Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP). In this article we give a compact overview of primal heuristics for MINLP that have been suggested in the literature of recent years. We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations. A brief computational experiment sh...

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation (OA) and Partial Surrogate Cuts (PSC) used for solving convex Mixed Integer Nonlinear Programing (MINLP). The scaled quadratic cut is proved to be a stricter and tighter underestimation for the convex nonlinear functions than the classical supporti...

This paper presents a structural synthesis using the Mixed-Integer Non-Linear Programming (MINLP) approach. The MINLP is a combined discrete/continuous optimization technique, where discrete binary 0-1 variables are defined for optimization of discrete alternatives and continuous variables for optimization of parameters. The MINLP optimization to a structural synthesis is performed through thre...

This paper addresses the optimal design and planning of sustainable chemical supply chains (SCs) in the presence of uncertainty in the damage model used to evaluate their environmental performance. The environmental damage is assessed through the Eco-indicator 99, which includes the recent advances made in Life Cycle Assessment (LCA). The overall problem is formulated as a bi-criterion stochast...

Optimization of Mixed-Integer Non-Linear Programming (MINLP) supports important decisions in applications such as Chemical Process Engineering. But current solvers have limited ability for deductive reasoning or the use of domain-specific theories, and the management of integrality constraints does not yet exploit automated reasoning tools such as SMT solvers. This seems to limit both scalabili...

In this paper, we present results of a recently developed global optimization method as applied to water management problems. Our method deals effectively with MINLP problems with bilinear and univariate concave terms. Bilinear terms show up in these problems as products of flow rates and concentrations in component balances. In turn, concave terms are typically associated with equipment costs.

Recently, the so-called ψ-learning approach, the Support Vector Machine (SVM) classifier obtained with the ramp loss, has attracted attention from the computational point of view. A Mixed Integer Nonlinear Programming (MINLP) formulation has been proposed for ψ-learning, but solving this MINLP formulation to optimality is only possible for datasets of small size. For datasets of more realistic ...

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art...

Discrete-continuous non-linear optimization models are frequently used to formulate problems in Process System Engineering. Major modeling alternatives and solution algorithms include generalized disjunctive programming and MINLP. Both have advantages and drawbacks depending on the problem they are dealing with. In this work, we describe the theory behind LOGMIP, a new computer code for disjunc...