We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are compute...

In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a satisfies desired target performance? Here, we show the piecewise linear property, very common in everyday networks, allows an formulation based on mixed-integer programming. Our uncovers globa...

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...

This article addresses a general tri-objective two-echelon capacitated vehicle routing problem (2E-CVRP) to minimize the total travel cost, customers waiting times and carbon dioxide emissions simultaneously in distributing perishable products. In distributing perishable products, customers’ satisfaction is very important and is inversely proportional to the customers waiting times. The propose...

    Dynamic cellular manufacturing systems,   Mixed-integer non-linear programming,   Production planning, Manufacturing attributes   This paper presents a novel mixed-integer non-linear programming model for the design of a dynamic cellular manufacturing system (DCMS) based on production planning (PP) decisions and several manufacturing attributes. Such an integrated DCMS model with an extensi...

Purpose – To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed-integer non-linear programming (MINLP) problems. Design/methodology/approach – The platform combines features from classical non-linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around noninteger discrete-valued variables at lo...