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...

In this paper we survey recent work on the perspective reformulation approach that generates tight, tractable relaxations for convex mixed integer nonlinear programs (MINLP)s. This preprocessing technique is applicable to cases where the MINLP contains binary indicator variables that force continuous decision variables to take the value 0, or to belong to a convex set. We derive from first prin...

A campus based smart micro grid model that combined power and heat is presented. In this study, optimal scheduling of distributed generations inside these smart micro grids is determined based on demand forecasting, solar power forecasting and wind power forecasting by artificial neural network (ANN). The proposed model is then evaluated through economical efficiency, environment efficiency and...

This paper discusses an implementation of the Outer-Approximation/Equality-Relaxation algorithm for solving MINLP problems that arise in process systems engineering. The computer code DICOPT has been developed utilizing state-of-the-art optimization tools and a powerful modelling language. Computational experience in solving fifteen MINLP problems with DICOPT is reported. Applications include d...

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...

The following paper presents a mathematical formulation for the synthesis of heat exchanger networks (HEN’s), taking into account different types of heat exchangers (HE’s) and several conditions of operation. The model is developed using a disjunctive formulation into a preexistent multiperiod model. The Multiperiod-Disjunctive-MINLP was tested in an academic example comparing the results with ...

The problem of reactive power compensation in electric distribution networks is addressed this research paper from the point view combinatorial optimization using a new discrete-continuous version vortex search algorithm (DCVSA). To explore and exploit solution space, codification vector proposed, where discrete part determines nodes static compensator (D-STATCOM) will be installed, continuous ...