On the use of biased-randomized algorithms for solving non-smooth optimization problems

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

Preface: Special issue on the VeRoLog 2015 conference

International audienceVeRoLog is the annual conference sponsored by the EURO Working Group on Vehicle Routing and Logistics Optimization within EURO, the Association of the European Operational Research Societies. It brings together the large community of researchers and practitioners interested in vehicle routing optimization and its relations with logistics. The conference is open to high-quality methodological contributions as well as relevant real-world applications and case studies from the industry and service sectors. VeRoLog 2015, which forms the basis of the current special issue, was organized in Vienna. The former conferences were located in Bologna (2012), Southampton (2013), and Oslo (2014). Researchers in the field of Vehicle Routing and Logistics from many parts of Europe and beyond met at the University of Vienna from June 8th to June 10th, 2015. There were 181 participants from 29 countries (). The conference was organized into two plenaries (given by Martin Savelsbergh and Tolga Bektas) and 37 sessions including 123 presentations. A strong focus was on rich and real-world routing, especially in the field of green and electric vehicle routing problems, city logistics and bike sharing, and safe and secure routing. In total 28 presentations focused on one of these topics. VeRoLog now also has a solver challenge on rich vehicle routing. The paper of the winner is also included in the special issue. The following seven papers are a selection of the best papers presented during the conference. The paper by Belloso, Juan, Faulin, and Martinez, entitled "A Biased-Randomized Metaheuristic for the Vehicle Routing Problem with Clustered and Mixed Backhauls," analyzes the Vehicle Routing Problem with Backhauls, where delivery and pickup customers are served from a central depot. Initially, it focusses on the version with clustered backhauls (VRPCB), where all delivery customers on a route have to be served before the first pickup customer can be visited. This is motivated by the fact that vehicles are often rear loaded. The paper presents a relatively simple to implement yet efficient metaheuristic algorithm that employs a biased randomized version of the popular savings heuristic within a metaheuristic framework. A skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and the sequencing constraints are considered via penalty costs. On some classical benchmark instances for the VRPCB, competitive results are obtained and a new best-known solution is found. In order to show the robustness of the proposed approach, it is also applied-after a minor adaptation-to the Vehicle Routing Problem with Mixed Backhauls, where line-haul and backhaul customers might appear in any order during a route. The second paper, entitled "An Adaptive and Diversified Vehicle Routing Approach to Reducing the Security Risk of Cash-in-Transit Operations" and authored by Bozkaya, Salman, and Telciler, considers the new problem class of inconsistent vehicle routing problems. The authors consider the transportation of valuables (e.g., cash). Due to the high-risk nature of this operation (e.g., robberies), they consider a bi-objective function where the

A biased-randomized iterated local search for the vehicle routing problem with optional backhauls

[EN] The vehicle routing problem with backhauls integrates decisions on product delivery with decisions on the collection of returnable items. In this paper, we analyze a scenario in which collection of items is optional-but subject to a penalty cost. Both transportation costs and penalties associated with non-collecting decisions are considered. A mixed-integer linear model is proposed and solved for small instances. Also, a metaheuristic algorithm combining biased randomization techniques with iterated local search is introduced for larger instances. Our approach yields cost savings and is competitive when compared to other state-of-the-art approaches.This work has been partially supported by COLCIENCIAS - Colombia, the School of Industrial Engineering of Universidad del Valle, the IoF2020, the AGAUR (2018-LLAV-00017), and the Erasmus+ Program (2018-1-ES01-KA103-049767). We also acknowledge the support of the doctoral programs at the Universitat Oberta de Catalunya and the Universidad de La Sabana.Londoño, JC.; Tordecilla, RD.; Do C. Martins, L.; Juan, AA. (2021). A biased-randomized iterated local search for the vehicle routing problem with optional backhauls. Top. 29(2):387-416. https://doi.org/10.1007/s11750-020-00558-x387416292Al Chami Z, El Flity H, Manier H, Manier MA (2018) A new metaheuristic to solve a selective pickup and delivery problem. In: 2018 4th international conference on logistics operations management (GOL), IEEE, pp 1–5Arab R, Ghaderi S, Tavakkoli-Moghaddam R (2018) Bi-objective inventory routing problem with backhauls under transportation risks: two meta-heuristics. Transportation Letters, pp 1–17Assis LP, Maravilha AL, Vivas A, Campelo F, Ramírez JA (2013) Multiobjective vehicle routing problem with fixed delivery and optional collections. 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