Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposi...

This paper proposes on-line optimal operation planning and control of cogeneration systems (CGS). CGS is usually connected to various facilities such as refrigerators, reservoirs, and cooling towers. In order to generate optimal operation planning for CGS, startup/shutdown status and/or input/output values of the facilities for each control interval should be determined. The facilities may have...

Sudoku, the popular logic puzzle, would have a greater artistic appeal if the final completed puzzle could be transformed into an image similar to nonogram outputs. To do this, we solve a mixed-integer nonlinear programming problem (MINLP) to find the Sudoku configuration that most closely represents a target image via an integer-colour mapping. This alone produces inadequate results, so we rel...

This paper presents an optimisation model for the synthesis of heat exchanger networks (HEN) including the detailed design of the equipments formulated as a decomposition method. Shell and tube pressure drops and fouling are considered, as well as mechanical aspects, like shell and tube bundle diameters, internal and external diameter of tubes, number of tubes, number of baffles, number of shel...

This contribution proposes a Mixed Integer Non Linear Programming (MINLP) formulation for optimal design of a catalytic distillation column based on a generic nonequilibrium model (NEQ). The solution strategy for the global optimization combines Simulated Annealing (SA) and Sequential Quadratic Programming (SQP) in order to minimize the objective function. The solution of this MINLP problem yie...

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principal and a strategy of developing model-specific valid inequalities (some nonlinear), which e...

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixedinteger nonlinear programming (MINLP) formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of t...

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...