Christian Prins

A Simple and Effective Evolutionary Algorithm for the Vehicle Routing Problem

Abstract The vehicle routing problem (VRP) plays a central role in the optimization of distribution networks. Since some classical instances with 75 nodes resist the best exact solution methods, most researchers concentrate on metaheuristics for solving real-life problems. Contrary to the VRP with time windows, no genetic algorithm (GA) can compete with the powerful tabu search (TS) methods designed for the VRP. This paper bridges the gap by presenting a relatively simple but effective hybrid GA. In terms of average solution cost, this algorithm outperforms most published TS heuristics on the 14 classical Christofides instances and becomes the best solution method for the 20 large-scale instances generated by Golden et al. Scope and purpose The framework of this research is the development of effective metaheuristics for hard combinatorial optimization problems met in vehicle routing. It is surprising to notice in the literature the absence of effective genetic algorithms (GA) for the vehicle routing problem (VRP, the main capacitated node routing problem), contrary to node routing problems with time windows or arc routing problems. Earlier attempts were based on chromosomes with trip delimiters and needed a repair procedure to get feasible children after each crossover. Such procedures are known to weaken the genetic transmission of information from parents to children. This paper proposes a GA without trip delimiters, hybridized with a local search procedure. At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence), thanks to a special splitting procedure. This design choice avoids repair procedures and enables the use of classical crossovers like OX. The resulting algorithm is flexible, relatively simple, and very effective when applied to two sets of standard benchmark instances ranging from 50 to 483 customers.

A survey of recent research on location-routing problems

The design of distribution systems raises hard combinatorial optimization problems. For instance, facility location problems must be solved at the strategic decision level to place factories and warehouses, while vehicle routes must be built at the tactical or operational levels to supply customers. In fact, location and routing decisions are interdependent and studies have shown that the overall system cost may be excessive if they are tackled separately. The location-routing problem (LRP) integrates the two kinds of decisions. Given a set of potential depots with opening costs, a fleet of identical vehicles and a set of customers with known demands, the classical LRP consists in opening a subset of depots, assigning customers to them and determining vehicle routes, to minimize a total cost including the cost of open depots, the fixed costs of vehicles used, and the total cost of the routes. Since the last comprehensive survey on the LRP, published by Nagy and Salhi (2007), the number of articles devoted to this problem has grown quickly, calling a review of new research works. This paper analyzes the recent literature (72 articles) on the standard LRP and new extensions such as several distribution echelons, multiple objectives or uncertain data. Results of state-of-the-art metaheuristics are also compared on standard sets of instances for the classical LRP, the two-echelon LRP and the truck and trailer problem.

A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows

The paper presents an efficient Hybrid Genetic Search with Advanced Diversity Control for a large class of time-constrained vehicle routing problems, introducing several new features to manage the temporal dimension. New move evaluation techniques are proposed, accounting for penalized infeasible solutions with respect to time-window and duration constraints, and allowing to evaluate moves from any classical neighbourhood based on arc or node exchanges in amortized constant time. Furthermore, geometric and structural problem decompositions are developed to address efficiently large problems. The proposed algorithm outperforms all current state-of-the-art approaches on classical literature benchmark instances for any combination of periodic, multi-depot, site-dependent, and duration-constrained vehicle routing problem with time windows.

Competitive Memetic Algorithms for Arc Routing Problems

The Capacitated Arc Routing Problem or CARP arises in applications like waste collection or winter gritting. Metaheuristics are tools of choice for solving large instances of this NP-hard problem. The paper presents basic components that can be combined into powerful memetic algorithms (MAs) for solving an extended version of the CARP (ECARP). The best resulting MA outperforms all known heuristics on three sets of benchmark files containing in total 81 instances with up to 140 nodes and 190 edges. In particular, one open instance is broken by reaching a tight lower bound designed by Belenguer and Benavent, 26 best-known solutions are improved, and all other best-known solutions are retrieved.

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants.

Solving the capacitated location-routing problem by a GRASP complemented by a learning process and a path relinking

As shown in recent researches, the costs in distribution systems may be excessive if routes are ignored when locating depots. The location routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a new metaheuristic to solve the LRP with capacitated routes and depots. A first phase executes a GRASP, based on an extended and randomized version of Clarke and Wright algorithm. This phase is implemented with a learning process on the choice of depots. In a second phase, new solutions are generated by a post-optimization using a path relinking. The method is evaluated on sets of randomly generated instances, and compared to other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem. Furthermore, the algorithm is competitive with a metaheuristic published for the case of uncapacitated depots.

Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic

Most of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances.

A Branch-and-Cut method for the Capacitated Location-Routing Problem

Most of the time in a distribution system, depot location and vehicle routing are interdependent and recent researches have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents two formulations of the location-routing problem with capacities on routes and depots and proposes an exact method based on a branch and cut approach using these formulations. The method is evaluated on two sets of randomly generated instances, and compared to heuristics and another lower bound

A GRASP×ELS approach for the capacitated location-routing problem

This paper addresses the capacitated location-routing problem (CLRP), raised by distribution networks involving depot location, fleet assignment and routing decisions. The CLRP is defined by a set of potential depot locations, with opening costs and limited capacities, a homogeneous fleet of vehicles, and a set of customers with known demands. The objective is to open a subset of depots, to assign customers to these depots and to design vehicle routes, in order to minimize both the cost of open depots and the total cost of the routes. The proposed solution method is a greedy randomized adaptive search procedure (GRASP), calling an evolutionary local search (ELS) and searching within two solution spaces: giant tours without trip delimiters and true CLRP solutions. Giant tours are evaluated via a splitting procedure that minimizes the total cost subject to vehicle capacity, fleet size and depot capacities. This framework is benchmarked on classical instances. Numerical experiments show that the approach outperforms all previously published methods and provides numerous new best solutions.

A memetic algorithm with dynamic population management for an integrated production-distribution problem

This paper studies an NP-hard multi-period production-distribution problem to minimize the sum of three costs: production setups, inventories and distribution. This problem is solved by a very recent form of metaheuristic called memetic algorithm with population management (MA|PM). Contrary to classical two-phase methods (production planning, then distribution planning), the algorithm simultaneously tackles production and distribution decisions. Several versions with different population management strategies are evaluated and compared with a two-phase heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP), on 90 randomly generated instances with 20 periods and 50, 100 or 200 customers. The significant savings obtained compared to the two other methods confirm both the interest of integrating production and distribution decisions and of using the MA|PM template.