Algorithms for the proportional rounding of a nonnegative vector, and for the biproportional rounding of a nonnegative matrix are discussed. Here we view vector and matrix rounding as special instances of a generic optimization problem that employs an additive version of the objective function of Gaffke and Pukelsheim (2007). The generic problem turns out to be a separable convex integer optimi...

Mixed Integer Optimization has been a topic of active research in past decades. It has been used to solve Statistical problems of classification and regression involving massive data. However, there is an inherent degree of vagueness present in huge real life data. This impreciseness is handled by Fuzzy Sets. In this Paper, Fuzzy Mixed Integer Optimization Method (FMIOM) is used to find solutio...

We introduce a new technique to generate good feasible points of mixedinteger nonlinear optimization problems which are granular in the sense that a certain inner parallel set of their continuously relaxed feasible set is consistent. The latter inner parallel set was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101...

In many evolutionary algorithms, as fitness functions, penalty functions play an important role. In order to solve zero-one nonlinear optimization problems, a new objective penalty function is defined in this paper and some of its properties for solving integer nonlinear optimization problems are given. Based on the objective penalty function, an algorithm with global convergence for integer no...

This paper presents use of Particle Swarm Optimization (PSO) algorithm introduced by Kennedy and Eberhart [1] for solving Integer and Mixed Integer Optimization problems. In PSO, The potential solutions, called particles, are flown through the problem space by learning from the current optimal particle and its memory. PSO is started with a group of feasible solutions and a feasibility function ...

Although the Lagrangian method is a powerful dual search approach in integer programming, it often fails to identify an optimal solution of the primal problem. The p-th power Lagrangian method developed in this paper ooers a success guarantee for the dual search in generating an optimal solution of the primal integer programming problem in an equivalent setting via two key transformations. One ...

Optimization is being increasing applied to engineering design problems throughout the world. iSIGHT is a generic engineering design environment that provides engineers with an optimization toolkit of leading optimization algorithms and an optimization advisor to solve their optimization needs. This paper focuses on the key role played by the toolkit’s genetic algorithm in providing a robust, g...

Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. In this work, we present a novel algorithm for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer quadratic programming problems (B-...