A Very Large-Scale Neighborhood Search Algorithm for the Combined Through-Fleet-Assignment Model

The fleet-assignment model (FAM) for an airline assigns fleet types to the set of flight legs that satisfies a variety of constraints and minimizes the cost of the assignment. A through connection at a station is a connection between an arrival flight and a departure flight at the station, both of which have the same fleet type assigned to them, which ensures that the same plane flies both legs. Typically, passengers are willing to pay a premium for through connections. The through-assignment model (TAM) identifies a set of profitable throughs between arrival and departure flights flown by the same fleet type at each station to maximize the through benefits. TAM is usually solved after obtaining the solution from FAM. In this sequential approach, TAM cannot change the fleeting to get a better through assignment, and FAM does not take into account the through benefits. The goal of the combined through-fleet-assignment model (ctFAM) is to come up with a fleeting and through assignment that achieves the maximum combined benefit of the integrated model. We give a mixed integer-programming (MIP) formulation of ctFAM that is too large to be solved to even near optimality within allowable time for the data obtained by a major U.S. airline. We thus focus on neighborhood search algorithms for solving ctFAM, in which we start with the solution obtained by the previous sequential approach (that is, solving FAM first, followed by TAM) and improve it successively. Our approach is based on generalizing the swap-based neighborhood search approach of Talluri (1996) for FAM, which proceeds by swapping the fleet assignment of two flight paths flown by two different plane types that originate and terminate at the same stations and the same times. An important feature of our approach is that the size of our neighborhood is very large; hence the suggested algorithm is in the category of very large-scale neighborhood (VLSN) search algorithms. Another important feature of our approach is that we use integer programming to identify improved neighbors. We provide computational results that indicate that the neighborhood search approach for ctFAM provides substantial savings over the sequential approach of solving FAM and TAM.

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.

We present a very large-scale neighborhood (VLSN) search algorithm for the capacitated facility location problem with single-source constraints. The neighborhood structures are induced by customer multi-exchanges and by facility moves. We consider both traditional single-customer multi-exchanges, detected on a suitably defined customer improvement graph, and more innovative multicustomer multi-exchanges, detected on a facility improvement graph dynamically built through the use of a greedy scheme. Computational results for some benchmark instances are reported that demonstrate the effectiveness of the approach for solving large-scale problems. A further test on real data involving an Italian factory is also presented.

The past few decades have witnessed numerous applications of operations research in logistics, and these applications have resulted in substantial cost savings. However, the U.S. railroad industry has not benefited from the advances, and most of the planning and scheduling processes do not use modeling and optimization. Indeed, most of the planning and scheduling problems arising in railroads, which involve billions of dollars of resources annually, are currently being solved manually. The main reason for not using OR models and methodologies is the mathematical difficulty of these problems, which prevented the development of decision tools that railroads can use to obtain implementable solutions. However, now this situation is gradually changing. We are developing cutting-edge operations research algorithms, by using state-of-the-art ideas from linear and integer programming, network flows, discrete optimization, heuristics, and very large-scale neighborhood (VLSN) search, that railroads have already started using and from which they have started deriving immense benefits. This chapter gives an overview of the railroad planning and scheduling problems, including the railroad blocking problem, train scheduling problem, yard location problem, train dispatching problem, locomotive scheduling problem, and crew scheduling problem. Some of these problems are very large-scale integer programming problems containing billions or even trillions of integer variables. We will describe algorithms that can solve these problems to near-optimality within one to two hours of computational time. We present computational results of these algorithms on the data provided by several U.S. railroads, demonstrating potential benefits from tens to hundreds of millions annually.

Tariff concessions in production sourcing

Fleet assignment is one of the four major steps in airline planning. The objective of the fleet assignment problem (FAP) is to determine which type of aircraft should fly on each flight leg while considering different characteristics and costs associated with different fleet types. This article proposes a multiphase approach to solving the FAP. Backward arcs were used to solve basic FAPs. Then the backward arcs were eliminated by using linear programming. By allowing backward time, our formulation has a similar level of flexibility as the fleet assignment model with time-window (FAMTW), but the problem size grows much slower than FAMTW. Examples using real data obtained from a major airline are included in this article.

Very large-scale neighborhood search

The airline fleet assignment problem involves assigning aircraft to flights to maximize profit. Different fleet assignment solutions cause dramatically different performance in subsequent crew-planning and operational processes. We have developed an integrated fleet and crew robust planning method to provide fleet assignment solutions that are both friendly to crew planning and robust to real-time operations. The three challenges of this work are (1) to understand the influence of fleet assignment on crew scheduling; (2) to address crew scheduling in a tractable way in the integrated model; and (3) to achieve robustness. We address these challenges by developing a new approach that integrates crew connections within the fleet assignment model and imposes station purity by limiting the number of fleet types and crew bases allowed to serve each airport. Computational results demonstrate that the proposed approach can reduce crew-planning cost, improve robustness, and solve industrial-size problems with good computational efficiency.

