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...

Throughout the history of integer programming, the field has been guided by research into solution approaches to combinatorial problems. We discuss some of the highlights and defining moments of this area. 1 Combinatorial integer programming Integer-programming models arise naturally in optimization problems over combinatorial structures, most notably in problems on graphs and general set syste...

Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: P = { (w, x) ∈ R× {0, 1}N : w ≤ f (a′x + d), b′x ≤ B } where N is a positive integer, f : R 7→ R is a concave function, a, b ∈ RN are nonnegative vectors, d is a real number and B is a positive real number. We propose a family of inequalities for the convex hull...

this paper investigates the problem of selecting and scheduling a set of projects among available projects. each project consists of several tasks and to perform each one some resource is required. the objective is to maximize total benefit. the paper constructs a mathematical formulation in form of mixed integer linear programming model. three effective metaheuristics in form of the imperialis...

Recent adaptive memory and evolutionary metaheuristics for mixed integer programming have included proposals for introducing inequalities and target objectives to guide the search. These guidance approaches are useful in intensification and diversification strategies related to fixing subsets of variables at particular values, and in strategies that use linear programming to generate trial solu...

The business environment is full of uncertainty. Allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term. In this paper, we propose a mixed singlestage R&D projects and multi-stage securities portfolio selection model. Specifically, we present a bi-objective mixed-integer stochastic programming mode...

This paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. The objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. A 0-1 mixed intege...

Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically form...

Nogood learning has proven to be an effective CSP technique critical to success in today’s top SAT solvers. We extend the technique for use in combinatorial optimization problems, as opposed to mere constraint satisfaction. In particular, we examine 0-1 integer programming (0-1 IP). Our technique generates globally valid cutting planes for the 01 IP search algorithm from information learned thr...