Large Neighborhood Search Framework Research Articles

Adaptive Constraint Partition Based Optimization Framework for Large-Scale Integer Linear Programming (Student Abstract)

Integer programming problems (IPs) are challenging to be solved efficiently due to the NP-hardness, especially for large-scale IPs. To solve this type of IPs, Large neighborhood search (LNS) uses an initial feasible solution and iteratively improves it by searching a large neighborhood around the current solution. However, LNS easily steps into local optima and ignores the correlation between variables to be optimized, leading to compromised performance. This paper presents a general adaptive constraint partition-based optimization framework (ACP) for large-scale IPs that can efficiently use any existing optimization solver as a subroutine. Specifically, ACP first randomly partitions the constraints into blocks, where the number of blocks is adaptively adjusted to avoid local optima. Then, ACP uses a subroutine solver to optimize the decision variables in a randomly selected block of constraints to enhance the variable correlation. ACP is compared with LNS framework with different subroutine solvers on four IPs and a real-world IP. The experimental results demonstrate that in specified wall-clock time ACP shows better performance than SCIP and Gurobi.

Modeling and solving a multi-trip multi-distribution center vehicle routing problem with lower-bound capacity constraints

Vehicle routing problem (VRP) for delivering goods from distribution centers to customers is one of the main operations in logistics. Optimizing route plans for vehicles allows companies to save a huge amount of operational costs. The VRP problem is also one of the most studied problems in the domain of operations research. There are several variants of the VRP problem that have been considered in the literature. This paper proposes a new variant of the vehicle routing problem taking into account most of the well-studied features, especially with a new constraint on the lower bound of the capacity of vehicles which has not been investigated in the literature. The problem requirements come from one of the biggest dairy distribution companies in Vietnam. With over 1000 customer points included in a plan on average, the company takes at least one working day to make a route plan. We formulate the considered problem as a mixed-integer linear programming problem, analyze the challenges of the lower-bound capacity constraints and propose an adaptive large neighborhood search framework for solving it. Experimental results on large realistic and randomly generated instances show the efficiency and the applicability of the proposed method. The application of the proposed method led to the rapidity in generating the solution; this task that used to take one day is decreased to just two hours.

A Coordinated Vehicle-Drone Arc Routing Approach Based on Improved Adaptive Large Neighborhood Search.

Through urban traffic patrols, problems such as traffic congestion and accidents can be found and dealt with in time to maintain the stability of the urban traffic system. The most common way to patrol is using ground vehicles, which may be inflexible and inefficient. The vehicle–drone coordination maximizes utilizing the flexibility of drones and addresses their limited battery capacity issue. This paper studied a vehicle–drone arc routing problem (VD-ARP), consisting of one vehicle and multiple drones. Considering the coordination mode and constraints of the vehicle–drone system, a mathematical model of VD-ARP that minimized the total patrol time was constructed. To solve this problem, an improved, adaptive, large neighborhood search algorithm (IALNS) was proposed. First, the initial route planning scheme was generated by the heuristic rule of “Drone-First, Vehicle-Then”. Then, several problem-based neighborhood search strategies were embedded into the improved, adaptive, large neighborhood search framework to improve the quality of the solution. The superiority of IALNS is verified by numerical experiments on instances with different scales. Several critical factors were tested to determine the effects of coordinated traffic patrol; an example based on a real road network verifies the feasibility and applicability of the algorithm.

Robust eBuses Charging Location Problem

The implementation of a sustainable and efficient electric bus (eBus) transportation network requires addressing multiple concerns, such as limited driving range and battery charging/discharging time. Currently, eBuses can travel between 200 to 300 km on a single charge, and fast charging stations can fully recharge a battery in a matter of minutes. However, a failure in a charging station might negatively impact the operation of the system with unnecessary delays for the users. Taking this into account, we propose and implement a model for the Robust eBuses Charging Location problem that takes into account potential vulnerabilities of the transportation system. Our model incorporates a protection mechanism that allows eBuses to reach a backup charging station in case the regular one is down. We propose a MIP model to tackle this problem with minimal disruptions in the regular operation of the eBuses. Furthermore, we also present a Large Neighbourhood Search framework to efficiently tackle the problem. Our empirical evaluation suggests that our framework can operate a robust service with a small number of charging stations for three Irish cities and our Large Neighbourhood Search approach largely outperforms a popular commercial MIP solver.

