Two novel extensions for the well known Ant Colony Optimization (ACO) framework are introduced here, which allow the solution of Mixed Integer Nonlinear Programs (MINLP). Furthermore, a hybrid implementation (ACOmi) based on this extended ACO framework, specially developed for complex non-convex MINLPs, is presented together with numerical results. These extensions on the ACO framework have bee...

In this article we will give a brief overview of the start-of-the-art on software for the solution of mixed integer nonlinear programs (MINLP). We establish several groupings with respect to various features and give concise individual descriptions for each solver.

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in R and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the ESTP. Our main emphasis ...

This paper contributes with a new two-stage optimization methodology to solve the problem of optimal placement and sizing solar photovoltaic (PV) generation units in medium-voltage distribution networks. The is formulated mixed-integer nonlinear programming (MINLP) model, where it combines binary variables regarding nodes PV generators will be located continuous associated power flow solution. ...

The aim of this work is to propose a mathematical programming model for the Economic Lot Scheduling Problem (ELSP) with performance decay. The main difficulties related to this model are the nonlinearities and/or nonconvexities associated with the dynamic behavior of the system with time. Firstly, the problem is formulated as a Mixed Integer Non Linear Program (MINLP), which is found to be nonc...

We present a method, based on formulation symmetry, for generating Mixed-Integer Linear Programming (MILP) relaxations with fewer variables than the original symmetric MILP. Our technique also extends to convex MINLP, and some nonconvex MINLP with a special structure. We showcase the effectiveness of our relaxation when embedded in a decomposition method applied to two important applications (m...

In this paper some high-performance mixed integer non-linear programming (MINLP) solvers in GAMS (General Algebraic Modeling System) are evaluated. AlphaECP, Baron, Dicopt and SBB are the MINLP (mixed integer non-linear programming) solvers in focus. A large test set with 250 problems is used and special attention is given to a new GAMS solver, GAMS/AlphaECP, which has recently been included in...

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...