Bilevel programming problems are hierarchical optimization problems in which the feasible set is determined by the set of optimal solutions of a second, parametric optimization problem. In this paper we consider problems where this second problem is a discrete one. We start with addressing the problem of the existence of optimal solutions. Then, an algorithm is proposed solving these problems. ...

Many an agent needs to make a decision of what do to given a limited amount of resources. This is a discrete optimization problem. Recent advances in discrete optimization modelling technology have made it easier than ever before to model difficult ad hoc optimization problems, and apply off the shelf solving technology rapidly and efficiently, while rapid advances in discrete optimization solv...

Recently a general mathematical framework has been developed [3] for studying mathematical programming problems described by means of increasing functions, or more generally, differences of increasing functions. It has been shown in [3] that any mathematical programming problem of this class can be reduced to an equivalent problem of the following form, called canonical monotonic optimization p...

Discrete particle swarm optimization (DPSO) is a powerful stochastic evolutionary algorithm that is used to solve the large-scale, discrete and nonlinear optimization problems. However, it has been observed that standard DPSO algorithm has premature convergence when solving a complex optimization problem like transmission expansion planning (TEP). To resolve this problem an advanced discrete pa...

The paper presents the Mixed-Integer Non-Linear Programming (MINLP) approach to structural optimization. MINLP is a combined discrete/continuous optimization technique, where discrete binary 0-1 variables are defined for optimization of discrete alternatives and continuous variables for optimization of parameters. The MINLP optimization is performed through three steps: i.e. the generation of a...