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Title: On the use of biased-randomized algorithms for solving non-smooth optimization problems
Author: Juan Pérez, Ángel Alejandro
Gunes Corlu, Canan
Tordecilla Madera, Rafael David
Torre Martínez, Rocío de la
Ferrer Biosca, Albert
Others: Universitat Oberta de Catalunya. Internet Interdisciplinary Institute (IN3)
Boston University
Universidad Pública de Navarra
Universitat Politècnica de Catalunya
Keywords: non-smooth optimization
biased-randomized algorithms
soft constraints
Issue Date: Jan-2020
Publisher: Algorithms
Citation: Juan, A.A., Gunes Corlu, C., Tordecilla, R.D., Torre, R. de la & Ferrer, A. (2020). On the Use of Biased-Randomized Algorithms for Solving Non-Smooth Optimization Problems. Algorithms, 13(1), 1-14. doi: 10.3390/a13010008
Project identifier: info:eu-repo/grantAgreement/2018-1-ES01-KA103-049767
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Abstract: Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines.
Language: English
ISSN: 1999-4893MIAR
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