Very Large-scale Neighborhood Search Research Articles

Experimental analysis of algorithms for the independent quadratic assignment problem

The independent quadratic assignment problem is a variation of the well-known Koopmans–Beckman quadratic assignment problem. The model has a wide variety of applications but it is strongly NP-hard and is also hard to approximate. In this paper we present innovative and simple heuristic algorithms to optimize the problem based on the paradigms of local search, very large-scale neighborhood (VLSN) search, and local search with path-relinking. The performance of these algorithms are analyzed using results generated by extensive computational experiments. Our experimental study highlights that the strategies of path-relinking and VLSN search when worked in unison produced superior outcomes, outperforming algorithms that employ these strategies individually. This underscores the power of hybrid algorithmic approaches in solving complex optimization problems, in particular, the independent quadratic assignment problem. This is the first experimental study available on the independent quadratic assignment problem. We also have constructed (and made available) test instances with different characteristics which can be used as benchmarks in future experimental studies on the problem.

Very Large-Scale Neighborhood Search for Steel Hot Rolling Scheduling Problem With Slab Stack Shuffling Considerations

We study a steel hot rolling scheduling (HRS) problem considering slab stack shuffling (SSS), which is a kind of key issues in the steel strip production. The HRS problem is to select suitable slabs for a predefined sequence of hot rolling slots, from their respective candidate slab sets so that the number of shuffling operations of slabs is minimized. Different from the most researches, we consider a situation where there are intersections among candidate slab sets and shuffled slabs will not return original stacks. Basing on a special index method of slabs, we present an integer linear programming (ILP) to compute approximation solutions of the problem. In order to improve the solutions obtained by the ILP model, we propose a very large-scale neighborhood (VLSN) search algorithm. In the VLSN search process, the solutions of HRS problems are improved by an iteration procedure that partial solutions are interactively destroyed and repaired. In each iteration, partitioned hot rolling slots correspond to a sub-problem. In the repair operations, we propose an efficient branch-and-bound algorithm for solving sub-problem. The computational results on a number of different scale simulated instances show that the VLSN search algorithm is efficient for solving this kind of HRS problems.

Iterated local and very-large-scale neighborhood search for a novel uncapacitated exam scheduling model

We consider a novel uncapacitated exam scheduling model where the soft constraint stipulates that the exams should be spread over the periods so as to avoid adjacent conflicts as much as possible. The proposed method starts by constructing an initial feasible timetable. A two-phase method is then iterated. The first phase is a local search (LS) heuristic where two neighborhoods, ExamShift and KempeSwap, are searched using the token-ring strategy. The second phase takes as input the local optimum obtained during the first phase and performs a very-large-scale neighborhood (VLSN) search. We prove that searching the exponential neighborhood is NP-hard. Hence a polynomial-time heuristic based on reordering the periods is proposed for exploring a polynomial sized part of the neighborhood. The incumbent of the VLSN search is then perturbed and the method iterated. The practicability and effectiveness of our approach is studied by testing it on the university of Toronto benchmark instances and comparing it to an established method adapted to the new model.

Optimization-Based Very Large-Scale Neighborhood Search for Generalized Assignment Problems with Location/Allocation Considerations

This paper introduces a novel class of generalized assignment problems with location/allocation considerations that arises in several applications including retail shelf space allocation. We consider a set of items where each item may represent a family of products and a set of variable-sized knapsacks that may represent shelves, which comprise contiguous segments having distinct attractiveness. The decision-maker seeks to assign the set of items to these knapsacks, specify their segment assignments within knapsacks, and determine their total allocated space within predetermined lower/upper bounds in a fashion that maximizes a reward-based objective function. We develop an effective optimization-based very large-scale neighborhood search (VLNS), which greatly outperforms the best solution identified by CPLEX within one CPU hour, whereas general-purpose solver heuristics failed to provide feasible solutions to most of the larger instances within a time limit comparable to the VLNS algorithm run times. Our computational study was carried out on randomly generated computationally challenging instances with up to 210 items and 42 knapsacks and on a case study motivated by a shelf space allocation problem. Our results demonstrate that the proposed approach consistently produces high-quality solutions.

