Heuristic methods for the sectoring arc routing problem

Constructive heuristics for the Mixed Capacity Arc Routing Problem under Time Restrictions with Intermediate Facilities

The Capacitated Arc Routing Problem (CARP) involves the routing of vehicles to service a set of arcs in a network. This NP-hard problem is extended to a multiperiod horizon, giving a new tactical problem called the Periodic CARP (PCARP). This problem actually occurs in municipal waste collection. Its objective is to assign arcs to periods and to compute the trips in each period, to minimize an overall cost on the horizon. An integer linear program, two insertion heuristics and a two-phase heuristic are developed. These very first algorithms for the PCARP are evaluated on PCARP instances derived from standard CARP benchmarks from literature: the insertion heuristics are very fast but the two-phase method yields better solution costs.

A variable neighborhood descent heuristic for arc routing problems with time-dependent service costs

Consider an undirected graph with demands scattered over the edges and a homogeneous fleet of vehicles to service the demands. In the open capacitated arc routing problem (OCARP) the objective is to find a set of routes that collectively service all demands with the minimum cost. Each vehicle has limited capacity and it can start and finish the route at any node. The OCARP is NP-hard, and its applications include meter reading and cutting path determination problems. State-of-the-art solution methods developed for the OCARP are heuristics, which show good tradeoffs between solution quality and processing time, but do not provide optimality certificates of the obtained solutions. This work focuses on a lower bounding method for the OCARP which can be used to better assess the quality of heuristic solutions. We propose the Relaxed Flow method (RF(k)) which involves the resolution of a mixed integer linear formulation where all vehicles' capacities are modeled as flows on an augmented graph. A parameter k controls the model tightness and RF(k) is shown to be at least as tight as the well-known Belenguer and Benavent's formulation for any k⩾0. To strengthen the model, capacity cuts were included in RF(k) by means of a branch-and-cut framework. Extensive computational experiments conducted on a set of benchmark instances revealed that our method outperformed previous methods. Computational experiments also demonstrated the importance of the parameterization technique to obtain good results. The previously known lower bounds were improved substantially and optimality certificates were attained in 78.9% of the instances. As far as we know this is the first parameterized lower bounding method proposed for an arc routing problem, and we argue it can be generalized to other variants of arc routing problems and general routing problems.

Lower and upper bounds for location-arc routing problems with vehicle capacity constraints

In this paper, the dam-break problem is numerically simulated using two-phase moving particle semi-implicit (MPS) method. Firstly, the two-phase MPS method is extended from single-phase MPS method. The present method treats the multiphase system as a multi-density and multi-viscosity fluid, and a single set of equations could be used for the whole system. The interaction between particles of different phases is considered through the applications of inter-particle viscosity and density smoothing technique. The two-phase MPS method is then successfully applied to violent dam-break problem. The numerical results obtained by single-phase and two-phase method are both compared with experimental results in the open literature. The characteristics of air cavity are analyzed, including the pressure inside the cavity and the cavity shape deformation.

This article proposes a new transformation of undirected arc-routing problems into equivalent node-routing problems, with emphasis on the transformation of Capacitated Arc Routing Problems (CARP) i...

Lower and upper bounds for the mixed capacitated arc routing problem

International audience

Arc routing problems (ARPs) arise naturally in several applications where streets require maintenance, or customers located along road must be serviced. The undirected rural postman problem (URPP) is to determine a least cost tour traversing at least once each edge that requires a service. When demands are put on the edges and this total demand must be covered by a fleet of identical vehicles of capacity Q based at a depot, one gets the undirected capacitated arc routing problem (UCARP). The URPP and UCARP are known to be NP-hard. This chapter reports on recent exact and heuristic algorithms for the URPP and UCARP.

This paper considers the stochastic capacitated arc routing problem (SCARP), obtained by taking random demands in the CARP. For real-world problems, it is important to create solutions that are insensitive to changes in demand, because these quantities are not deterministic but randomly distributed. This paper provides the basic concept of a new technique to compute such solutions, based upon the best method published for CARP: a hybrid genetic algorithm (HGA). The simulation analysis was achieved with the well-known DeArmon's, Eglese's and Belenguer's instances. This intensive evaluation process was carried out with 1000 replications providing high-quality statistical data. The results obtained prove that there is a great interest to optimize not only the solution cost but also the robustness of solutions. This work is a step forward to treat more realistic problems including industrial goals and constraints linked to demand variations.

The Uncertain Capacited Arc Routing Problem (UCARP) is an important variant of arc routing problems that is capable of modelling uncertainties of real-world scenarios. Genetic Programming is utilised to evolve routing policies for vehicles to enable them to make real-time decisions and handle environment uncertainties. However, when the properties of a solved problem change, the trained routing policy becomes ineffective and a new routing policy is needed to be trained. The training process is time-consuming. Nevertheless, by extraction and transfer of some knowledge learned from the previous similar problem, the retraining process can be improved. Transfer learning is a challenging task that entails many aspects to decide about, which can influence the degree by which knowledge transfer can be effective. Consequently, in this paper we propose a parametric framework to formalise these details so that it can facilitate studying different aspects of using transfer learning for handling scenario changes of UCARP. Conducting a large number of experiments, we utilise this framework to analyse different transfer learning mechanisms and demonstrate how it can help with understanding dynamics of knowledge transfer for UCARP.

This paper deals with a complex production planning problem with lost sales, overtimes, safety stock and sequence dependent setup times on parallel and unrelated machines. The main challenge of this work is to propose a solution approach to obtain a good feasible plan in a short execution time (around 2 min) for large industrial instances. We develop a genetic algorithm that combines several operations already defined in the literature to solve the problem. Preliminary numerical results obtained with our algorithm are presented and compared to a straightforward MIP resolution. The method appears to be an appealing alternative on large instances when the computational time is limited.

The capacitated arc routing problem is a classical NP-hard problem to solve in the field of combinatorial optimization. In recent years, due to its extensive use in our daily life, its importance has gradually emerged. Multi-objective capacitated arc routing problem (MO-CARP) is more close to real life, so it arouses widespread concern. The Multi-objective evolution algorithm based on decomposition provides a suitable frame for solving MO-CARP. In this paper, a memetic algorithm based on decomposition and extended search (ED-MAENS) is proposed to deal with MO-CARP. Firstly, decompose the MO-CARP into many single-objective sub-problems using weight vectors. Then assign represent solution for each single-objective problem. To make sure that each single-objective problems can get a reasonable represent solution, the rank conception is proposed. After that, MAENS algorithm is adopted to solve each single-objective problem using the information of its neighborhood. Finally, we proposed an extended search operator to enlarge the searching space to improve the solution quality. The new proposed algorithm is evaluated on medium and large scale instance set and experimental results demonstrate the proposed method can obtain the better non-dominated solution than compared algorithms especially on large-scale instance.

The purpose of this paper is to study the periodic arc-routing problem when the arcs of a network behave as customers, and sufficient material is delivered so that each achieves its desired inventory level. Therefore, routing and inventory decisions are made simultaneously. Applications include dust suppression in open-pit mines or forest roads and plant watering along sidewalks or street medians. A truck periodically sprays water along the edges of a network. The humidity reaches a desired level and is then consumed over time until water is delivered again. The quantity of water delivered can be fixed or variable; we consider both scenarios and propose a mathematical model for each. Results are reported to validate the model. The contribution of this paper is the first mathematical model that combines inventory and routing decisions in the arc-routing domain.