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

Supply chain management: An opportunity for metaheuristics

In today’s highly competitive and global marketplace the pressure on organizations to find new ways to create and deliver value to customers grows ever stronger. In the last two decades, logistics and supply chain has moved to the center stage. There has been a growing recognition that it is through an effective management of the logistics function and the supply chain that the goal of cost reduction and service enhancement can be achieved. The key to success in Supply Chain Management (SCM) require heavy emphasis on integration of activities, cooperation, coordination and information sharing throughout the entire supply chain, from suppliers to customers. To be able to respond to the challenge of integration there is the need of sophisticated decision support systems based on powerful mathematical models and solution techniques, together with the advances in information and communication technologies. The industry and the academia have become increasingly interested in SCM to be able to respond to the problems and issues posed by the changes in the logistics and supply chain. We present a brief discussion on the important issues in SCM. We then argue that metaheuristics can play an important role in solving complex supply chain related problems derived by the importance of designing and managing the entire supply chain as a single entity. We will focus specially on the Iterated Local Search, Tabu Search and Scatter Search as the ones, but not limited to, with great potential to be used on solving the SCM related problems. We will present briefly some successful applications.Supply chain management, metaheuristics, iterated local search, tabu search and scatter search

A review of the Tabu Search Literature on Traveling Salesman Problems

The Traveling Salesman Problem (TSP) is one of the most widely studied problems inrncombinatorial optimization. It has long been known to be NP-hard and hence research onrndeveloping algorithms for the TSP has focused on approximate methods in addition to exactrnmethods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. Inrnthis paper, we review the tabu search literature on the TSP, point out trends in it, and bringrnout some interesting research gaps in this literature.

Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times and costs, time windows, and incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. To face this challenge, we propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 existing instances within one hour. Scalability experiments on even larger problems demonstrate that it can optimally solve problems with around 60 ships and 200 cargoes (i.e., 400 pickup and delivery services) and find optimality gaps below 1.04% on the largest cases with up to 260 cargoes. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since these instances are comparable in size with the largest problems routinely solved by shipping companies

Combining statistical learning with metaheuristics for the multi-depot vehicle routing problem with market segmentation

In real-life logistics and distribution activities it is usual to face situations in which the distribution of goods has to be made from multiple warehouses or depots to the nal customers. This problem is known as the Multi-Depot Vehicle Routing Problem (MDVRP), and it typically includes two sequential and correlated stages: (a) the assignment map of customers to depots, and (b) the corresponding design of the distribution routes. Most of the existing work in the literature has focused on minimizing distance-based distribution costs while satisfying a number of capacity constraints. However, no attention has been given so far to potential variations in demands due to the tness of the customerdepot mapping in the case of heterogeneous depots. In this paper, we consider this realistic version of the problem in which the depots are heterogeneous in terms of their commercial o er and customers show di erent willingness to consume depending on how well the assigned depot ts their preferences. Thus, we assume that di erent customer-depot assignment maps will lead to di erent customer-expenditure levels. As a consequence, market-segmentation strategies need to be considered in order to increase sales and total income while accounting for the distribution costs. To solve this extension of the MDVRP, we propose a hybrid approach that combines statistical learning techniques with a metaheuristic framework. First, a set of predictive models is generated from historical data. These statistical models allow estimating the demand of any customer depending on the assigned depot. Then, the estimated expenditure of each customer is included as part of an enriched objective function as a way to better guide the stochastic local search inside the metaheuristic framework. A set of computational experiments contribute to illustrate our approach and how the extended MDVRP considered here diré in terms of the proposed solutions from the traditional one.Peer ReviewedPreprin

