Two phased hybrid local search for the periodic capacitated arc routing problem

The periodic capacitated arc routing problem (PCARP) is a challenging general model with important applications. The PCARP has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (F_v) and a secondary objective of minimizing the total cost (F_c). In this paper, we propose an effective two phased hybrid local search (HLS) algorithm for the PCARP. The first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space. For both phases, combined local search heuristics are devised to ensure an effective exploration of the search space. Experimental results on 63 benchmark instances demonstrate that HLS performs remarkably well both in terms of computational efficiency and solution quality. In particular, HLS discovers 44 improved best known values (new upper bounds) for the total cost objective F_c while attaining all the known optimal values regarding the objective of the number of vehicles F_v. To our knowledge, this is the first PCARP algorithm reaching such a performance. Key components of HLS are analyzed to better understand their contributions to the overall performance.     

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.     

A variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit.     

Local search methods for the flowshop scheduling problem with flowtime minimization

Flowshop scheduling is a very active research area. This problem still attracts a considerable amount of interest despite the sheer amount of available results. Total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years. New best solutions have been found for common benchmarks at a rapid pace. However, these improvements many times come at the cost of sophisticated algorithms. Complex methods hinder potential applications and are difficult to extend to small problem variations. Replicability of results is also a challenge. In this paper, we examine simple and easy to implement methods that at the same time result in state-of-the-art performance. The first two proposed methods are based on the well known Iterated Local Search (ILS) and Iterated Greedy (IG) frameworks, which have been applied with great success to other flowshop problems. Additionally, we present extensions of these methods that work over populations, something that we refer to as population-based ILS (pILS) and population-based IG (pIGA), respectively. We calibrate the presented algorithms by means of the Design of Experiments (DOE) approach. Extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature. The results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective. Furthermore, we show that, despite their simplicity, the presented methods are able to improve 12 out of 120 best known solutions of Taillard’s flowshop benchmark with total flowtime criterion.     

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt^*, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.     

An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We propose an iterated local search algorithm for the vehicle routing problem with time window constraints. We treat the time window constraint for each customer as a penalty function, and assume that it is convex and piecewise linear. Given an order of customers each vehicle to visit, dynamic programming (DP) is used to determine the optimal start time to serve the customers so that the total time penalty is minimized. This DP algorithm is then incorporated in the iterated local search algorithm to efficiently evaluate solutions in various neighborhoods. The amortized time complexity of evaluating a solution in the neighborhoods is a logarithmic order of the input size (i.e., the total number of linear pieces that define the penalty functions). Computational comparisons on benchmark instances with up to 1000 customers show that the proposed method is quite effective, especially for large instances.     

The capacitated arc routing problem with refill points

This article introduces the capacitated arc routing problem with refill points (CARP-RP). The vehicle servicing arcs must be refilled on the spot by using a second vehicle. The problem consists on simultaneously determining the vehicles routes that minimize the total cost. An integer linear programming model is proposed and tested.     

Simulated annealing metaheuristics for the vehicle routing problem with time windows

This paper develops simulated annealing metaheuristics for the vehicle routing and scheduling problem with time window constraints. Two different neighborhood structures, the λ-interchange mechanism of Osman and thek-node interchange process of Christofides and Beasley, are implemented. The enhancement of the annealing process with a short-term memory function via a tabu list is examined as a basis for improving the metaheuristic approach. Computational results on test problems from the literature as well as large-scale real-world problem are reported. The metaheuristics achieve solutions that compare favorably with previously reported results.     

Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem

The vehicle routing problem (VRP) under capacity and distance restrictions involves the design of a set of minimum cost delivery routes, originating and terminating at a central depot, which services a set of customers. Each customer must be supplied exactly once by one vehicle route. The total demand of any vehicle must not exceed the vehicle capacity. The total length of any route must not exceed a pre-specified bound. Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated. A special data structure for the tabu search algorithm is implemented which has reduced notably the computational time by more than 50%. An estimate for the tabu list size is statistically derived. Computational results are reported on a sample of seventeen bench-mark test problems from the literature and nine randomly generated problems. The new methods improve significantly both the number of vehicles used and the total distances travelled on all results reported in the literature.     

EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.     

An iterated local search algorithm for the vehicle routing problem with backhauls

The Vehicle Routing Problem with Backhauls (VRPB) is an extension of the VRP that deals with two types of customers: the consumers (linehaul) that request goods from the depot and the suppliers (backhaul) that send goods to the depot. In this paper, we propose a simple yet effective iterated local search algorithm for the VRPB. Its main component is an oscillating local search heuristic that has two main features. First, it explores a broad neighborhood structure at each iteration. This is efficiently done using a data structure that stores information about the set of neighboring solutions. Second, the heuristic performs constant transitions between feasible and infeasible portions of the solution space. These transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions. An extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters. The results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the VRPB. Additionally, new best solutions have been found for two instances in one of the benchmark sets. These results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components. In particular, it shows that by expanding the exploration area and improving the efficiency of the local search heuristic, it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained.     

