Emmanouil E. Zachariadis

A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints

We present a metaheuristic methodology for the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L-CVRP). 2L-CVRP is a generalisation of the Capacitated Vehicle Routing Problem, in which customer demand is formed by a set of two-dimensional, rectangular, weighted items. The purpose of this problem is to produce the minimum cost routes, starting and terminating at a central depot, to satisfy the customer demand. Furthermore, the transported items must be feasibly packed into the loading surfaces of the vehicles. We propose a metaheuristic algorithm which incorporates the rationale of Tabu Search and Guided Local Search. The loading aspects of the problem are tackled using a collection of packing heuristics. To accelerate the search process, we reduce the neighbourhoods explored, and employ a memory structure to record the loading feasibility information. Extensive experiments were conducted to calibrate the algorithmic parameters. The effectiveness of the proposed metaheuristic algorithm was tested on benchmark instances and led to several new best solutions.

A Hybrid Metaheuristic Algorithm for the Integrated Vehicle Routing and Three-Dimensional Container-Loading Problem

This paper examines a recently addressed practical variant of the capacitated vehicle routing problem (VRP) called the capacitated vehicle routing problem with 3-D loading constraints (3L-CVRP). This problem considers customer demand to be formed by 3-D rectangular items. Additional loading constraints often encountered in real-life applications of transportation logistics are imposed on the examined problem model. In addition to 3L-CVRP, we also introduce and solve a new practical problem version that was dictated by a transportation logistics company and covers cases in which transported items are manually unloaded from the loading spaces of the vehicles. Both problem versions are solved by a hybrid metaheuristic methodology that combines the strategies of tabu search (TS) and guided local search (GLS). The loading characteristics are tackled by employing a collection of packing heuristics. The proposed algorithms robustness was tested for both problem versions, solving benchmark instances derived from the literature and new benchmark problems with diverse features in terms of customer set size and transported-item dimensions. It produced fine results, improving most of the best solutions that were previously reported.

A hybrid metaheuristic algorithm for the vehicle routing problem with simultaneous delivery and pick-up service

This article addresses a vehicle routing problem variant which considers customers to require simultaneous delivery and pick-up service (VRPSPD). The objective of this problem is to determine the optimal set of routes to totally satisfy both the delivery and pick-up demand of the customer population. VRPSPD is an NP-hard combinatorial optimization problem; therefore exact methods are incapable of dealing with large scale VRPSPD instances arising in a wide variety of practical operations. We propose a hybrid solution approach incorporating the rationale of two well-known metaheuristics which have proven to be effective for routing problem variants, namely tabu search and guided local search. The intelligence of the proposed hybrid was designed to achieve a vast exploration of the search space, by escaping from local optima and intensifying at promising solution regions. The performance of our metaheuristic algorithm was tested on benchmark instances involving from 50 to 400 customers. It produced high quality results, improving several best solutions previously reported.

A Hybrid Guided Local Search for the Vehicle-Routing Problem with Intermediate Replenishment Facilities

We propose a three-step algorithmic framework for solving a new variant of the vehicle-routing problem (VRP) called the vehicle-routing problem with intermediate replenishment facilities (VRPIRF). The aim of this problem is to determine optimal routes for a fleet of vehicles that can renew their capacity at intermediate replenishment stations. Although this problem is often met in real-life scenarios of transportation logistics, it has not received much attention by researchers. Our proposed framework employs a combination of algorithmic blocks based on powerful metaheuristic methodologies designed to achieve a desirable intensification and diversification interplay. In the first step of the solution approach, the initial solution is obtained by a cost-saving construction heuristic. In the second step, the initial solution is improved by employing tabu search within the variable neighborhood search methodology. Finally, guided local search is applied in the third step, to eliminate low-quality features from the final solution produced. The proposed algorithmic framework was successfully applied to benchmark instances in the literature, generating several new best solutions. To motivate the proposed algorithmic choices and test the robustness of the algorithm, we also developed new classes of VRPIRF benchmark instances with diverse problem characteristics.

A local search metaheuristic algorithm for the vehicle routing problem with simultaneous pick-ups and deliveries

This article proposes a local search metaheuristic solution approach for the vehicle routing problem with simultaneous pick-ups and deliveries (VRPSPD), which models numerous practical transportation operations in the context of reverse logistics. The proposed algorithm is capable of exploring wide solution neighborhoods by statically encoding moves into special data structures. To avoid cycling and induce diversification, the overall search is coordinated by the use of the promises concept which is based on the aspiration criteria of tabu search. The proposed promises implementation is applied to basic solution features, namely solution arcs. In terms of the challenging capacity constraints imposed by the VRPSPD model, we present a constant-time feasibility checking procedure for the employed local search operators. The presented metaheuristic development was tested on eighteen large-scale VRPSPD benchmark instances derived from the literature. It proved to be both robust and effective, improving most of the previously best-known solutions of the examined test problems.

