Given a graph G together with a capacity function c : V (G) → N, we call S ⊆ V (G) a capacitated dominating set if there exists a mapping f : (V (G) \ S) → S which maps every vertex in (V (G) \S) to one of its neighbors such that the total number of vertices mapped by f to any vertex v ∈ S does not exceed c(v). In the Planar Capacitated Dominating Set problem we are given a planar graph G, a ca...

We consider the single item capacitated lot–sizing problem, a well-known production planning model that often arises in practical applications, and derive new classes of valid inequalities for it. We first derive new, easily computable valid inequalities for the continuous 0–1 knapsack problem, which has been introduced recently and has been shown to provide a useful relaxation of mixed 0-1 int...

The problem of finding a Capacitated Minimum Spanning Tree asks for connecting a set of client nodes to a root node through a minimum cost tree network, subject to capacity constraints on all links. This paper reports on our design, implementation and performance evaluation of a hybrid Ant Colony Optimization algorithm for finding Capacitated Minimum Spanning Trees. Our Ant Colony Optimization ...

In a geometric k-clustering problem the goal is to partition a set of points in R into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S: given a query box Q and an integer k > 2, compute an optimal k-clustering for S ∩Q. We obtain the following results. – We present a general method to...

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...

We demonstrate the use of Ant Colony System (ACS) to solve the capacitated vehicle routing problem associated with collection of recycling waste from households, treated as nodes in a spatial network. For networks where the nodes are concentrated in separate clusters, the use of k-means clustering can greatly improve the efficiency of the solution. The ACS algorithm is extended to model the use...

The soft-clustered vehicle-routing problem is a variant of the classical capacitated (CVRP) in which customers are partitioned into clusters and all same cluster must be served by vehicle. We introduce novel symmetric formulation clustering part modeled with an asymmetric sub-model. solve new model branch-and-cut algorithm exploiting some known valid inequalities for CVRP that can adapted. In a...

k-median is a classic optimization problem which has been studied extensively in the last few decades. The current best known approximation ratio for this problem is (2.675 + ). A more generalized version of this problem also considers the capacities of the given facilities. That is, each facility cannot serve more clients than its own capacity. Unfortunately, there is no known constant-factor ...

In this paper, we deal with a network design problem arising from the deployment of synchronous optical networks (SONET), a standard of transmission using optical fiber technology. The problem is to find an optimal clustering of traffic demands in the network such that the total number of node assignments (and, hence, add–drop multiplexer equipment requirements) is minimized, while satisfying t...