The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very large-scale neighborhood search algorithms give consistently better solutions compared the popular 2-exchange neighborhood algorithms considering both the solution time and solution accuracy.

The airline industry is notably one of the success stories with respect to the use of optimization based methods and tools in planning. Both in planning of the assignment of available aircraft to flights and in crew scheduling, these methods play a major role. Plans are usually made several months prior to the actual day of operation. As a consequence, changes often occur in the period from the construction of the plan to the day of operation. Optimization tools play an important role also in handling these changes. However, at the day of operation, no planning tool have been able to cope with the complexity of the re-planning given that the time span for proposing a solution is only a few minutes. Numerous suggestions for such subsystems have been put forward, but today no general tool is able to handle aircraft, crew, and passenger concurrently in a single system. Currently, there is a gap between the reality faced in operations control and the decision support offered by the commercial it-systems targeting the recovery process. Though substantial achievements have been made with respect to solution methods, and hardware has become much more powerful, even the most advanced prototype systems for integrated recovery have severe limitations. The current review accounts for the majority of subsystems mentioned in the literature in terms of the sub-problem addressed and the method used in each particular contribution. For each proposed system, also the computational experiments supporting the practical usability of the system is reported.

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The ability to effectively match supply and demand can result in significant revenue benefits in the airline industry, where supply and demand mismatches are common. We study the benefits of a decision postponement strategy for aircraft assignment under uncertainty. Our Demand Driven Swapping approach takes advantage of the inherent flexibilities in the system, and dynamically swaps aircraft as departures near and more accurate demand information is gathered. We analyze several swapping strategies characterized in terms of their frequency and timing. Our analytical results show that strategies that make the swapping decision early in time (so as to minimize disturbances to operations) perform very well on routes, where the demand uncertainty is low and the expected demands on the legs are well balanced. Otherwise, a swapping strategy, which revises the swapping decision over time, should be implemented. Our simulation results, based on real data obtained from United Airlines, confirm our analytical findings.

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