Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

A general parallel simulated annealing library and its application in airline industry

Abstract: To solve real-world discrete optimization problems approximately metaheuristics such as simulated annealing and other local search methods are commonly used. For large instances of these problems or those with a lot of hard constraints even fast heuristics require a considerable amount of computational time. At the same time, especially for sensitivity analyses, fast response times are necessary in real-world applications. Therefore, to speed up the computation a parallelization of metaheuristics is very desirable. We present parSA, an object-oriented simulated annealing library based on C++ and using the MPI message passing interface. It provides an automatic, transparent way of parallelizing simulated annealing. The efficient communication in parSA is the main reason for its success in several real-world applications. To demonstrate performance of parSA we address the weekly fleet assignment problem (FAP) as a real-world application. It is one of the optimization problems which occur in the process of operating an airline. Given a flight schedule and aircraft of different types (subfleets), to each flight leg a subfleet has to be assigned. Large real-world instances have been provided by internationally operating airlines. We show that our heuristic approach using our library parSA is very competitive to the commonly used integer-program (IF) approach.

On Information-Maximization Clustering: Tuning Parameter Selection and Analytic Solution

Abstract: Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it only involves continuous optimization of model parameters, which is substantially easier to solve than discrete optimization of cluster assignments. However, existing methods still involve non-convex optimization problems, and therefore finding a good local optimal solution is not straightforward in practice. In this paper, we propose an alternative information-maximization clustering method based on a squared-loss variant of mutual information. This novel approach gives a clustering solution analytically in a computationally efficient way via kernel eigenvalue decomposition. Furthermore, we provide a practical model selection procedure that allows us to objectively optimize tuning parameters included in the kernel function. Through experiments, we demonstrate the usefulness of the proposed approach.

System Reliability-Based Configuration Optimization of Trusses

Abstract: Reliability-based structural optimization (RBSO) considering probability distributions of random variables pertaining to load and strength parameters and satisfying system level reliability requirements is essential for optimization of practical structures. The computational and modeling complexities in RBSO using system level reliability constraints and the limitations of mathematical programming techniques are briefly discussed. The assessment of system reliability of real structures by the failure mode approach leads to numerous failure modes and requires complex modeling. A modified branch-and-bound algorithm is proposed to perform the system reliability assessment of discrete structures by failure-mode approach, and its computational efficiency in the optimization process is illustrated. Genetic algorithm based methodology for reliability-based configuration optimization of trusses is proposed, which satisfactorily addresses the computational and convergence problems. It is concluded that genetic alg...

Discrete stochastic optimization using variants of the stochastic ruler method

Abstract: We present two random search methods for solving discrete stochastic optimization problems. Both of these methods are variants of the stochastic ruler algorithm. They differ from our earlier modification of the stochastic ruler algorithm in that they use different approaches for estimating the optimal solution. Our new methods are guaranteed to converge almost surely to the set of global optimal solutions under mild conditions. We discuss under what conditions these new methods are expected to converge faster than the modified stochastic ruler algorithm. We also discuss how these methods can be used for solving discrete optimization problems when the values of the objective function are estimated using either transient or steady-state simulation. Finally, we present numerical results that compare the performance of our new methods with that of the modified stochastic ruler algorithm when applied to solve buffer allocation problems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

Abstract: We propose an equivalent reduction of the quantile optimization problem with a discrete distribution of random parameters to a partially integer programming problem of large dimension. The number of integer (Boolean) variables in this problem equals the number of possible values for the random parameters vector. The resulting problems can be solved with standard discrete optimization software. We consider applications to quantile optimization of a financial portfolio and show results of numerical experiments.