A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem

We address in this paper the one-commodity pickup-and-delivery traveling salesman problem, which is characterized by a set of customers, each of them supplying (pickup customer) or demanding (delivery customer) a given amount of a single product. The objective is to design a minimum cost Hamiltonian route for a capacitated vehicle in order to transport the product from the pickup to the delivery customers. The vehicle starts the route from a depot, and its initial load also has to be determined. We propose a hybrid algorithm that combines the GRASP and VND metaheuristics. Our heuristic is compared with other approximate algorithms described in Hernández-Pérez and Salazar-González [Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Transportation Science 2004;38:245–55]. Computational experiments on benchmark instances reveal that our hybrid method yields better results than the previously proposed approaches.     

A GRASP algorithm based new heuristic for the capacitated location routing problem

Abstract

In this paper, the capacitated location-routing problem (CLRP) is studied. CLRP is composed of two hard optimisation problems: the facility location problem and the vehicle routing problem. The objective of CLRP is to determine the best location of multiple depots with their vehicle routes such that the total cost of the solution is minimal. To solve this problem, we propose a greedy randomised adaptive search procedure. The proposed method is based on a new heuristic to construct a feasible CLRP solution, and then a local search-based simulated annealing is used as improvement phase. We have used a new technique to construct the clusters around the depots. To prove the effectiveness of our algorithm, several LRP instances are used. The results found are very encouraging.     

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2‐opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path‐relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best‐known solutions are made available for download and benchmarking purposes.     

A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering

The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with path-relinking heuristic for the set k-covering problem, as well as the template of a family of Lagrangean heuristics. The hybrid GRASP Lagrangean heuristic employs the GRASP with path-relinking heuristic using modified costs to obtain approximate solutions for the original problem. Computational experiments carried out on 135 test instances show experimentally that the Lagrangean heuristics performed consistently better than GRASP as well as GRASP with path-relinking. By properly tuning the parameters of the GRASP Lagrangean heuristic, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, the GRASP Lagrangean heuristic makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, when other Lagrangean strategies fail to find new improving solutions.     

A GRASP with adaptive large neighborhood search for pickup and delivery problems with transshipment

The pickup and delivery problem (PDP) has been studied extensively for applications ranging from courier, cargo and postal services, to public transportation. The work presented here was inspired by a daily route planning problem at a regional air carrier who was trying to determine the benefits of transshipment. Accordingly, a primary goal of this paper is identify the circumstances under which measurable cost saving can be achieved when one aircraft transports a request from its origin to an intermediate point and a second aircraft picks it up and delivers it to its final destination. In structuring the analysis, we describe a unique way to model this transshipment option on a directed graph and introduce a specialized two-route insertion heuristic that considers when to exploit this option. Based on the new representation, most existing heuristics for the PDP can be readily extended to handle transshipments.To find solutions, we developed a greedy randomized adaptive search procedure (GRASP) with several novel features. In the construction phase, shipment requests are inserted into routes until all demand is satisfied or no feasible insertion exists. In the improvement phase, an adaptive large neighborhood search algorithm is used to modify portions of the feasible routes. Specialized removal and insertion heuristics were designed for this purpose. In the absence of test cases in the literature, we also developed a procedure for randomly generating problem instances. Testing was done on 56 existing PDP instances which have 50 requests each, and on 50 new data sets with 25 requests each and one transshipment location. For the former, the performance and solution quality of the GRASP were comparable to the best known heuristics. For the latter, GRASP found the solutions within 1% of optimality on 88% of the instances.     

A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem

In this paper we deal with the survivable internet protocol (IP)/multi-protocol label switching (MPLS)-over-wavelength switched optical network (WSON) multi-layer network optimization problem (SIMNO). This problem entails planning an IP/MPLS network layer over a photonic mesh infrastructure whilst, at the same time, ensuring the highest availability of services and minimizing the capital expenditures (CAPEX) investments. Such a problem is currently identified as an open issue among network operators, and hence, its solution is of great interest. To tackle SIMNO, we first provide an integer linear programming (ILP) formulation which provides an insight into the complexity of its managing. Then, a greedy randomized adaptive search procedure (GRASP) with path-relinking (PR) together with a biased random-key genetic algorithm (BRKGA) are specifically developed to help solve the problem. The performance of both heuristics is exhaustively tested and compared making use of various network and traffic instances. Numerical experiments show the benefits of using GRASP instead of BRKGA when dealing with highly complex network scenarios. Moreover, we verified that the use of GRASP with PR remarkably improves the basic GRASP algorithm, particularly in real-sized, complex scenarios such as those proposed in this paper.     

GRASP with exterior path-relinking and restricted local search for the multidimensional two-way number partitioning problem

In this work, we tackle multidimensional two-way number partitioning (MDTWNP) problem by combining GRASP with Exterior Path Relinking. In the last few years, the combination of GRASP with path relinking (PR) has emerged as a highly effective tool for finding high-quality solutions for several difficult problems in reasonable computational time. However, in most of the cases, this hybridisation is limited to the variant known as interior PR. Here, we couple GRASP with the “exterior form” of path relinking and perform extensive experimentation to evaluate this variant. In addition, we enhance our GRASP with PR method with a novel local search method specially designed for the MDTWNP problem. Our computational experiments show the superiority of this approach compared with the previous best method for MDTWNP and with alternative methods for this problem that use other forms of PR.     

A GRASP approach for the extended car sequencing problem

This paper presents a solution procedure for a new variant of the Car Sequencing Problem (CSP) based on the GRASP metaheuristic. In this variant, called xCSP (extended CSP), the aim is to satisfy the hard constraints of the CSP while scheduling the maximum possible number of cars with specific options at specific times of the day in order to satisfy other production requirements. Additional constraint ratios are likewise considered that force at least a minimum specific number of consecutive options. An extension of the CSP is formalized in this paper and computational results are presented using available on-line instances that verify the good performance of a GRASP procedure defined for the xCSP.     

A GRASP with evolutionary path relinking for the truck and trailer routing problem

In the truck and trailer routing problem (TTRP) a heterogeneous fleet composed of trucks and trailers has to serve a set of customers, some only accessible by truck and others accessible with a truck pulling a trailer. This problem is solved using a route-first, cluster-second procedure embedded within a hybrid metaheuristic based on a greedy randomized adaptive search procedure (GRASP), a variable neighborhood search (VNS) and a path relinking (PR). We test PR as a post-optimization procedure, as an intensification mechanism, and within evolutionary path relinking (EvPR). Numerical experiments show that all the variants of the proposed GRASP with path relinking outperform all previously published methods. Remarkably, GRASP with EvPR obtains average gaps to best-known solutions of less than 1% and provides several new best solutions.     

A tabu search algorithm with a new neighborhood structure for the job shop scheduling problem

Tabu search (TS) algorithms are among the most effective approaches for solving the job shop scheduling problem (JSP) which is one of the most difficult NP-complete problems. However, neighborhood structures and move evaluation strategies play the central role in the effectiveness and efficiency of the tabu search for the JSP. In this paper, a new enhanced neighborhood structure is proposed and applied to solving the job shop scheduling problem by TS approach. Using this new neighborhood structure combined with the appropriate move evaluation strategy and parameters, we tested the TS approach on a set of standard benchmark instances and found a large number of better upper bounds among the unsolved instances. The computational results show that for the rectangular problem our approach dominates all others in terms of both solution quality and performance.     

A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows

This paper presents a new hybrid variable neighborhood-tabu search heuristic for the Vehicle Routing Problem with Multiple Time windows. It also proposes a minimum backward time slack algorithm applicable to a multiple time windows environment. This algorithm records the minimum waiting time and the minimum delay during route generation and adjusts the arrival and departure times backward. The implementation of the proposed heuristic is compared to an ant colony heuristic on benchmark instances involving multiple time windows. Computational results on newly generated instances are provided.     

A hybrid genetic algorithm for the phylogeny problem using path-relinking as a progressive crossover strategy

A phylogenetic tree relates taxonomic units using their similarities over a set of characteristics. Given a set of taxonomic units and their characteristics, the phylogeny problem under the parsimony criterion consists in finding a phylogenetic tree with a minimum number of evolutionary steps. We developed a hybrid genetic algorithm for the problem of building a phylogenetic tree minimizing parsimony. The algorithm combines local search with a crossover strategy based on path-relinking, an intensification technique originally used in the context of other metaheuristics such as scatter search and GRASP. Computational experiments on benchmark and randomly generated instances show that the proposed algorithm is very robust and outperforms other heuristics in terms of solution quality and running times.     

