this paper addresses a reliable facility location problem with considering facility capacity constraints. in reliable facility location problem some facilities may become unavailable from time to time. if a facility fails, its clients should refer to other facilities by paying the cost of retransfer to these facilities. hence, the fail of facilities leads to disruptions in facility location dec...

in this paper a new method is proposed for path planning of planar manipulators amid obstacles through mathematical programming in a way that the robot’s links avoid collision with obstacles throughout their motion from an initial to a goal configuration. after inputting the workspace geometry, the shortest feasible path for the robot’s end-effector is planned toward its goal position using gen...

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete...

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equiv...

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Becau...

Many optimization problems require the modelling of discrete and continuous variables, giving rise to mixed-integer linear and mixed-integer nonlinear programming (MILP / MINLP). An alternative representation of MINLP is Generalized Disjunctive Programming (GDP)1. GDP models are represented through continuous and Boolean variables, and involve algebraic equations, disjunctions, and logic propos...

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...

Many industrial problems can be naturally formulated using Mixed Integer Nonlinear Programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the de...

The analytical target cascading (ATC) methodology for optimizing hierarchical systems has demonstrated convergence properties for continuous, convex formulations. However, many practical problems involve both continuous and discrete design variables, resulting in mixed integer nonlinear programming (MINLP) formulations. While current ATC methods have been used to solve such MINLP formulations i...

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...