A comparison of three metaheuristics for the workover rig routing problem

The workover rig routing problem (WRRP) is a variant of the Vehicle Routing Problem with Time Windows (VRPTW) and arises in the operations of onshore oil fields. In this problem, a set of workover rigs located at different positions must service oil wells requesting maintenance as soon as possible. When a well requires maintenance, its production is reduced or stopped for safety reasons and some workover rig must service it within a given deadline. It is therefore important to service the wells in a timely fashion in order to minimize the production loss. Whereas for classical VRPTWs the objective is to minimize route length, in the WRRP the objective is to minimize the total lost production, equal to the sum of arrival times at the wells, multiplied by production loss rates. The WRRP generalizes the Delivery Man Problem with Time Windows by considering multiple open vehicle routes and multiple depots. This paper compares three metaheuristics for the WRRP: an iterated local search, a clustering search, and an Adaptive Large Neighborhood Search (ALNS). All approaches, in particular ALNS, have yielded good solutions for instances derived from a real-life setting.     

Heuristic solution approaches for the cumulative capacitated vehicle routing problem

Cumulative capacitated vehicle routing problem (CCVRP) is an extension of the well-known capacitated vehicle routing problem, where the objective is minimization of sum of the arrival times at nodes instead of minimizing the total tour cost. This type of routing problem arises when a priority is given to customer needs or dispatching vital goods supply after a natural disaster. This paper focuses on comparing the performances of neighbourhood and population-based approaches for the new problem CCVRP. Genetic algorithm (GA), an evolutionary algorithm using particle swarm optimization mechanism with GA operators, and tabu search (TS) are compared in terms of required CPU time and obtained objective values. In addition, a nearest neighbourhood-based initial solution technique is also proposed within the paper. To the best of authors’ knowledge, this paper constitutes a base for comparisons along with GA, and TS for further possible publications on the new problem CCVRP.     

A variable neighborhood search heuristic for periodic routing problems

The aim of this paper is to propose a new heuristic for the Periodic Vehicle Routing Problem (PVRP) without time windows. The PVRP extends the classical Vehicle Routing Problem (VRP) to a planning horizon of several days. Each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits. Hence, one has to choose the visit days for each customer and to solve a VRP for each day. Our method is based on Variable Neighborhood Search (VNS). Computational results are presented, that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature. Also considered is the special case of a single vehicle, i.e. the Periodic Traveling Salesman Problem (PTSP). It is shown that slight changes of the proposed VNS procedure is also competitive for the PTSP.     

Local search in routing problems with time windows

We develop local search algorithms for routing problems with time windows. The presented algorithms are based on thek-interchange concept. The presence of time windows introduces feasibility constraints, the checking of which normally requires O(N) time. Our method reduces this checking effort to O(1) time. We also consider the problem of finding initial solutions. A complexity result is given and an insertion heuristic is described.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

Tabu search and GRASP for the maximum diversity problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naïve ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. The constructive method can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.     

A tabu search heuristic for the vehicle routing problem with private fleet and common carrier

This paper describes a tabu search heuristic for a vehicle routing problem where the owner of a private fleet can either visit a customer with one of his vehicles or assign the customer to a common carrier. The owner’s objective is to minimize the variable and fixed costs for operating his fleet plus the total costs charged by the common carrier. The proposed tabu search is shown to outperform the best approach reported in the literature on 34 benchmark instances with a homogeneous fleet.     

A new branch-and-cut algorithm for the capacitated vehicle routing problem

We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts. For each of these classes of inequalities we describe our separation algorithms in detail. Also we describe the other important ingredients of our branch-and-cut algorithm, such as the branching rules, the node selection strategy, and the cut pool management. Computational results, for a large number of instances, show that the new algorithm is competitive. In particular, we solve three instances (B-n50-k8, B-n66-k9 and B-n78-k10) of Augerat to optimality for the first time.     

A memetic algorithm for the multiperiod vehicle routing problem with profit

In this paper, we extend upon current research in the vehicle routing problem whereby labour regulations affect planning horizons, and therefore, profitability. We call this extension the multiperiod vehicle routing problem with profit (mVRPP). The goal is to determine routes for a set of vehicles that maximizes profitability from visited locations, based on the conditions that vehicles can only travel during stipulated working hours within each period in a given planning horizon and that the vehicles are only required to return to the depot at the end of the last period. We propose an effective memetic algorithm with a giant-tour representation to solve the mVRPP. To efficiently evaluate a chromosome, we develop a greedy procedure to partition a given giant-tour into individual routes, and prove that the resultant partition is optimal. We evaluate the effectiveness of our memetic algorithm with extensive experiments based on a set of modified benchmark instances. The results indicate that our approach generates high-quality solutions that are reasonably close to the best known solutions or proven optima, and significantly better than the solutions obtained using heuristics employed by professional schedulers.