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

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.

A Real-Time Energy-Saving Mechanism in Internet of Vehicles Systems

“…This methodology employs skewed probability distributions, such as the geometric and triangular ones, to extend the constructive behavior of deterministic heuristics [39]. Many applications of biasedrandomized heuristics can be found in the literature [40]. The first use of a non-uniform probability distribution to induce a biased random effect into a constructive heuristic was given in [41], where the authors solved a capacitated vehicle routing problem.…”

The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints

“…Likewise, De Armas et al [18] used a biased-randomized algorithm to cope with the non-smooth arc routing problem, while Estrada-Moreno et al [19] developed a similar approach for the non-smooth facility location problem. A recent review on the use of biased-randomized algorithms in non-smooth optimization problems is also available [20]. These algorithms have been also employed in other smooth optimization problems [21].…”

“…These algorithms are efficient and they can work with a reduced number of parameters (hence reducing the need for time-consuming fine-tuning processes). This makes them an excellent option for solving non-smooth optimization problems [20]. Algorithm 1 depicts the main characteristics of the two-stage BR-VNS algorithms.…”

Special Issue “Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov”: Foreword by Guest Editors

“…The fourth article, "On the Use of Biased-Randomized Algorithms for Solving Non-Smooth Optimization Problems" by Angel Alejandro Juan, Canan Gunes Corlu, Rafael David Tordecilla, Rocio de la Torre and Albert Ferrer [16], introduces the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and NSO problems in many practical applications, in particular, those including so called soft constraints. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them.…”