The technical equipment developed and used in both installation and operation processes in refineries, oil and gas pipelines, and gas booster stations has always been expensive. Hence, managers at different organizational levels are keen to find methods to control and reduce these costs. Generally speaking, the operators in a gas booster station choose the operating devices without considering ...

We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of th...

GAMS Development and ARKI Consulting use Quality Assurance (QA) as an integral part of their software development and software publishing process. Research and development in the global optimization area has resulted in promising implementations. Initiated by customer demand, we have been adding three different global codes, BARON, LGO, and OQNLP, to our portfolio of nonlinear optimization solv...

This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to well-known techniques for solving ...

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MI...

This paper presents a general mathematical formulation for the simultaneous design and scheduling of multipurpose plants. The formulation is based on the Resource Task Network process representation, uses a periodic, uniform time grid, continuous-time representation and originates mixed integer nonlinear programs (MINLPs) or mixed integer linear programs (MILPs), depending on the type of tasks ...

We propose mathematical programming models for solving problems arising from planning and running an energy production process based on burning biomasses. The models take into account different aspects of the problem: determination of the biomasses to produce and/or buy, transportation decisions to convey the materials to the respective plants, and plant design. Whereas the “running model” is l...

The lift-gas allocation problem with pressure-drop constraints and well-separator routing is a mixed-integer nonlinear program considerably hard to solve. To this end, a mixed-integer linear programming formulation was developed by multidimensional piecewiselinearization of pressure drop functions using standard (CC) and logarithmic (Log) aggregated models. These models were compared by means o...

We study mixed integer nonlinear programs (MINLP)s that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is “turned off”, forces some of the decision variables to assume fixed values, and, when it is “turned on”, forces them to belong to a convex set. Many practical MINLPs contain integer ...

Decomposition models with integer variables usually decompose into a master problem that comprises all the integer variables and subproblems, which evaluate the remaining variables. Subproblems with integer variables introduce additional difficulties and require the use of nonlinear duality theory. In this paper we address the solution of a mixed integer hydrothermal coordination problem combin...