In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. We give a complete, non-redundant characterization of the polytope defined by the convex hull of the incidence vectors of two-capacitated spanning trees. This polytope is the intersection of the spanning tree polytope on the given ...

Many graph problems seek subsets of their vertices that maximize or minimize objective functions on the vertices. Among these are the capacitated p-median problem, the geometric connected dominating set problem, the capacitated k-center problem, and the traveling tourist problem. Prior genetic algorithms research in this area applied a simple mutation of an allele by random replacement. Recentl...

The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot...

The nongenomic action of progesterone (P) on capacitated sperm in mediating acrosomal exocytosis operates through transmembrane signal transduction involving increased intracellular calcium ions and modulation of protein kinases and phospholipid metabolism through a second messenger pathway. Conflicting views exist regarding the nature of the nongenomic receptor of P. It is thought to be a cell...

The NP-complete Vertex Cover problem has been intensively studied in the field of parameterized complexity theory. However, there exists only little work concerning important generalizations of Vertex Cover like Partial Vertex Cover, Connected Vertex Cover, and Capacitated Vertex Cover which are of high interest in theory as well as in real-world applications. So far research was mainly focused...

This paper describes a project that was done for the Shad Valley Program, where it was required to assign students to seminars so as to maximize the satisfaction of the students with their assignments. We begin by describing the problem, its inputs and constraints. Two models are proposed to determine optimal assignments. The first model is based on the Capacitated Transportation Problem and a ...

In this paper, we establish a novel duality relationship between node-capacitated multiflows and tree-shaped facility locations. We prove that the maximum value of a tree-distance-weighted maximum node-capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree, and the maximum is attained by a half-integral multiflow. Utilizing this duality, we sho...

Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of vertices that can cover all of the graph’s demand without exceeding any of the capacities. In this paper we look specifically at domination with hard-capacit...

We present an adaptation of the active-guided evolution strategies metaheuristic for the capacitated vehicle routing problem. The capacitated vehicle routing problem is a classical problem in operations research in which a set of minimum total cost routes must be determined for a fleet of identical capacitated vehicles in order to service a number of demand or supply points. The applied metaheu...