An adaptive memory methodology for the vehicle routing problem with simultaneous pick-ups and deliveries

This paper deals with a routing problem variant which considers customers to simultaneously require delivery and pick-up services. The examined problem is referred to as the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries (VRPSPD). VRPSPD is an NP-hard combinatorial optimization problem, practical large-scale instances of which cannot be solved by exact solution methodologies within acceptable computational times. Our interest was therefore focused on metaheuristic solution approaches. In specific, we introduce an Adaptive Memory (AM) algorithmic framework which collects and combines promising solution features to generate high-quality solutions. The proposed strategy employs an innovative memory mechanism to systematically maximize the amount of routing information extracted from the AM, in order to drive the search towards diverse regions of the solution space. Our metaheuristic development was tested on numerous VRPSPD instances involving from 50 to 400 customers. It proved to be rather effective and efficient, as it produced high-quality solutions, requiring limited computational effort. Furthermore, it managed to produce several new best solutions.

A strategy for reducing the computational complexity of local search-based methods for the vehicle routing problem

This article focuses on the mechanism of evaluating solution neighborhoods, an algorithmic aspect which plays a crucial role on the efficiency of local-search based approaches. In specific, it presents a strategy for reducing the computational complexity required for applying local search to tackle various combinatorial optimization problems. The value of this contribution is two-fold. It helps practitioners design efficient local search implementations, and it facilitates the application of robust commercial local search-based algorithms to practical instances of very large size. The central rationale underlying the proposed complexity reduction strategy is straightforward: when a local search operator is applied to a given solution, only a limited part of this solution is modified. Thus, to exhaustively examine the neighborhood of the new solution, only the tentative moves that refer to the modified solution part have to be evaluated. To reduce the complexity of neighborhood evaluation, the static move descriptor (SMD) data structures are introduced, which encode local search moves in a systematic and solution independent manner. The proposed strategy is applied to the vehicle routing problem (VRP) which is of high importance both from the practical and theoretical viewpoints. The use of the SMD concept, for encoding three commonly applied quadratic local search operators, results into a VRP local search method which exhibits an almost linearithmic complexity in respect to the instance size. Furthermore, exploiting the SMD representation of tentative moves, a metaheuristic strategy is proposed, which is aimed at diversifying the conducted search via a simple penalization policy. The proposed metaheuristic was tested on various large and very large scale VRP benchmark instances. It produced fine results, and managed to improve several best known solutions. The method was also executed on real-world instances of 3000 customers, the data of which reflects the actual geographic distribution of customers within four major cities.

An open vehicle routing problem metaheuristic for examining wide solution neighborhoods

This paper examines a practical transportation model known as the open vehicle routing problem (OVRP). OVRP aims at designing the minimum cost set of routes originating from a central depot for satisfying customer demand. Vehicles do not need to return to the depot after completing their delivery services. In methodological terms, we propose an innovative local search metaheuristic which examines wide solution neighborhoods. To explore these wide neighborhoods within reasonable computational effort, local search moves are statically encoded into static move descriptor (SMD) entities. When a local search operator is applied to the candidate solution, only a limited solution part is modified. Therefore, to explore the next neighborhood only the tentative moves that refer to this affected solution part have to be re-evaluated, or in other words, only a subset of the SMD instances has to be updated, according to the modified solution state. The conducted search is efficiently performed by storing the SMD entities in Fibonacci heaps, which are special priority queue structures offering fast minimum retrievals, insertions and deletions. To diversify the search, we employ a tabu scheme and a penalization strategy, both compatible with the SMD design. The proposed metaheuristic was tested on well-known OVRP instances, for two objective configurations. The first one primarily aims at minimizing the number of routes and secondarily minimizing the routing cost, whereas the second one only aims at minimizing the cost of the generated route set. For both configurations, it managed to produce fine results improving several previously best-known solutions.

An effective local search approach for the Vehicle Routing Problem with Backhauls

This paper deals with a practical transportation model known as the Vehicle Routing Problem with Backhauls (VRPB), which aims at designing the minimum cost route set for satisfying both delivery and pick-up demands. In methodological terms, we propose a local search metaheuristic which explores rich solution neighborhoods composed of exchanges of variable-length customer sequences. To efficiently investigate these rich solution neighborhoods, tentative local search move are statically encoded by data structures stored in Fibonacci Heaps which are special priority queue structures offering fast minimum retrieval, insertion and deletion capabilities. To avoid cycling phenomena and induce diversification, we introduce the concept of promises, which is a parameter-free mechanism based on the regional aspiration criterion used in Tabu Search implementations. The proposed metaheuristic development was tested on well-known VRPB benchmark instances. It exhibited fine performance, as it consistently generated the best-known solutions for all the examined benchmark problems.

Integrated distribution and loading planning via a compact metaheuristic algorithm

The present article examines a vehicle routing problem integrated with two-dimensional loading constraints, called 2L-CVRP. The problem is aimed at generating the optimal route set for satisfying customer demand. In addition, feasible loading arrangements have to be determined for the transported products. To solve 2L-CVRP, we propose a metaheuristic solution approach. The basic advantage of our approach lies at its compact structure, as in total, only two parameters affect the algorithmic performance. To optimize the routing aspects, we propose a local-search method equipped with an effective diversification component based on the regional aspiration criteria. The problem’s loading requirements are tackled by employing a two-dimensional packing heuristic which repetitively attempts to develop feasible loading patterns. These attempts are effectively coordinated via an innovative, simple-structured memory mechanism. The overall solution framework makes use of several memory components for drastically reducing the computational effort required. The performance of our metaheuristic development has been successfully evaluated on benchmark instances considering two distinct versions of the loading constraints. More specifically, the algorithm managed to improve or match the majority of best known solution scores for both problem versions.