A three-level relief chain including a number of suppliers in fixed locations, candidate distribution centers and affected areas at certain points are considered. A mixed integer nonlinear programming model is proposed for open transportation location routing problem by considering split delivery of demand. To solve a realistic problem, foregoing parameters are considered as fuzzy in our propos...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; (c) solving the modified problem. Sometimes (b) and (c) are performed concurrently: the solution al...

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop...

zinc is the first modelling language which supports solver and technique independence. this means that a high level conceptual model can be automatically mapped into an appropriate low level design model for a specific solver or technique. to date, zinc uses three different techniques to solve a model: constraint programming (cp), local search (ls), and mixed integer programming (mip). in this ...

presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...

Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a paramete...

A variety of combinatorial problems (e.g., in capital budgeting, scheduling, allocation) can be expressed as a linear integer programming problem. However, the standard devices for doing this often produce an inordinate number of variables and constraints, putting the problem beyond the practical reach of available integer programming methods. This paper presents new formulation techniques for ...

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

The truss design problem is to nd the optimal placement and size of structural bars that can support a given load The problem is nonlinear and in the version addressed here the bars must take certain discrete sizes It is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve sub stantially larger problems than mixed integer ...