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.

Mathematical programming and the optimization of computer simulations

Abstract: Mathematical programming techniques can be combined with response surface experimental design methods to optimize simulated systems. A computer simulation model has controllable input variables x i , i=1,…, n and yields responses η j , j=1,…, m. A simulation trial at a particular set of values x i k , i=1,…n produces an estimate y i k for the system response η j . This paper describes several formulations of the so-called “simulation/optimization” problem, including constrained optimization and multiple-objective optimization. It also describes several procedures for obtaining a solution to this problem, including a direct search technique, a first-order response surface method, and a second-order response surface approach. Each of these techniques combines simulation, response surface methodology, and mathematical programming.

An investigation of structural optimization in crashworthiness design using a stochastic approach

Abstract: In this paper the response surface methodology (RSM) and stochastic optimization (SO) are compared with regard to their efficiency and applicability in crashworthiness design. Optimization of simple analytic expressions and optimization of a front rail structure are the applications used to assess the respective qualities of both methods. A low detail vehicle structure is optimized to demonstrate the applicability of the methods in engineering practice. The investigations reveal that RSM is better compared to SO for fewer than 10–15 design variables. The convergence behaviour of SO improves compared to RSM when the number of design variables is increased. A novel zooming method is proposed which improves the convergence behaviour. A combination of both the RSM and the SO is efficient, stochastic optimization could be used in order to determine appropriate starting points for an RSM optimization, which continues the optimization. Two examples are investigated using this combined method.

Stochastic quasigradient methods for optimization of discrete event systems

Abstract: In this paper, stochastic programming techniques are adapted and further developed for applications to discrete event systems. We consider cases where the sample path of the system depends discontinuously on control parameters (e.g. modeling of failures, several competing processes), which could make the computation of estimates of the gradient difficult. Methods which use only samples of the performance criterion are developed, in particular finite differences with reduced variance and concurrent approximation and optimization algorithms. Optimization of the stationary behavior is also considered. Results of numerical experiments and convergence results are reported.