Constraint Logic Programming for Real-World Test Laboratory Scheduling

The Test Laboratory Scheduling Problem (TLSP) and its subproblem TLSP-S are real-world industrial scheduling problems that are extensions of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, TLSP includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. For TLSP-S such a grouping is already part of the input. In this work, we show how TLSP-S can be solved by Answer-set Programming extended with ideas from other constraint solving paradigms. We propose a novel and efficient encoding and apply an answer-set solver for constraint logic programs called clingcon. Additionally, we utilize our encoding in a Very Large Neighborhood Search framework and compare our methods with the state of the art approaches. Our approach provides new upper bounds and optimality proofs for several existing benchmark instances in the literature.

A heuristic and a benchmark for the stowage planning problem

The stowage planning problem has recently gained the attention of a number of academic researchers. Unfortunately, many of the published works are either based on oversimplified assumptions or on confidential data. This practice hinders the research field from growing. In this paper, we present a novel set of realistic vessel data along with a set of benchmark instances. Moreover, a formal definition of a single-port stowage planning problem, based on the current state of the art, is presented. The proposed optimisation problem is solved using a variant of the adaptive large neighbourhood search framework, where novel repair and destroy methods are presented. Computational results show that the solution approach is able to find high-quality seaworthy stowage plans within 60 s.

The Humanitarian Pickup and Distribution Problem

Food rescue—the collection of perishable products from food suppliers who are willing to make donations, and their distribution to welfare agencies that serve individuals in need—has become increasingly widespread in recent years. This phenomenon is a result of economic crises, but it is also encouraged by the tax and good image it provides to donor companies. The problem we study in this paper focuses on the logistic challenges of a food bank that on a daily basis uses vehicles of limited capacity to distribute food collected from suppliers in the food industry to welfare agencies, under an imposed maximal traveling time. We model this problem as a routing resource allocation problem, with the aim of maintaining equitable allocations to the different agencies while delivering overall as much food as possible. We introduce an innovative objective function that satisfies desired properties of the allocation, that is easy to compute and implement within a mathematical formulation, and that balances effectiveness and equity acceptably. We present both an exact solution method and a heuristic approach, based on the large neighborhood search framework, which relies on the fact that a certain subproblem is easy to solve. Numerical experiments on several real-life and randomly generated data sets confirm that high-quality solutions may be obtained. The online appendices are available at https://doi.org/10.1287/opre.2018.1751 .

A case study of combined winter road snow plowing and de-icer spreading

In this article, we address a winter maintenance problem where the streets need to be plowed and gritted in a sequence that depends on the class of the road. The maintenance fleet includes vehicles equipped for plowing, some for spreading, and some for both at once. The objective is to complete the operations as rapidly as possible while considering street hierarchy, turn restrictions, heterogeneous speeds, and street–vehicle compatibility. An adaptive large neighborhood search framework is developed to solve the problem. Analysis of the results obtained can provide both a good basis for vehicle routing and help managers plan long-term policies and investments.

Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs

We present a parallel large neighborhood search framework for finding high quality primal solutions for general mixed-integer programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary MIPs, where subsets of the variables are fixed. In contrast to prior approaches, ours does not require a feasible starting solution. We leverage parallelism to perform multiple searches simultaneously, with the objective of increasing the effectiveness of our heuristic. We computationally compare the proposed framework with a state-of-the-art MIP solver in terms of solution quality, scalability, reproducibility, and parallel efficiency. Results show the efficacy of our approach in finding high quality solutions quickly both as a standalone primal heuristic and when used in conjunction with an exact algorithm.

