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

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

Multi-echelon distribution systems in city logistics

In the last decades , the increasing quality of services requested by the cust omer, yields to the necessity of optimizing the whole distribution process. This goal may be achieved through a smart exploitation of existing resources other than a clever planning of the whole distribution process. For doing that, it is necessary to enha nce goods consolidation. One of the most efficient way to implement it is to adopt Multi - Echelon distribution systems which are very common in City Logistic context, in which they allow to keep large trucks from the city center, with strong environmental a dvantages . The aim of the paper is to review routing problems arising in City Logistics , in which multi - e chelon distribution systems are involved: the Two Echelon Location Routing Problem ( 2E - LRP) , the Two Echelon Vehicle Routing Problem (2E - VRP) and Truck and Trailer Routing Problem (TTRP), and to discuss literature on optimization methods, both exact and heuristic, developed to address these problems

Enhanced Iterated local search for the technician routing and scheduling problem

Most public facilities in the European countries, including France, Germany, and the UK, were built during the reconstruction projects between 1950 and 1980. Owing to the deteriorating state of such vital infrastructure has become relatively expensive in the recent decades. A significant part of the maintenance operation costs is spent on the technical staff. Therefore, the optimal use of the available workforce is essential to optimize the operation costs. This includes planning technical interventions, workload balancing, productivity improvement, etc. In this paper, we focus on the routing of technicians and scheduling of their tasks. We address for this purpose a variant of the workforce scheduling problem called the technician routing and scheduling problem (TRSP). This problem has applications in different fields, such as transportation infrastructure (rail and road networks), telecommunications, and sewage facilities. To solve the TRSP, we propose an enhanced iterated local search (eILS) approach. The enhancement of the ILS firstly includes an intensification procedure that incorporates a set of local search operators and removal-repair heuristics crafted for the TRSP. Next, four different mechanisms are used in the perturbation phase. Finally, an elite set of solutions is used to extensively explore the neighborhood of local optima as well as to enhance diversification during search space exploration. To measure the performance of the proposed method, experiments were conducted based on benchmark instances from the literature, and the results obtained were compared with those of an existing method. Our method achieved very good results, since it reached the best overall gap, which is three times lower than that of the literature. Furthermore, eILS improved the best-known solution for $34$ instances among a total of $56$ while maintaining reasonable computational times.Comment: Submitted manuscript to Computers and Operations Research journal. 34 pages, 7 figures, 6 table

A statistical learning based approach for parameter fine-tuning of metaheuristics

Metaheuristics are approximation methods used to solve combinatorial optimization problems. Their performance usually depends on a set of parameters that need to be adjusted. The selection of appropriate parameter values causes a loss of efficiency, as it requires time, and advanced analytical and problem-specific skills. This paper provides an overview of the principal approaches to tackle the Parameter Setting Problem, focusing on the statistical procedures employed so far by the scientific community. In addition, a novel methodology is proposed, which is tested using an already existing algorithm for solving the Multi-Depot Vehicle Routing Problem.Peer ReviewedPostprint (published version