Integrating tabu search and VLSN search to develop enhanced algorithms: A case study using bipartite boolean quadratic programs

The bipartite boolean quadratic programming problem (BBQP) is a generalization of the well studied boolean quadratic programming problem. The model has a variety of real life applications; however, empirical studies of the model are not available in the literature, except in a few isolated instances. In this paper, we develop efficient heuristic algorithms based on tabu search, very large scale neighborhood (VLSN) search, and a hybrid algorithm that integrates the two. The computational study establishes that effective integration of simple tabu search with VLSN search results in superior outcomes, and suggests the value of such an integration in other settings. Complexity analysis and implementation details are provided along with conclusions drawn from experimental analysis. In addition, we obtain solutions better than the best previously known for almost all medium and large size benchmark instances.

A study of different metaheuristics to solve the urban transit crew scheduling problem

This paper explores different local search methods associated with the metaheuristic Iterated Local Search (ILS) to solve the Crew Scheduling Problem (CSP) of a Public Transportation System. The results from ILS were compared to those obtained in a previous work from the same authors that used the Variable Neighborhood Search (VNS). Initially, both metaheuristics were implemented using, as local search, the classical First Improvement Method, performing "guided" reallocation and exchange of crew tasks. The guided reallocation/exchange replaces random components from the classical method by searching the best position to insert the task. Further, the Very Large-scale Neighborhood Search (VLNS) technique was used as a local search procedure in the metaheuristics. This technique has substantially more neighbors than the 2-opt neighborhoods, since it performs a chain exchange of tasks from different crews. Both versions of metaheuristics were applied to a set of real data from a company operating in the city of Belo Horizonte, producing more economical schedules than those adopted by the company. The results are presented and discussed in this work.

Constrained Weapon–Target Assignment: Enhanced Very Large Scale Neighborhood Search Algorithm

Optimization problems solved using very large scale neighborhood (VLSN) search algorithms include scheduling problems, the capacitated minimum spanning tree problem, the traveling salesman problem, and weapon-target assignment (WTA). This correspondence paper presents an enhanced VLSN search algorithm for obtaining feasible solutions and constructing improvement graphs. This enhanced VLSN search algorithm solves the constrained WTA (CWTA) problem, in which the number of interceptors available to each weapon and the number of interceptors allowed to fire at each target have upper bounds. The proposed enhanced VLSN search algorithm can solve a CWTA problem with 100 targets and 100 weapons (where the upper bound on the number of interceptors for each weapon is one and both the lower and upper bounds on the number of interceptors for each target are equal to one) within an average of 3 s. This study demonstrates that the proposed Enhanced VLSN is superior to existing approaches.

A neighborhood search algorithm for the combined through and fleet assignment model with time windows

AbstractThe fleet assignment model (FAM) for an airline assigns fleet types to a set of flight legs that satisfies a variety of constraints and minimizes the cost of the assignment. The through assignment model matches inbound flight legs into a city with the outbound flight legs at the same city that are flown by the same plane types and creates through connections (that is, flight connections with one stopover). The combined through and fleet assignment model (ctFAM) integrates both the models into a single model and obtains optimal fleet and through assignments by varying both sets of decision variables simultaneously. In a recent article, Ahuja et al. (2001) proposed a very large‐scale neighborhood (VLSN) search algorithm for the ctFAM. In this article, we generalize this approach to incorporate time windows. In the model considered in this article, each flight leg has a time window associated with its departure time. The objective is to determine fleet assignment, departure time of all flight legs, and through connections between flights to minimize the total cost of fleet assignment and through connections. We call this model ctFAM with time windows or ctFAM‐TW. Allowing flexibility in the flight departure time creates greater opportunities for fleet assignment and through connections, and can reduce costs substantially. We describe the details of a VLSN search algorithm for ctFAM‐TW and also present computational results of our algorithm on the data provided by a large U.S. airline. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 160–171 2004