Improved bounds for large scale capacitated arc routing problem

AbstractThe Capacitated Arc Routing Problem (CARP) stands among the hardest combinatorial problems to solve or to find high quality solutions. This becomes even more true when dealing with large instances. This paper investigates methods to improve on lower and upper bounds of instances on graphs with over 200 vertices and 300 edges, dimensions that, today, can be considered of large scale. On the lower bound side, we propose to explore the speed of a dual ascent heuristic to generate capacity cuts. These cuts are next improved with a new exact separation enchained to the linear program resolution that follows the dual heuristic. On the upper bound, we implement a modified Iterated Local Search procedure to Capacitated Vehicle Routing Problem (CVRP) instances obtained by applying a transformation from the CARP original instances. Computational experiments were carried out on the set of large instances generated by Brandão and Eglese and also on the regular size sets. The experiments on the latter allow for evaluating the quality of the proposed solution approaches, while those on the former present improved lower and upper bounds for all instances of the corresponding set

Solving arc routing problems for winter road maintenance operations

For winter road maintenance, a fleet of snowplow trucks is operated by government agencies to remove snow and ice on roadways and spread materials for anti-icing, de-icing, or increasing friction. Winter road maintenance is essential for providing safe and efficient service for road users (Usman et al., 2010). It is also costly due to the high cost of equipment, crew, and materials. Optimizing winter road maintenance operations could result in significant cost savings, improved safety and mobility, and reduced environmental and social impacts (Salazar-Aguilar et al., 2012). The first topic in this study focuses on designing routes for winter maintenance trucks from a single depot. Real-world winter road maintenance constraints, including road segment service cycle time, heterogeneous vehicle capacity, fleet size, and road-vehicle dependency, are taken into consideration. The problem is formulated as a variation of the capacitated arc routing problem (CARP) to minimize total travel distance. A metaheuristic algorithm, memetic algorithm (MA), is developed to find nearly optimal solutions. This is the first study that developed the model that includes all the constraints listed. This is the first study that used the MA to solve the routing problem with all those constraints, and the first study that developed the route split procedure that satisfies all those constraints. In addition, a paralleled metaheuristic algorithm is proposed to enhance the solution quality and computation efficiency. The second topic of this study focuses on designing routes from multiple depots with intermediate facilities. The service boundaries of depots are redesigned. Each truck must start and end at its home depot, but they can reload at other depots or reload stations (i.e., intermediate facilities). This problem is a variation of the multi-depot CARP with intermediate facilities (MDCARPIF). The second topic includes all constraints employed in the first topic. Since the trucks can be reloaded at any stations, a constraint that restricts the length of work time for truck drivers is also included in this topic. This is the first study that developed the model that includes all the constraints listed. This is the first study that uses the MA to solve the problem and the first study that developed the route split procedure that satisfies all those constraints. The proposed algorithms are implemented to solve real-world problems. Deadhead (travelling without servicing) speed, service speed, and the spreading rate are estimated by the sample from historical winter road maintenance data. Eighteen traffic networks are used as instances for the first topic. The optimized route in the first topic reduced 13.2% of the deadhead distance comparing to the current practice. Comparing to the single core result, the parallel computation improved the solution fitness on 2 of the 18 instances tested, with slightly less time consumed. Based on the optimized result in the first topic, the reduction of the deadhead distance of the second topic is insignificant. This could be due to the network structure and depot location of the current operation. A test instance is created to verify the effectiveness of the proposed algorithm. The result shows 10.4% of deadhead distance can be saved by using the reload and multiple depot scenario instead of the single depot scenario on the test instance

A global repair operator for capacitated arc routing problem

Capacitated arc routing problem (CARP) has attracted much attention during the last few-years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable for small instances, heuristics and metaheuristic methods are widely adopted when solving CARP. This paper demonstrates one major disadvantage encountered by traditional search algorithms and proposes a novel operator named global repair operator (GRO) to address it. We further embed GRO in a recently proposed tabu search algorithm (TSA) and apply the resultant repair-based tabu search (RTS) algorithm to five well-known benchmark test sets. Empirical results suggest that RTS not only outperforms TSA in terms of quality of solutions but also converges to the solutions faster. Moreover, RTS is also competitive with a number of state-of-the-art approaches for CARP. The efficacy of GRO is thereby justified. More importantly, since GRO is not specifically designed for the referred TSA, it might be a potential tool for improving any existing method that adopts the same solution representatio

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects