Variable Neighborhood Descent Procedure Research Articles

An iterated local search for a multi‐period orienteering problem arising in a car patrolling application

AbstractThis paper addresses a real‐world multi‐period orienteering problem arising in a large Italian company that needs to patrol an area in order to provide security services to a set of customers. Each customer requires different services on a weekly basis. Some services are mandatory, while others are optional. It might be impossible to perform all optional services, and each of them is assigned a score when performed. The challenge is to determine a set of routes, one per day, that maximizes a weighted sum of the total collected score and total working time, while meeting several operational constraints, including hard time windows, maximum riding time, minimum number of services performed, and minimum time between two consecutive visits for the same service at the same customer. To solve the problem, we propose an iterated local search that invokes at each iteration an inner variable neighborhood descent procedure. Computational tests performed on a large number of real‐world instances prove that the developed algorithm is very efficient, and finds in a short time solutions that are consistently better than those produced by a mathematical model, and those in use at the company.

Effective metaheuristics for the latency location routing problem

AbstractThe latency location routing problem (LLRP), a combination of the facility location problem and the cumulative capacitated vehicle routing problem, is a recently proposed variant of location routing problems. It corresponds to a customer‐centric problem, in which the aim is to minimize the sum of the arrival times at the customers. This paper proposes three novel metaheuristic algorithms to solve the LLRP. They use a simulated annealing framework, which after each temperature reduction is intensified through a variable neighborhood descent procedure. Each algorithm uses a different search strategy as intensification. Results on 76 benchmark instances indicate that the proposed metaheurstics outperform the state‐of‐the‐art algorithms, finding new best solutions for all the large‐sized instances (over 100 customers), or the currently known optimal ones for most of the small‐ and medium‐sized instances, in comparable computing times. Furthermore, in more than 80% of the instances the average value of the solutions found by the proposed algorithms is better than or equal to that of the current best known solution.

A hierarchical solution evaluation method and a hybrid algorithm for the vehicle routing problem with drones and multiple visits

Vehicle routing problem with drones (VRPD) has recently gained much traction among the research community due to its potential to improve efficiency and reduce costs for delivery. However, limited research investigates feasibility evaluation methods for the VRPD due to complex synchronization requirements between truck routes and drone trips. This paper proposes an efficient hierarchical solution evaluation method for a general VRPD problem with multiple visits (VRPD-MV), in which each vehicle is equipped with a single drone capable of serving multiple customers per trip. The endurance model is based on both the payload and flight time of the drone. The solution evaluation method decomposes a combined truck–drone route into its constituent truck segment and drone segment, which are collectively recognized as a route segment. Thereafter, efficient processing methods are developed for each segment type. We hybridize an iterative local search heuristic with a variable neighborhood descent procedure (ILS-VND) to solve the VRPD-MV. The algorithm obtains promising computational results in reasonable times for the VRPD-MV. Specifically, the proposed evaluation method is shown to accelerate the feasibility evaluation of a solution and reduce the time complexity to O(1) independent of the length of the route. The computational results also show a positive impact of powerful drones on reducing solution costs. Lastly, the ILS-VND outperforms a state-of-the-art algorithm on the multi-visit traveling salesman problem with multi-drones in terms of both solution qualities and computational times required.

Metaheuristics with restart and learning mechanisms for the no-idle flowshop scheduling problem with makespan criterion

The no-idle permutation flowshop scheduling problem (NIPFSP) extends the well-known permutation flowshop scheduling problem, where idle time is not allowed on the machines. This study proposes a new mixed-integer linear programming (MILP) model and a new constraint programming (CP) model for the NIPFSP with makespan criterion. To the best of our knowledge, this study presents a CP model for the NIPFSP for the first time in the literature. We also compare the performance of the proposed MILP and CP models with a well-known MILP model from the literature. Since the studied problem is NP-hard, we also develop a new iterated greedy algorithm with restart and learning mechanisms (IG_RL) and a new iterated local search with restart and learning mechanisms (ILS_RL) as metaheuristics for the problem. In the proposed algorithms, all the parameters are determined by a learning mechanism in a self-adaptive way. Furthermore, a restart mechanism is employed in the proposed IG_RL and ILS_RL algorithms to guarantee the variety of the initial solutions and to assist the algorithm in avoiding the local optima. A variable neighborhood descent procedure is also embedded in the proposed algorithms. We use two well-known benchmark sets, i.e., VRF and Ruiz benchmark suites, to evaluate the performance of proposed solution methods. For almost half of the 240 small VRF instances, optimal results are reported by the MILP and CP models, whereas time-limited model results are reported for the rest. The results on small instances show that the proposed MILP and CP models outperform the MILP model from literature, where the CP model performs better than both MILP models. We compare the performance of the proposed IG_RL and ILS_RL algorithms with the state-of-the-art metaheuristics from the literature on both large VRF instances and Ruiz benchmark instances. The computational results show the effectiveness and superiority of the proposed ILS_RL and IG_RL algorithms for solving the NIPFSP. Primarily, this study improves the current best-known solutions for 102 out of the 250 Ruiz benchmark instances. Additionally, this study reports the NIPFSP results for the well-known VRF benchmark set for the first time in the literature.

A hybrid iterated local search heuristic for the traveling salesperson problem with hotel selection

Companies have given close attention to new ways to reduce operational costs, and a way to achieve this point is focusing on optimizing the planning of routes. A variant of the traveling salesperson problem (TSP), called the traveling salesperson problem with hotel selection, was introduced in the last years. Herein, the salesperson needs to visit all customers just once, ensuring that a length-traveled daily not exceeds a length limit constraint. If necessary, a hotel can be used to connect tours on different days. This work proposes a hybrid Iterated Local Search heuristic using a random variable neighborhood descent procedure with a variable perturbation procedure. Furthermore, to perform better, a data mining technique is sporadically executed to construct new solutions based on patterns extracted by frequent itemset mining. Computational experiments show the potential of this algorithm to significantly improve the number of best known solutions when using the same computational time of the principal works available in literature.

Iterated local search for the generalized independent set problem

The generalized independent set problem (GISP) can be conceived as a relaxation of the maximum weight independent set problem. GISP has a number of practical applications, such as forest harvesting and handling geographic uncertainty in spatial information. This work presents an iterated local search (ILS) heuristic for solving GISP. The proposed heuristic relies on two new neighborhood structures, which are explored using a variable neighborhood descent procedure. Experimental results on a well-known GISP benchmark indicate our proposal outperforms the best existing heuristic for the problem. In particular, our ILS approach was able to find all known optimal solutions and to present new improved best solutions.

An iterated greedy algorithm with variable neighborhood descent for the planning of specialized diagnostic services in a segmented healthcare system

In this paper, a problem arising in the planning of specialized diagnostic services in a segmented public healthcare system is addressed. The problem consists of deciding which hospitals will provide the service and their capacity levels, the allocation of demand in each institution, and the reallocation of uncovered demand to other institutions or private providers, while minimizing the total equivalent annual cost of investment and operating cost required to satisfy all the demand. An associated mixed-integer linear programming model can be solved by conventional branch and bound for relatively small instances; however, for larger instances the problem becomes intractable. To effectively address larger instances, a hybrid metaheuristic framework combining iterated greedy (IGA) and variable neighborhood descent (VND) components for this problem is proposed. Two greedy construction heuristics are developed, one starting with an infeasible solution and iteratively adding capacity and the other starting with a feasible, but expensive, solution and iteratively decrease capacity. The iterated greedy algorithm includes destruction and reconstruction procedures. Four different neighborhood structures are designed and tested within a VND procedure. In addition, the computation of local search components benefit from an intelligent exploitation of problem structure since, when the first-level location variables (hospital location and capacity) are fixed, the remaining subproblem can be solved efficiently as it is very close to a transshipment problem. All components and different strategies were empirically assessed both individually and within the IGA-VND framework. The resulting metaheuristic is able to obtain near optimal solutions, within 3% of optimality, when tested over a data base of 60- to 300-hospital instances.

The Multiple Traveling Salesman Problem with Backup Coverage

We consider a variant of the classical Multiple Traveling Salesmen Problem in which the distance between any two vehicles is never greater than a fixed distance D. This new feature allows salesmen to help each other timely if an emergency happens, with an estimated backup response time related to D. To achieve this goal, a spatial and temporal synchronization is required, and it incorporates routes interdependence difficulties to be overcomed. A Genetic Algorithm and a Local Search Genetic Algorithm that embodies a Variable Neighborhood Descent procedure are proposed to solve this problem. Computational results are reported on modified benchmark instances taken from TSPLIB in order to exhibit prospects of the proposed algorithms. Through an analysis of results, the highly effective performance of our proposed Local Search Genetic Algorithm is shown in comparison to the classical Genetic Algorithm.

Adaptive Tabu search and variable neighborhood descent for packing unequal circles into a square

This paper proposes a hybrid metaheuristic for Packing Unequal Circles into a Square (PUCS), denoted by Adaptive Tabu search and Variable Neighborhood Descent (ATS-VND). The metaheuristic is an adaptive combination of Tabu search (TS) and Variable Neighborhood Descent (VND). It is also an extension to TS-VND (Tabu search and Variable Neighborhood descent). Supplementary neighborhoods (SNs) used in VND procedures are often complex and time-consuming. To reduce the employments of SNs in TS-VND, the metaheuristic proposes an adaptive tradeoff mechanism. It divides the unitary VND procedure and TS procedure into different levels respectively, and schedules them dynamically according to their efficiencies. Since VND procedures that use complex SNs are only scheduled when other more efficient options have failed, their employments are reduced considerably. The metaheuristic is applied to the problem of Packing Unequal Circles into a Square (PUCS), and enhanced by an Iterated Local search (ILS) framework to form the final IATS-VND algorithm. Experimental results show that IATS-VND is effective to the problem. For a total of 68 instances chosen from two well established benchmark sets, it improves the world records on 60 instances and matches the other 8 within a reasonable time. Further experimental results also show that the new adaptive mechanism reduces the employments of supplementary neighborhoods considerably, and hence can improve the efficiency of TS-VND. Although we only use the hybrid metaheuristic for PUCS, the basic idea is general and may be applicable to other similar problems.

A hybrid iterated local search heuristic for the maximum weight independent set problem

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.

Pickup and Delivery Service with Manpower Planning in Hong Kong Public Hospitals

This paper deals with a real-life healthcare problem derived from the Non-Emergency Ambulance Transfer Service for Hong Kong public hospitals which provides transportation services for disabled or elderly patients between their residences and clinics. The problem is modeled as a multitrip pickup and delivery problem with time windows and manpower planning (MTPDPTW-MP) that not only needs to design and schedule ambulance routes satisfying a series of constraints but also requires staff scheduling. Because of the strict limits on route duration, each ambulance traverses several routes per day, which, starting and terminating at the depot, complete a series of pickup and delivery operations to serve the clients. A feasible route demands a driver and several assistants to serve the clients and needs to satisfy some constraints, such as capacity, pickup before delivery, time windows, etc. The objective is hierarchical in that it primarily serves as many clients as possible, then minimizes the operational cost, and finally strikes a balance for the staff workload. Theoretically, MTPDPTW-MP, which is a combination of two well known NP-hard problems (i.e., the pickup and delivery problem with time windows and the staff scheduling problem), is difficult to solve. In this study, we propose an iterated local search metaheuristic that uses a variable neighborhood descent procedure in the local search phase. We use a modified regret insertion method to construct solutions; a heuristic backtracking algorithm is designed to schedule staff. To speed up the process, we adapt the segment-based evaluation for moves and reduce the neighborhoods explored based on the characteristics of the problem. The effectiveness of the proposed algorithm was tested in real-world instances. Results showed that it can serve more requests than the manually designed plans. In addition, the performance of the proposed algorithm was evaluated on a simplified problem: the multitrip vehicle routing problem with time windows.

Automatic instantiation of a Variable Neighborhood Descent from a Mixed Integer Programming model

In this paper we describe the automatic instantiation of a Variable Neighborhood Descent procedure from a Mixed Integer Programming model. We extend a recent approach in which a single neighborhood structure is automatically designed from a Mixed Integer Programming model using a combination of automatic extraction of semantic features and automatic algorithm configuration. Computational results on four well-known combinatorial optimization problems show improvements over both a previous model-derived Variable Neighborhood Descent procedure and the approach with a single automatically-designed neighborhood structure.

A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines

Production scheduling of open-pit mines is an important problem arising in surface mine planning as it determines the raw materials to be produced yearly over the life of the mine, assesses the value of the mine, and contributes to the sustainable utilization of mineral resources. Finding the optimal schedule is a complex task, involving large data sets and multiple constraints. This paper introduces a two-phase hybrid solution method. The first phase relies on solving a series of linear programming problems to generate an initial solution. In the second phase, a variable neighborhood descent procedure is applied to improve the solution. Upper bounds provided by CPLEX are used to evaluate the efficiency of the proposed method. Its performance is also assessed by comparing it to recent solution methods proposed in the literature and to an alternate method implemented in commercial mine planning software commonly used by professional mine planners. The results of these computational experiments indicate the efficiency of the proposed method and its superiority over the other methods. It finds excellent solutions (within less than 3.2 % of optimality on average) for large instances of the problem in a few seconds up to a few minutes. It also provides new best-known solutions for benchmark instances from the literature, and it can solve instances recently-published algorithms have found intractable.

A multi-criteria master production scheduling approach for special purpose machinery

This paper presents a multi-criteria master production scheduling approach as the final assembly of special purpose machines is known to be very cost intensive. These costs are mainly influenced by the master production schedule (MPS). Two major cost drivers arise. First, long assembly lead-times (up to several months) combined with high product values result in high capital commitments; thus, lead-times need to be minimized. Moreover, the factory calendar must be considered while calculating the MPS because the factory calendar can significantly influence the resulting lead-times. Second, contractual penalties and compensation costs arise if confirmed delivery dates cannot be kept. Therefore, resource requirements must be accounted for, and an MPS that is executable on the assembly shop floor must be calculated. To increase planning flexibility, we do not restrict the resource utilization with a formal constraint; instead, we introduce the additional objective of resource leveling. Consequently, the conflicting objectives lead-time minimization and resource leveling are integrated into a single objective function, in which the decision maker's preferences are represented by a weighting factor. To calculate such an MPS, we develop a tailor-made construction heuristic combined with a randomized variable neighborhood descent procedure. We evaluate our solution method by solving small instances with a commercial solver and large-scale instances from an application case of an aerospace company. Our results reveal that the decision maker's preferences are adequately reflected by the weighting factor. Moreover, we can provide a rule of thumb for selecting an appropriate initial weighting factor.

A Hybrid PSO Algorithm for Vehicle Routing Problem with Simultaneous Delivery and Pickup

In this paper a hybrid algorithm named IPSO-VND is proposed and applied to solving the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The IPSO-VND algorithm combines two meta-heuristics: Improved Particle Swarm Optimization (IPSO) is used to find a group of excellent solutions, and then the Variable Neighborhood Descent (VND) is implemented to deeply search to achieve the optimal solution around these solutions. During the IPSO procedure, in order to make up for the change of a particle’s position, a velocity component is added to the movement of any particle which has been optimized or made feasible. During the VND procedure, three different neighborhood structures: insertion, swap and cross are successively used. Computational results on the benchmark problems show that our IPSO-VND algorithm is effective.

Vehicle Routing Problem with Time Windows for Reducing Fuel Consumption

Most of the studies on vehicle routing problem with time windows (VRPTW) aim to minimize total travel distance or travel time. This paper presents the VRPTW with a new objective function of minimizing the total fuel consumption. A mathematical model is proposed to formulate this problem. Then, a novel tabu search algorithm with a random variable neighborhood descent procedure (RVND) is given, which uses an adaptive parallel route construction heuristic, introduces six neighborhood search methods and employs a random neighborhood ordering and shaking mechanisms. Computational experiments are performed on realistic instances which shed light on the tradeoffs between various parameters such as total travel distance, total travel time, total fuel consumption, number of vehicles utilized and total wait time. The results show that the solution of minimizing total fuel consumption has the potential of saving fuel consumption contrary to the solution of the traditional VRPTW, and is beneficial to develop environmental-friendly economies.

An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem

This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP is $\mathcal{NP}$ -hard since it is a generalization of the classical Vehicle Routing Problem (VRP), in which clients are served by a heterogeneous fleet of vehicles with distinct capacities and costs. The objective is to design a set of routes in such a way that the sum of the costs is minimized. The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase. To the best of our knowledge, this is the first ILS approach for the HFVRP. The developed heuristic was tested on well-known benchmark instances involving 20, 50, 75 and 100 customers. These test-problems also include dependent and/or fixed costs according to the vehicle type. The results obtained are quite competitive when compared to other algorithms found in the literature.

Single machine scheduling to minimize maximum lateness subject to release dates and precedence constraints

This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within 1 minute of CPU time.

A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery

This paper presents a parallel approach for solving the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). The parallel algorithm is embedded with a multi-start heuristic which consists of a variable neighborhood descent procedure, with a random neighborhood ordering (RVND), integrated in an iterated local search (ILS) framework. The experiments were performed in a cluster with a multi-core architecture using up to 256 cores. The results obtained on the benchmark problems, available in the literature, show that the proposed algorithm not only improved several of the known solutions, but also presented a very satisfying scalability.