We show that if one can find the optimal value of an integer linear programming problem in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to (general) integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Among other things, our results...

In the rst part of the paper we present a framework for describing basic tech niques to improve the representation of a mixed integer programming problem We elaborate on identi cation of infeasibility and redundancy improvement of bounds and coe cients and xing of binary variables In the second part of the paper we discuss recent extensions to these basic techniques and elaborate on the investi...

resource limitation in zero time may cause to some profitable projects not to be selected in project selection problem, thus simultaneous project portfolio selection and scheduling problem has received significant attention. in this study, budget, investment costs and earnings are considered to be stochastic. the objectives are maximizing net present values of selected projects and minimizing v...

This paper presents a multi-start iterated local search (MS-ILS), an exact approach based on improved integer linear programming (ILP) model, and matheuristic combining the ILP with MS-ILS through solution merging for minimum capacitated dominating set (CAPMDS) problem undirected graphs. is extension of well-known problem, where there cap number nodes that each node can dominate, goal to find c...

In a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of conve...

This paper presents new structural properties for the carrier–vehicle traveling salesman problem. The authors provide a mixed-integer second-order conic optimization formulation, with associated optimality cuts based on properties, and an iterated local search (ILS) algorithm. Computational experiments instances from literature demonstrate superiority of formulation to existing models algorithm...

The location routing problem (LRP) integrates operational decisions on vehicle operations with strategic the of facilities or depots from which distribution will take place. In other words, it combines well-known (VRP) facility (FLP). Hence, LRP is an NP-hard combinatorial optimization problem, justifies use metaheuristic approaches whenever large-scale instances need to be solved. this paper, ...

This paper considers a bi-objective model for a scheduling problem of unrelated parallel batch processing machines to minimize the makespan and maximum tardiness, simultaneously. Each job has a specific size and the data corresponding to its ready time, due date and processing time-dependent machine are uncertain and determined by trapezoidal fuzzy numbers. Each machine has a specific capacity,...

Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...