The location routing problem with facility sizing decisions

The location routing problem (LRP) integrates operational decisions on vehicle routing operations with strategic decisions on the location of the facilities or depots from which the distribution will take place. In other words, it combines the well-known vehicle routing problem (VRP) with the facility location problem (FLP). Hence, the LRP is an NP-hard combinatorial optimization problem, which justifies the use of metaheuristic approaches whenever large-scale instances need to be solved. In this paper, we explore a realistic version of the LRP in which facilities of different capacities are considered, i.e., the manager has to consider not only the location but also the size of the facilities to open. In order to tackle this optimization problem, three mixed-integer linear formulations are proposed and compared. As expected, they have been proved to be cost- and time- inefficient. Hence, a biased-randomized iterated local search algorithm is proposed. Classical instances for the LRP with homogeneous facilities are naturally extended to test the performance of our approach.Peer ReviewedPostprint (published version

Simheuristics to support efficient and sustainable freight transportation in smart city logistics

La logística urbana intel·ligent constitueix un factor crucial en la creació de sistemes de transport urbà eficients i sostenibles. Entre altres factors, aquests sistemes es centren en la incorporació de dades en temps real i en la creació de models de negoci col·laboratius en el transport urbà de mercaderies, considerant l’augment dels habitants en les ciutats, la creixent complexitat de les demandes dels clients i els mercats altament competitius. Això permet als que planifiquen el transport minimitzar els costos monetaris i ambientals del transport de mercaderies a les àrees metropolitanes. Molts problemes de presa de decisions en aquest context es poden formular com a problemes d’optimació combinatòria. Tot i que hi ha diferents enfocaments de resolució exacta per a trobar solucions òptimes a aquests problemes, la seva complexitat i grandària, a més de la necessitat de prendre decisions instantànies pel que fa a l’encaminament de vehicles, la programació o la situació d’instal·lacions, fa que aquestes metodologies no s’apliquin a la pràctica. A causa de la seva capacitat per a trobar solucions pseudoòptimes en gairebé temps real, els algorismes metaheurístics reben una atenció creixent dels investigadors i professionals com a alternatives eficients i fiables per a resoldre nombrosos problemes d’optimació en la creació de la logística de les ciutats intel·ligents. Malgrat el seu èxit, les tècniques metaheurístiques tradicionals no representen plenament la complexitat dels sistemes més realistes. En assumir entrades (inputs) i restriccions de problemes deterministes, la incertesa i el dinamisme experimentats en els escenaris de transport urbà queden sense explicar. Els algorismes simheurístics persegueixen superar aquests inconvenients mitjançant la integració de qualsevol tipus de simulació en processos metaheurístics per a explicar la incertesa inherent a la majoria de les aplicacions de la vida real. Aquesta tesi defineix i investiga l’ús d’algorismes simheurístics com el mètode més adequat per a resoldre problemes d’optimació derivats de la logística de les ciutats. Alguns algorismes simheurístics s’apliquen a una sèrie de problemes complexos, com la recollida de residus urbans, els problemes de disseny de la cadena de subministrament integrada i els models de transport innovadors relacionats amb la col·laboració horitzontal entre els socis de la cadena de subministrament. A més de les discussions metodològiques i la comparació d’algorismes desenvolupats amb els referents de la bibliografia acadèmica, es mostra l’aplicabilitat i l’eficiència dels algorismes simheurístics en diferents casos de gran escala.Las actividades de logística en ciudades inteligentes constituyen un factor crucial en la creación de sistemas de transporte urbano eficientes y sostenibles. Entre otros factores, estos sistemas se centran en la incorporación de datos en tiempo real y la creación de modelos empresariales colaborativos en el transporte urbano de mercancías, al tiempo que consideran el aumento del número de habitantes en las ciudades, la creciente complejidad de las demandas de los clientes y los mercados altamente competitivos. Esto permite minimizar los costes monetarios y ambientales del transporte de mercancías en las áreas metropolitanas. Muchos de los problemas de toma de decisiones en este contexto se pueden formular como problemas de optimización combinatoria. Si bien existen diferentes enfoques de resolución exacta para encontrar soluciones óptimas a tales problemas, su complejidad y tamaño, además de la necesidad de tomar decisiones instantáneas con respecto al enrutamiento, la programación o la ubicación de las instalaciones, hacen que dichas metodologías sean inaplicables en la práctica. Debido a su capacidad para encontrar soluciones pseudoóptimas casi en tiempo