Correspondence of projected 3‐D points and lines using a continuous GRASP

The field of computer vision has experienced rapid growth over the past 50 years. Many computer vision problems have been solved using theory and ideas from algebraic projective geometry. In this paper, we look at a previously unsolved problem from object recognition, namely object recognition when the correspondences between the object and image data are not known a priori. We formulate this problem as a mixed‐integer non‐linear optimization problem in terms of the unknown projection relating the object and image, as well as the unknown assignments of object points and lines to those in the image. The global optimum of this problem recovers the relationship between the object points and lines with those in the image. When certain assumptions are enforced on the allowable projections mapping the object into the image, a proof is provided which permits one to solve the optimization problem via a simple decomposition. We illustrate this decomposition approach on some example scenarios.     

GRASP with evolutionary path-relinking for the capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter reading. A Greedy Randomized Adaptive Search Procedure (GRASP) with Path-Relinking (PR) is proposed and compared with other successful CARP metaheuristics. Some features of this GRASP with PR are (i) reactive parameter tuning, where the parameter value is stochastically selected biased in favor of those values which historically produced the best solutions in average; (ii) a statistical filter, which discard initial solutions if they are unlikely to improve the incumbent best solution; (iii) infeasible local search, where high-quality solutions, though infeasible, are used to explore the feasible/infeasible boundaries of the solution space; (iv) evolutionary PR, a recent trend where the pool of elite solutions is progressively improved by successive relinking of pairs of elite solutions. Computational tests were conducted using a set of 81 instances, and results reveal that the GRASP is very competitive, achieving the best overall deviation from lower bounds and the highest number of best solutions found.     

A variable neighborhood descent algorithm for a real waste collection problem with mobile depots

We consider a waste collection problem encountered in Due Carrare, a town located in Northern Italy. The original feature of the problem consists in the need for arranging appointments between vehicles along their routes so that small vehicles can dump their contents in the large ones and continue their work. This feature identifies the problem as a generalization of the well‐known Capacitated Arc Routing Problem (CARP). We propose a local search heuristic obtained from a variable neighborhood procedure suggested by Hertz and Mittaz (2001) for the CARP. In the Due Carrare instance, the proposed algorithm decreases the total route duration, apart from the required time for any feasible set of routes, of about 30% with respect to the routes so far adopted.     

A GRASP with path‐relinking and restarts heuristic for the prize‐collecting generalized minimum spanning tree problem

Given a graph with its vertex set partitioned into a set of groups, nonnegative costs associated to its edges, and nonnegative prizes associated to its vertices, the prize‐collecting generalized minimum spanning tree problem consists in finding a subtree of this graph that spans exactly one vertex of each group and minimizes the sum of the costs of the edges of the tree less the prizes of the selected vertices. It is a generalization of the NP‐hard generalized minimum spanning tree optimization problem. We propose a GRASP (greedy randomized adaptive search procedure) heuristic for its approximate solution, incorporating path‐relinking for search intensification and a restart strategy for search diversification. The hybridization of the GRASP with path‐relinking and restarts heuristic with a data mining strategy that is applied along with the GRASP iterations, after the elite set is modified and becomes stable, contributes to making the heuristic more robust. The computational experiments show that the heuristic developed in this work found very good solutions for test problems with up to 439 vertices. All input data for the test instances and detailed numerical results are made available from Mendeley Data.     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

A new heuristic algorithm for the circular packing problem with equilibrium constraints

The circular packing problem with equilibrium constraints is an optimization problem about simplified satellite module layout design.A heuristic algorithm based on tabu search is put forward for solving this problem.The algorithm begins from a random initial configuration and applies the gradient method with an adaptive step length to search for the minimum energy configuration.To jump out of the local minima and avoid the search doing repeated work,the algorithm adopts the strategy of tabu search.In the pr...     

A guided reactive GRASP for the capacitated multi-source Weber problem

The capacitated multi-source Weber problem entails finding both the locations of capacitated facilities on a plane and their customer allocations. A framework that uses adaptive learning and functional representation to construct the restricted candidate list (RCL) within a greedy randomized adaptive search procedure (GRASP) is put forward. An implementation of restricted regions that forbids new facilities to be located too close to the previously found facilities is also embedded into the search to build up the RCL more efficiently. The performance of this GRASP based approach is tested on three classes of instances with constant and variable capacities. Very competitive results are obtained when compared to the best known results from the literature.     

A tabu search heuristic for the truck and trailer routing problem

Two new construction heuristics and a tabu search heuristic are presented for the truck and trailer routing problem, a variant of the vehicle routing problem. Computational results indicate that the heuristics are competitive to the existing approaches. The tabu search algorithm obtained better solutions for each of 21 benchmark problems.