A set of examples of global and discrete optimization: application of Bayesian heuristic. Approach I
Volume 8, Issue 2 (1997), pp. 237–264
Pub. online: 1 January 1997 Type: Research Article Open Access
1 January 1997
1 January 1997
The following topics are important teaching operation research:
– games theory;
– decision theory;
– utility theory;
– queuing theory;
– scheduling theory;
– discrete optimization.
These topics are illustrated and the connection with global optimization is shown considering the following mathematical models:
– competition model with fixed resource prices, Nash equilibrium;
– competition model with free resource prices, Walras equilibrium;
– Inspector's problem, multi-stage game model;
– “Star War” problem, differential game model;
– “Portfolio” problem, resource investment model;
– exchange rate prediction, auto-regression-moving-average (ARMA) model;
– optimal scheduling, Bayesian heuristic model;
– “Bride's” problem, sequential statistical decisions model.
The first seven models are solved using a set of algorithms of continuous global and stochastic optimization. The global optimization software GM (see Mockus, 1996) is used. The underlying theory of this software and algorithms of solution are described in Mockus (1989, 1996). The last model is an example of stochastic dynamic programming.
For better understanding, all the models are formulated in simplest terms as “classroom” examples. However, each of these models can be regarded as simple representations of important families of real-life problems. Therefore the models and solution algorithms may be of interest for application experts, too.
The paper is split into two parts. In the part one the first five models are described. In the part two the rest three models and accompanying software are considered.