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.

Gradient-based simulation optimization

Abstract: We present a review of methods for simulation optimization In particular, we focus on gradient-based techniques for continuous optimization We demonstrate the main concepts using as an example the multidimensional newsvendor problem We also discuss mathematical techniques and results that are useful in verifying and analyzing the simulation optimization procedures

An exact penalty function method for nonlinear mixed discrete programming problems

Abstract: In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.

Multiobjective trajectory optimization by goal programming with fuzzy decisions

Abstract: A sequential goal programming approach is considered for not only well-defined flight trajectory problems but also ill-defined problems that have no feasible solutions satisfying all design requirements due to strict boundary conditions or tight path constraints. By using a time integration algorithm, trajectory optimization problems are transformed into numerical optimization problems that seek optimal control variables at discrete time points to minimize an objective function and satisfy various design constraints. By defining the target goal values of both the constraints and the objective functions and by prioritizing each goal according to its significance, the GP formulation modifies ill-defined problems as multiobjective design problems. Additionally, a fuzzy decision making method is applied for those goals that are prioritized, not precisely, but in a fuzzy manner. Numerical applications for simple ascent trajectory problems show that this method can efficiently find the trajectories when various kinds of design requirements are imposed for the ill-defined problem.

Stacking sequence optimization with genetic algorithm using a two-level approximation

Abstract: We propose a new method for laminate stacking sequence optimization based on a two-level approximation and genetic algorithm (GA), and establish an optimization model including continuous size variables (thicknesses of plies) and discrete variables (0/1 variables that represent the existence of each ply). To solve this problem, a first-level approximate problem is constructed using the branched multipoint approximate (BMA) function. Since mixed-variables are involved in the first-level approximate problem, a new optimization strategy is introduced. The discrete variables are optimized through the GA. When calculating the fitness of each member in the population of GA, a second-level approximate problem that can be solved by the dual method is established to obtain the optimal thicknesses corresponding to the each given ply orientation sequence. The two-level approximation genetic algorithm optimization is performed starting from a ground laminate structure, which could include relatively arbitrarily discrete set of angles. The method is first applied to cylindrical laminate design examples to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using a design example. With the presented method, the stacking sequence in analytical tools can be directly taken as design variables and no intermediate variables need be adopted.