A rich vehicle routing problem dealing with perishable food: a case study

This paper presents a successful application of operations research techniques in guiding the decision making process to achieve a superior operational efficiency in core activities. We focus on a rich vehicle routing problem faced by a Portuguese food distribution company on a daily basis. This problem can be described as a heterogeneous fleet site dependent vehicle routing problem with multiple time windows. We use the adaptative large neighbourhood search framework, which has proven to be effective to solve a variety of different vehicle routing problems. Our plans are compared against those of the company and the impact that the proposed decision support tool may have in terms of cost savings is shown. The algorithm converges quickly giving the planner considerably more time to focus on value-added tasks, rather than manually correct the routing schedule. Moreover, contrarily to the necessary adaptation time of the planner, the tool is quite flexible in following market changes, such as the introduction of new customers or new products.

Optimizing yard assignment in an automotive transshipment terminal

This paper studies a yard management problem in an automotive transshipment terminal. Groups of cars arrive to and depart from the terminal in a given planning period. These groups must be assigned to parking rows under some constraints resulting from managerial rules. The main objective is the minimization of the total handling time. Model extensions to handle application specific issues such as a rolling horizon and a manpower leveling objective are also discussed. The main features of the problem are modeled as an integer linear program. However, solving this formulation by a state-of-the-art solver is impractical. In view of this, we develop a metaheuristic algorithm based on the adaptive large neighborhood search framework. Computational results on real-life data show the efficacy of the proposed metaheuristic algorithm.

The double travelling salesman problem with multiple stacks – Formulation and heuristic solution approaches

This paper introduces the double travelling salesman problem with multiple stacks and presents four different metaheuristic approaches to its solution. The double TSP with multiple stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed, instead each item can be positioned in one of several rows in the container, such that each row can be considered a LIFO (last in, first out) stack, but no mutual constraints exist between the rows. Two different neighbourhood structures are developed for the problem and used with each of three local search metaheuristics. Additionally some simpler removal and reinsertion operators are used in a Large neighbourhood search framework. Finally some computational results are given along with lower bounds on the objective value.

An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions

Evolutionary algorithms adopt a natural-selection analogy, exploiting concepts such as population, combination, mutation, and selection to explore a diverse space of possible solutions to combinatorial optimization problems while, at the same time, retaining desirable properties from known solutions. This paper describes an evolutionary approach to improving solutions to mixed integer programming (MIP) models. We propose coarse-grained approaches to mutating and combining MIP solutions, both built within a large-neighborhood search framework. These techniques are then integrated within a MIP branch-and-bound framework. The resulting solution-polishing heuristic often finds significantly better feasible solutions to very difficult MIP models than do available alternatives. In contrast to most evolutionary algorithms, our polishing heuristic is domain-independent, requiring no structural information about the underlying combinatorial problem, above and beyond the information contained in the original MIP formulation.

A general heuristic for vehicle routing problems

We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP). All problem variants are transformed into a rich pickup and delivery model and solved using the adaptive large neighborhood search (ALNS) framework presented in Ropke and Pisinger [An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, to appear]. The ALNS framework is an extension of the large neighborhood search framework by Shaw [Using constraint programming and local search methods to solve vehicle routing problems. In: CP-98, Fourth international conference on principles and practice of constraint programming, Lecture notes in computer science, vol. 1520, 1998. p. 417–31] with an adaptive layer. This layer adaptively chooses among a number of insertion and removal heuristics to intensify and diversify the search. The presented approach has a number of advantages: it provides solutions of very high quality, the algorithm is robust, and to some extent self-calibrating. Moreover, the unified model allows the dispatcher to mix various variants of VRP problems for individual customers or vehicles. As we believe that the ALNS framework can be applied to a large number of tightly constrained optimization problems, a general description of the framework is given, and it is discussed how the various components can be designed in a particular setting. The paper is concluded with a computational study, in which the five different variants of the vehicle routing problem are considered on standard benchmark tests from the literature. The outcome of the tests is promising as the algorithm is able to improve 183 best known solutions out of 486 benchmark tests. The heuristic has also shown promising results for a large class of vehicle routing problems with backhauls as demonstrated in Ropke and Pisinger [A unified heuristic for a large class of vehicle routing problems with backhauls. European Journal of Operational Research, 2004, to appear].