An extended version of Kelley’s cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley’s cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP prob...

This paper has as a major objective to present a unified overview and derivation of mixedinteger nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented firs...

This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are sufficiently close to other points already used to...

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...

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of ...

A chance constrained optimization problem over a finite distribution involves a set of scenario constraints from which a small subset can be violated. We consider the setting where all scenario constraints are mixed-integer convex. Existing works typically consider a mixed integer nonlinear programming (MINLP) formulation of this problem by introducing binary variables to indicate which constra...

Abstract : Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear BB, SMIN– BB, and the General structure Mixed Integer Nonlinear BB, GMIN– BB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twice–differentiable nonconvex functions in the continuous variables can be id...

The global optimization of mixed integer non-linear problems (MINLP), constitutes a major area of research in many engineering applications. In this work, a comparison is made between an algorithm based on Simulated Annealing (M-SIMPSA) and two Evolutionary Algorithms: Genetic Algorithms (GAs) and Evolution Strategies (ESs). Results concerning the handling of constraints, through penalty functi...

In this paper a new approach using Harmony Search (HS) algorithm is presented for placing Distributed Generators (DGs) in radial distribution systems. HS is used for multiple objective planning, to evaluate the DG placement and sizing by considering the power losses and voltage profile as objective functions. HS is operated on 12bus, 15-bus and 33-bus radial distribution system(RDS). Obtained r...