The reload cost spanning tree problem (RCSTP) is an NP-hard problem, where we are given a set of nonnegative pairwise demands between nodes, each edge is colored and a reload cost is incurred when a color change occurs on the path between a pair of demand nodes. The goal is to find a spanning tree with minimum reload cost. We propose a tree-nontree edge swap neighborhood for the RCSTP and an ef...

Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle and (3) the area balanced triangulation wh...

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC), which is a new variant of a recent powerful configuration checki...

An important issue in zigzag pocket machining is to design a machining strategy such that the resulting tool path requires a minimum number of tool retraction motions. The minimization is further classified as either local or global. In a local minimization, the inclination of a zigzag path is given a priori, and the goal is to partition the planar region to be machined into a minimum number of...

We describe a new neighborhood structure for the capacitated minimum spanning tree problem. This neighborhood structure is used by a local search strategy, leading to good trade-offs between solution quality and computation time. We also propose a GRASP with path-relinking heuristic. It uses a randomized version of a savings heuristic in the construction phase and an extension of the above loca...

The weighted spanning tree contraint is defined from a set of variables X and a value K. The variables X represent the nodes of a graph and the domain of a variable x ∈ X the neighbors of the node in the graph. In addition each pair (variable, value) is associated with a cost. This constraint states that the graph defined from the variables and the domains of the variables admits a spanning tre...

We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Thorough experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document t...

This paper addresses the problem of the local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics. A new technique, namely, the Lyapunov function with homogeneous derivative along solution curves has been developed to test the approximate stability of the dynamics on the center manifold. A set of convenient sufficient conditions are provided to test ...

The competition between local and global driving forces is significant in a wide variety of naturally occurring branched networks. We have investigated the impact of a global minimization criterion versus a local one on the structure of spanning trees. To do so, we consider two spanning tree structures-the generalized minimal spanning tree (GMST) defined by Dror et al. [1] and an analogous stru...

Lu = aij(x)Diju for u ∈ C(Ω). Suppose u ∈ C(Ω) is a supersolution in Ω, i.e. Lu ≤ 0. Then if φ ∈ C(Ω) satisfies Lφ > 0, we get L(u− φ) < 0 in Ω, hence by the maximum principle, u− φ does not have interior local minima in Ω. Put differently, if φ ∈ C(Ω) is such that u− φ has a local minimum at x0 ∈ Ω, then necessarily Lφ(x0) ≤ 0. Geometrically, u− φ having a local minimum at x0 means that the gr...