The Generalized Assignment Problem (GAP) is a classic scheduling problem with many applications. We propose a branch-and-cut-and-price for that problem featuring a stabilization mechanism to accelerate column generation convergence. We also propose ellipsoidal cuts, a new way of transforming the exact algorithm into a powerful heuristic, in the same spirit of the cuts recently proposed … Read more
This paper presents a genetic algorithm for the Resource Constrained Multi-Project Scheduling Problem (RCMPSP). The chromosome representation of the problem is based on random keys. The schedules are constructed using a heuristic that builds parameterized active schedules based on priorities, delay times, and release dates defined by the genetic algorithm. The approach is tested on … Read more
Test problems are generally used to effectively evaluate the algorithms for packing problem. Based on the engineering background of the layout optimization for a retrievable satellite module, this paper describes the test problems for circles packing problem with known optimization solution first. There are N(≦217) circular objects, different in size, packed in a circular container … Read more
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more
Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal integer solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median … Read more
Internet protocol (IP) traffic follows rules established by routing protocols. Shortest path based protocols, such as Open Shortest Path First (OSPF), direct traffic based on arc weights assigned by the network operator. Each router computes shortest paths and creates destination tables used for routing flow on the shortest paths. If a router has multiple outgoing … Read more
A traffic matrix $D^1$ dominates a traffic matrix $D^2$ if $D^2$ can be routed on every (capacitated) network where $D^1$ can be routed. We prove that $D^1$ dominates $D^2$ if and only if $D^1$, considered as a capacity vector, supports $D^2$. We show several generalizations of this result. Citation Centro Vito Volterra, Universita’ di Roma … Read more
In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson. We first develop a closed-form formula to compute the probability of … Read more
In this article, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) to generate a good approximation of the efficient or Pareto optimal set of a multi-objective combinatorial optimization problem. The algorithm is applied for the 0/1 knapsack problem with r objective functions. This problem is formulated as r classic 0/1 knapsack problems. n items, … Read more
Level of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize … Read more