Two key issues in local search algorithms are the definition of a neighborhood and the way to examine it. In this chapter we consider techniques for examining very large neighborhoods, in particular, ways for exactly searching them. We first illustrate such techniques using three paradigmatic examples. In the largest part of the chapter, we focus on the development and experimental study of very largescale neighborhood search algorithms for two coloring problems. The first example concerns the well-known (vertex) graph coloring problem. Despite initial promising results on the use of very large-scale neighborhoods, our final conclusion was negative: the usage of the proposed very large-scale neighborhoods did not help to improve the performance of effective stochastic local search algorithms. The second example, the graph set T-coloring problem, yielded more positive results. In this case, a very large-scale neighborhood that was specially tailored for this problem and that can be efficiently searched, resulted to be an essential component of a new state-of-the-art algorithm for various instance classes.

This paper addresses a multiple track vehicle (TV) scheduling problem with time window constraints (MTVSPTW) from medical supply transporting process in medical track vehicle system (MTVS). We establish a mathematical model to describe multi-TV scheduling in MTVS, which is close to the actual situation in real hospital. Based on this model, we propose a new hybrid algorithm for the MTVSPTW that executes genetic algorithm in combination with the large-scale neighborhood search algorithm (LNS-GA). Numerical experiments verify the effectiveness of the proposed method.

Constraint simplified mixed integer programming model was presented based on time transformation mechanism of no-wait flow shop. And a hybrid intelligence algorithm which combines the advantages of heuristic algorithm and neighborhood search algorithm was proposed. The initial population was generated by Johnson method, NEH method, Rajendran Method, Dannerbring method, and heuristic rules. The crossover and mutation operators in each generation were introduce neighborhood search (NS) and tabu search (TS). And the optimal individual was reserved in each generation. We compared the new hybrid intelligence algorithm (abbreviation H&NSGA ) with the algorithm blending heuristic and GA (NSGA), the algorithm blending neighborhood search and GA (HAGA), GA with the optimal individual reserved, and results show that the results and stability of solutions based on H&NSGA are better than the other three algorithms.

This paper introduces a market economics based neighborhood search and polishing algorithm to solve security constrained unit commitment (SCUC). The algorithm adaptively fixes binary and continuous variables and chooses lazy constraints based on hints from an initial solution and its associated neighborhood. A concurrent computing framework is developed to enable parallel neighborhood search and to start the algorithm from multiple initial solutions simultaneously. The initial solutions can come from historical commitments, relaxation or incumbent solutions from a MIP solver (obtained through callbacks), or any other algorithms. Testing on a large set of cases from Midcontinent Independent System Operator (MISO) (including both hourly interval and 15-min interval day ahead cases) on a high performance computing cluster with the concurrent neighborhood search and the polishing algorithm shows significant performance improvements compared to a MIP solver alone.

Service Overlay Networks (SONs) allow virtual operators to create and deploy value-added Internet services with Quality of Service guarantees, while leaving the underlying network infrastructure unchanged. The deployment of a SON can be very expensive, and hence its planning requires careful decisions, including the overlay nodes’ placement and the capacity provisioning of the access links that connect the end-users to the SON infrastructure.In this work we first propose a novel Integer Linear Programming (ILP) model for the overlay network design problem which selects the optimal number and position of overlay nodes, the capacity reserved on each overlay link, as well as the optimal routing of the incoming traffic demands.Since such model can be solved to the optimum only for small network instances, we further propose an efficient and novel tabu search based heuristic for the planning of SONs that combines polynomial size and very large-scale neighborhoods. The very large-scale neighborhood of the solution given by tabu search is explored efficiently to obtain in a short time a new one that is both far from the current solution and cost-decreasing.We provide numerical results of the proposed heuristic on a set of realistic, large-size instances, including real ISP topologies, and discuss the effect of different parameters on the characteristics of the planned networks. Furthermore, we compare such results with the bound obtained solving our ILP model in small network scenarios. We show that in the considered network topologies the proposed heuristic performs very close to the optimum with a short computation time, thus providing a promising framework for the design of SONs.

Background: Improper disposal of urban medical waste is likely to cause a series of neglective impacts. Therefore, we have to consider how to improve the efficiency of urban medical waste recycling and lowering carbon emissions when facing disposal. Methods: This paper considers the multi-cycle medical waste recycling vehicle routing problem with time windows for preventing and reducing the risk of medical waste transportation. First, a mixed-integer linear programming model is formulated to minimize the total cost consisting of the vehicle dispatch cost and the transportation costs. In addition, an improved neighborhood search algorithm is designed for handling large-sized problems. In the algorithm, the initial solution is constructed using the Clarke–Wright algorithm in the first stage, and the variable neighborhood search algorithm with a simulated annealing strategy is introduced for exploring a better solution in the second stage. Results: The computational results demonstrate the performance of the suggested algorithm. In addition, the total cost of recycling in the periodic strategy is lower than with the single-cycle strategy. Conclusions: The proposed model and algorithm have the management improvement value of the studied medical waste recycling vehicle routing problem.

After 20 years of development of multiobjective metaheuristics the procedures for solving multiple objective combinatorial optimization problems are generally the result of a blend of evolutionary, neighborhood search, and problem dependent components. Indeed, even though the first procedures were direct adaptations of single objective metaheuristics inspired by evolutionary algorithms or neighborhood search algorithms, hybrid procedures have been introduced very quickly. This paper discusses hybridations found in the literature and mentions recently introduced metaheuristic principles.