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Open AccessArticle

On the Use of Biased-Randomized Algorithms for Solving Non-Smooth Optimization Problems

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Internet Interdisciplinary Institute (IN3), Department of Computer Science, Multimedia and Telecommunication, Universitat Oberta de Catalunya & Euncet Business School, 08018 Barcelona, Spain
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Metropolitan College, Boston University, Boston, MA 02215, USA
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Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya & Universidad de La Sabana, 08018 Barcelona, Spain
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Institute for Advanced Research in Business and Economics (INARBE), Business Administration Department, Public University of Navarre, 31006 Pamplona, Spain
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Department of Applied Mathematics, Universitat Politecnica de Catalunya, 08028 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(1), 8; https://doi.org/10.3390/a13010008
Received: 13 December 2019 / Revised: 23 December 2019 / Accepted: 23 December 2019 / Published: 25 December 2019
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. View Full-Text
Keywords: non-smooth optimization; biased-randomized algorithms; heuristics; soft constraints non-smooth optimization; biased-randomized algorithms; heuristics; soft constraints
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Juan, A.A.; Corlu, C.G.; Tordecilla, R.D.; de la Torre, R.; Ferrer, A. On the Use of Biased-Randomized Algorithms for Solving Non-Smooth Optimization Problems. Algorithms 2020, 13, 8.

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