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.

Model predictive control for freeway traffic using discrete speed limit signals

Abstract: A model predictive control (MPC) approach for freeway traffic control using discrete signals for the activation of variable speed limit panels is proposed. The discrete characteristics of the panels and some necessary constraints for their real operation are usually underestimated in the literature, so first we propose a way to include them using the macroscopic traffic model METANET within an MPC framework. For obtaining practical discrete signals, the MPC controller has to solve a highly non-linear optimization problem, including mixed-integer variables. Since solving such a problem is complex and difficult to execute in real-time, we propose some methods to obtain reasonable control actions in a limited computation time. The methods consist of first relaxing the discrete constraints for the inputs; and then, based on this continuous solution and together with different search methods, to find discrete speed limit signals that provide the best performance, keeping the number of simulations reduced. The proposed methods are tested by simulation, showing not only a good performance but also keeping the computational time reduced.

Entropy‐Based Optimal Sensor Placement for Model Identification of Periodic Structures Endowed with Bolted Joints

Abstract: The number of sensors and the corresponding locations are very important for the information content obtained from the measured data, which is a recognized challenging problem for large-scale structural systems. This article pays special attention to the sensor placement issues on a large-scale periodically articulated structure representing typical pipelines to extract the most information from measured data for the purpose of model identification. The minimal model parameter estimation uncertainties quantified by the information entropy (IE) measure is taken as the optimality criterion for sensors placement. By utilizing the inherent periodicity property of this type of structure together with the Bloch theorem, a novel tailor-made modeling approach is proposed and the computational cost required for dynamic analysis to form the IE with respect to the entire periodic structure can be dramatically reduced regardless of the number of contained periodic units. In addition, to avoid the error of dynamic modeling induced by conventional finite element method based on static shape function, the spectral element method, a highly accurate dynamic modeling method, is employed for modeling the periodic unit. Moreover, a novel discrete optimization method is developed, which is very efficient in terms of the number of function evaluations. The proposed methodology is demonstrated by both numerical and laboratory experiments conducted for a bolt-connected periodic beam model.

Reliability-based multi-objective optimization using evolutionary algorithms

Abstract: Uncertainties in design variables and problem parameters are inevitable and must be considered in an optimization task including multi-objective optimization, if reliable optimal solutions are to be found. Sampling techniques become computationally expensive if a large reliability is desired. In this paper, first we present a brief review of statistical reliability-based optimization procedures. Thereafter, for the first time, we extend and apply multi-objective evolutionary algorithms for solving two different reliability-based optimization problems for which evolutionary approaches have a clear niche in finding a set of reliable, instead of optimal, solutions. The use of an additional objective of maximizing the reliability index in a multi-objective evolutionary optimization procedure allows a number of trade-off solutions to be found, thereby allowing the designers to find solutions corresponding to different reliability requirements. Next, the concept of single-objective reliability-based optimization is extended to multi-objective optimization of finding a reliable frontier, instead of an optimal frontier. These optimization tasks are illustrated by solving test problems and a well-studied engineering design problem. The results should encourage the use of evolutionary optimization methods to more such reliability-based optimization problems.

Numerical Optimization with Real-Valued Estimation-of-Distribution Algorithms

Abstract: In this chapter we focus on the design of real–valued EDAs for the task of numerical optimization. Here, both the problem variables as well as their encoding are real values. Concordantly, the type of probability distribution to be used for estimation and sampling in the EDA is continuous. In this chapter we indicate the main challenges in this area. Furthermore, we review the existing literature to indicate the current EDA practice for real–valued numerical optimization. Based on observations originating from this existing research and on existing work in the literature regarding dynamics of continuous EDAs, we draw some conclusions about the feasibility of existing EDA approaches. Also we provide an explanation for some observed deficiencies of continuous EDAs as well as possible improvements and future directions of research in this branch of EDAs.

Covering trees and lower-bounds on quadratic assignment

Abstract: Many computer vision problems involving feature correspondence among images can be formulated as an assignment problem with a quadratic cost function. Such problems are computationally infeasible in general but recent advances in discrete optimization such as tree-reweighted belief propagation (TRW) often provide high-quality solutions. In this paper, we improve upon these algorithms in two ways. First, we introduce covering trees, a variant of TRW which provide the same bounds on the MAP energy as TRW with far fewer variational parameters. Optimization of these parameters can be carried out efficiently using either fixed–point iterations (as in TRW) or sub-gradient based techniques. Second, we introduce a new technique that utilizes bipartite matching applied to the min-marginals produced with covering trees in order to compute a tighter lower-bound for the quadratic assignment problem. We apply this machinery to the problem of finding correspondences with pairwise energy functions, and demonstrate the resulting hybrid method outperforms TRW alone and a recent related subproblem decomposition algorithm on benchmark image correspondence problems.