A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex t...

This paper addresses the optimal location and sizing of photovoltaic (PV) sources in isolated direct current (DC) electrical networks, considering time-varying load renewable generation curves. The mathematical formulation this problem corresponds to mixed-integer nonlinear programming (MINLP), which is reformulated via convex optimization: ensures global optimum solving resulting optimization ...

We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) rogram. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimizati...

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical...

This article presents the formulation and the solution of a class of Mixed-integer Nonlinear Programming (MINLP) problems, applied to optimal synthesis of process systems in a modular simulator environment. The proposed algorithm makes use of module, reduces the work of calculation on model equations, makes the size of MINLP smaller. The algorithm consists of solving alternate sequences of MILP...

We define difficult optimization problems as problems which cannot be solved to optimality or to any guaranteed bound by any standard solver within a reasonable time limit. The problem class we have in mind are mixed integer programming (MIP) problems. Optimization and especially mixed integer optimization is often appropriate and frequently used to model real world optimization problems. While...

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear P...

We give a short introduction to mixed-integer nonlinear programming from a linear programming perspective. In this approach, all nonlinearities are approximated by linear inequalities and spatial branching, such that in the end only linear programs remain that can be solved efficiently. We present two transportation applications from rather different fields: Railway freight on one side, and nat...

The optimal scheduling of crude-oil operation in refineries has been studied by various groups during the past decade, leading to different mixed integer linear programming or mixed nonlinear programming formulations. This paper proposes a new MINLP formulation with an oil residency time constraint and common pipeline transportation that is based on single-operation sequencing (SOS). An effecti...