1 To appear as a chapter of the Handbook of Algorithms edited by M. Abstract Integer programming is an expressive framework for modeling and solving discrete optimization problems that arise in a variety of contexts in the engineering sciences. Integer programming representations work with implicit algebraic constraints (linear equations and inequalities on integer valued variables) to capture ...

We introduce a new technique to generate good feasible points of mixedinteger nonlinear optimization problems. It makes use of the so-called inner parallel set of the relaxed feasible set, which was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101–123, as well as O. Stein, Error bounds for mixed integer nonlinear o...

banking and financial services are important parts of the service industry. quality of service in the banking industry has a close relationship with customer satisfaction service system. banks could create competitive advantage by increasing customer satisfaction and reduce costs in today's competitive environment. this paper presents a decision-making model to obtain optimum tasks assigne...

in the real world, risk and uncertainty are two natural properties in the implementation of mega projects. most projects fail to achieve the pre-determined objectives due to uncertainty. a linear integer programming optimization model was used in this work to solve a problem in order to choose the most appropriate risk responses for the project risks. a mathematical model, in which work structu...

Robust optimization is an approach for optimization under uncertainty that has recently attracted attention both from theory and practitioners. While there is an elaborate and powerful machinery for continuous robust optimization problems, results on robust combinatorial optimization and robust linear integer programs are still rare and hardly general. In a seminal paper Bertsimas and Sim [7] s...

This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998–2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear o...

In this paper, ant colony optimization for continuous domains (ACOR) based integer programming is employed for size optimization in a hybrid photovoltaic (PV)–wind energy system. ACOR is a direct extension of ant colony optimization (ACO). Also, it is the significant ant-based algorithm for continuous optimization. In this setting, the variables are first considered as real then rounded in each...

Mixed-integer nonlinear optimization problems arise in scientific and operational applications ranging from the reordering of nuclear fuel rods to the design of wireless networks. We present some novel mixed-integer nonlinear optimization applications and review existing solution techniques. We also describe some experiments with nonlinear branch-and-bound branching techniques that lead us to p...

We present a procedure for constructing a group theoretic dual problem with no duality gap to a given bounded integer programming problem. An optimal solution of this dual problem is easily determined and an optimal solution of the integer programming problem can be obtained by solving only one group optimization problem.