real, los algoritmos metaheurísticos reciben cada vez más atención por parte de investigadores y profesionales como alternativas eficientes y fiables para resolver numerosos problemas de optimización en la creación de la logística de ciudades inteligentes. A pesar de su éxito, las técnicas metaheurísticas tradicionales no representan completamente la complejidad de los sistemas más realistas. Al asumir insumos y restricciones de problemas deterministas, se ignora la incertidumbre y el dinamismo experimentados en los escenarios de transporte urbano. Los algoritmos simheurísticos persiguen superar estos inconvenientes integrando cualquier tipo de simulación en procesos metaheurísticos con el fin de considerar la incertidumbre inherente en la mayoría de las aplicaciones de la vida real. Esta tesis define e investiga el uso de algoritmos simheurísticos como método adecuado para resolver problemas de optimización que surgen en la logística de ciudades inteligentes. Se aplican algoritmos simheurísticos a una variedad de problemas complejos, incluyendo la recolección de residuos urbanos, problemas de diseño de la cadena de suministro integrada y modelos de transporte innovadores relacionados con la colaboración horizontal entre los socios de la cadena de suministro. Además de las discusiones metodológicas y la comparación de los algoritmos desarrollados con los de referencia de la bibliografía académica, se muestra la aplicabilidad y la eficiencia de los algoritmos simheurísticos en diferentes estudios de casos a gran escala.Smart city logistics are a crucial factor in the creation of efficient and sustainable urban transportation systems. Among other factors, they focus on incorporating real-time data and creating collaborative business models in urban freight transportation concepts, whilst also considering rising urban population numbers, increasingly complex customer demands, and highly competitive markets. This allows transportation planners to minimize the monetary and environmental costs of freight transportation in metropolitan areas. Many decision-making problems faced in this context can be formulated as combinatorial optimization problems. While different exact solving approaches exist to find optimal solutions to such problems, their complexity and size, in addition to the need for instantaneous decision-making regarding vehicle routing, scheduling, or facility location, make such methodologies inapplicable in practice. Due to their ability to find pseudo-optimal solutions in almost real time, metaheuristic algorithms have received increasing attention from researchers and practitioners as efficient and reliable alternatives in solving numerous optimization problems in the creation of smart city logistics. Despite their success, traditional metaheuristic techniques fail to fully represent the complexity of most realistic systems. By assuming deterministic problem inputs and constraints, the uncertainty and dynamism experienced in urban transportation scenarios are left unaccounted for. Simheuristic frameworks try to overcome these drawbacks by integrating any type of simulation into metaheuristic-driven processes to account for the inherent uncertainty in most real-life applications. This thesis defines and investigates the use of simheuristics as a method of first resort for solving optimization problems arising in smart city logistics concepts. Simheuristic algorithms are applied to a range of complex problem settings including urban waste collection, integrated supply chain design, and innovative transportation models related to horizontal collaboration among supply chain partners. In addition to methodological discussions and the comparison of developed algorithms to state-of-the-art benchmarks found in the academic literature, the applicability and efficiency of simheuristic frameworks in different large-scaled case studies are shown

Combining heuristics with simulation and fuzzy logic to solve a flexible-size location routing problem under uncertainty

The location routing problem integrates both a facility location and a vehicle routing problem. Each of these problems are NP-hard in nature, which justifies the use of heuristic-based algorithms when dealing with large-scale instances that need to be solved in reasonable computing times. This paper discusses a realistic variant of the problem that considers facilities of different sizes and two types of uncertainty conditions. In particular, we assume that some customers’ demands are stochastic, while others follow a fuzzy pattern. An iterated local search metaheuristic is integrated with simulation and fuzzy logic to solve the aforementioned problem, and a series of computational experiments are run to illustrate the potential of the proposed algorithm.This work has been partially supported by the Spanish Ministry of Science (PID2019-111100RB-C21/AEI/10.13039/501100011033). In addition, it has received the support of the Doctoral School at the Universitat Oberta de Catalunya (Spain) and the Universidad de La Sabana (INGPhD-12-2020).Peer ReviewedPostprint (published version