A relax-and-cut algorithm for the knapsack node weighted Steiner tree problem

The Knapsack Node Weighted Steiner Tree Problem (KNWSTP) is a generalization of the Steiner Tree Problem on graphs, which takes into account the classical cost function defined on the edges, as well as a prize function defined on the vertices and a limit on the size of the solution. It has several applications to network design. We propose an exact branch-and-bound algorithm for this problem, based on a relax-and-cut approach: the algorithm relaxes an exponential family of generalized subtour elimination constraints and takes into account only the violated ones as the computation proceeds. The performance of the algorithm has been tested on a wide set of benchmark problems, up to three hundred vertices, whose structure reflects the features of the most likely applications (sparse graphs with Euclidean costs) and covers different cases with respect to the prize function (only positive, or both positive and negative prizes) and the weight threshold

Solution of Large Weighted Equicut Problems

Given a weighted undirected graph, the equicut problem consistsof finding a partition of the vertex set into two subsets ofequal cardinality such that the sum of the weights of the edgesbelonging to the cut defined by the partition is minimized.The problem is NP-hard and has several practical applications.In recent years a number of algorithms based on metaheuristictechniques have been proposed.In this work we first present a survey of the algorithms fromthe literature, then we propose a new tabu search algorithmand compare it with the other heuristics through extensivecomputational experiments on severalclasses of graphs with up to 4,000 nodes and 320,000 edges.The results show that our approach easily determines theoptimal solution for small graphs and its average performancesare greatly superior to those of the other approximating algorithms

An Exact Algorithm for the Node Weighted Steiner Tree Problem

The Node Weighted Steiner Tree Problem (NW-STP) is a generalization of the Steiner Tree Problem. A lagrangean heuristic presented in EngevallS: StrLBN: 98, and based on the work in Lucena: 92, solves the problem by relaxing an exponential family of generalized subtour elimination constraints and taking into account only the violated ones as the computation proceeds. In EngevallS: StrLBN: 98 the computational results refer to complete graphs up to one hundred vertices. In this paper, we present a branch-and-bound algorithm based on this formulation. Its performance on the instances from the literature confirms the effectiveness of the approach. The experimentation on a newly generated set of benchmark problems, more similar to the real-world applications, shows that the approach is still valid, provided that suitable refinements on the bounding procedures and a preprocessing phase are introduced. The algorithm solves to optimality all of the considered instances up to one thousand vertices, with the exception of 11 hard instances, derived from the literature of a similar problem, the Prize Collecting Steiner Tree Problem

A note on the approximation of the Asymmetric Traveling Salesman Problem

We show that some asymmetric traveling salesman problem (ATSP) instances are approximable within bounds equal to 3 and 9/5, when they satisfy sufficient conditions more restrictive than the triangle inequality, very simple to test and nicely structured: they only depend on a measure of satisfaction of the triangle inequality and a measure of the graph asymmetry. We discuss the applicability of such conditions and we present two preprocessing linear programs to reformulate ATSP instances into equivalent ones achieving data-dependent bounds by the same approximation algorithms

Applying Tabu Search to theJob-Shop Scheduling Problem

In this paper we apply the tabu-search technique to the job shop scheduling problem , a notoriously difficult problem in combinatorial optimization. We show that our implementation of this methods dominates both a previous approach with tabu search and other heuristics based on iterative improvements

SLA Based Profit Optimization in Multi-tier Systems

Nowadays, large service centers provide Web sites hosting to many customers by sharing a pool of IT resources. The service providers and their customers negotiate utility based Service Level Agreement (SLA) to determine the costs and penalties on the base of the achieved performance level. The system is often based on a multitier architecture to service requests to dynamic pages as well as various Web services. The service provider would like to maximize the SLA revenues, while minimizing its operating costs. The system we consider is based on a centralized network dispatcher which controls the allocation of applications to servers, the request volumes at various servers and the scheduling policy at each server. The dispatcher can also decide to turn ON or OFF servers depending on the system load. This paper designs a resource allocation scheduler for such multi-tier Web environments so as to maximize the profits associated with multiple class SLAs. The overall problem is NP-hard. We develop heuristic solutions by implementing a local-search algorithm. Experimental results are presented to demonstrate the benefits of our approach

A local-search-based heuristic for the demand-constrained multidimensional knapsack problem

We consider an extension of the 0\u20131 multidimensional knapsack problem in which there are greater-than-or- equal-to inequalities, called demand constraints, in addition to the standard less-than-or-equal-to constraints. Moreover, the objective function coefficients are not constrained in sign. This problem is worth considering because it is embedded in models of practical application, it has an intriguing combinatorial structure, and it appears to be a challenging problem for commercial ILP solvers. Our approach is based on a nested tabu-search algorithm in which neighborhoods with different structures are exploited. First, a tabu-search procedure is carried out in which mainly the infeasible region is explored. Once feasibility has been established, a second tabu-search procedure, which analyzes only feasible solutions, is applied. The algorithm has been tested on a wide set of instances. Computational results are discussed

An interactive simulator of emergency management systems

We illustrate an interactive software simulator we have developed in the context of the research project "Decembria" aiming at the optimization of the use of the ambulance fleet of the "118" emergency system in the province of Milan. The simulator is GIS-based allowing for exact geocoding of points of request, correct reproduction of ambulance travels and computation of shortest paths according to graph distances, also taking into account forbidden manoeuvres and streets accessibility constraints. The graphical interface has been designed in order to allow the user assigning calls to available ambulances and ambulances to parking places with one or two clicks of a mouse button. The simulator uses historical data taken from the data-base of the "118" system in Milan. The simulator also includes on-line optimization algorithms suggesting decisions to the user in real-time. The simulator is currently in use at the "118" Operating Centre, located at the Niguarda hospital in Milan