11), 313; https://doi.org/10.3390/a14110313 - 27 Oct 2021

Cited by 11 | Viewed by 4376

Abstract

This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems. Full article

(This article belongs to the Special Issue 2021 Selected Papers from Algorithms Editorial Board Members)

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30 pages, 459 KiB

Open AccessArticle

Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

by Nicolas Dupin, Frank Nielsen and El-Ghazali Talbi

Mathematics 2021, 9(4), 453; https://doi.org/10.3390/math9040453 - 23 Feb 2021

Cited by 10 | Viewed by 3525

Abstract

With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete and continuous versions, partial K-center problems, and their min-sum-K-radii variants. In dimension three (or upper), this induces NP-hard complexities. In the planar case, common optimality property is proven: non-nested optimal solutions exist. This induces a common dynamic programming algorithm running in polynomial time. Specific improvements hold for some variants, such as K-center problems and min-sum K-radii on a line. When applied to N points and allowing to uncover

M < N

points, K-center and min-sum-K-radii variants are, respectively, solvable in

O (K (M + 1) N log N)

and

O (K (M + 1) N^{2})

time. Such complexity of results allows an efficient straightforward implementation. Parallel implementations can also be designed for a practical speed-up. Their application inside multi-objective heuristics is discussed to archive partial Pareto fronts, with a special interest in partial clustering variants. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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25 pages, 783 KiB

Open AccessArticle

A New Chaotic-Based Approach for Multi-Objective Optimization

by Nassime Aslimani, Talbi El-ghazali and Rachid Ellaia

Algorithms 2020, 13(9), 204; https://doi.org/10.3390/a13090204 - 20 Aug 2020

Cited by 7 | Viewed by 3076

Abstract

Multi-objective optimization problems (MOPs) have been widely studied during the last decades. In this paper, we present a new approach based on Chaotic search to solve MOPs. Various Tchebychev scalarization strategies have been investigated. Moreover, a comparison with state of the art algorithms [...] Read more.

(This article belongs to the Special Issue Optimization Algorithms and Applications)

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29 pages, 692 KiB

Open AccessArticle

Machine Learning-Guided Dual Heuristics and New Lower Bounds for the Refueling and Maintenance Planning Problem of Nuclear Power Plants

by Nicolas Dupin and El-Ghazali Talbi

Algorithms 2020, 13(8), 185; https://doi.org/10.3390/a13080185 - 30 Jul 2020

Cited by 6 | Viewed by 4824

Abstract

This paper studies the hybridization of Mixed Integer Programming (MIP) with dual heuristics and machine learning techniques, to provide dual bounds for a large scale optimization problem from an industrial application. The case study is the EURO/ROADEF Challenge 2010, to optimize the refueling and maintenance planning of nuclear power plants. Several MIP relaxations are presented to provide dual bounds computing smaller MIPs than the original problem. It is proven how to get dual bounds with scenario decomposition in the different 2-stage programming MILP formulations, with a selection of scenario guided by machine learning techniques. Several sets of dual bounds are computable, improving significantly the former best dual bounds of the literature and justifying the quality of the best primal solution known. Full article

(This article belongs to the Special Issue Optimization Algorithms and Applications)

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