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. ...

Precedence constrained sequencing problem (PCSP) is related to locate the optimal sequence with the shortest traveling time among all feasible sequences. In PCSP, precedence relations determine sequence of traveling between any two nodes. Various methods and algorithms for effectively solving the PCSP have been suggested. In this paper we propose a cuckoo search algorithm (CSA) for effectively ...

We introduce a novel discrete optimization method for training in the context of a boosting framework for large scale binary classifiers. The motivation is to cast the training problem into the format required by existing adiabatic quantum hardware. First we provide theoretical arguments concerning the transformation of an originally continuous optimization problem into one with discrete variab...

We present a method for encoding unit vectors based on spherical coordinates that out-performs existing encoding methods both in terms of accuracy and encoding/decoding time. Given a tolerance ǫ, we solve a simple, discrete optimization problem to find a set of points on the unit sphere that can trivially be indexed such that the difference in angle between the encoded vector and the original a...

optimal reactive power dispatch (orpd) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. due to the stochastic behavior of loads, the orpd requires a probabilistic mathematical model. in this paper, monte carlo simulation (mcs) is used for modeling of load uncertainties in the orpd problem. the problem is formulated as a nonlinear constrained mul...

Based on introducing two optimization algorithms, group search optimization (GSO) algorithm and particle swarm optimization (PSO) algorithm, a new hybrid optimization algorithm which named particle swarm-group search optimization (PS-GSO) algorithm is presented and its application to optimal structural design is analyzed. The PS-GSO is used to investigate the spatial truss structures with discr...

This paper presents a robust hybrid improved dolphin echolocation and ant colony optimization algorithm (IDEACO) for optimization of truss structures with discrete sizing variables. The dolphin echolocation (DE) is inspired by the navigation and hunting behavior of dolphins. An improved version of dolphin echolocation (IDE), as the main engine, is proposed and uses the positive attributes of an...

The aim of this paper is to present a short survey of several new results concerning optimization of discrete inclusions. We study an optimization problem given by a discrete inclusion with end point constraints and we present several approaches concerning first and secondorder necessary optimality conditions for this problem.