In this paper, a capacitated vehicle routing problem is discussed which occurs in the context of glass waste collection. Supplies of several different product types (glass of different colors) are available at customer locations. The supplies have to be picked up at their locations and moved to a central depot at minimum cost. Different product types may be transported on the same vehicle, howe...

In this study, we improved the variable neighborhood search (VNS) algorithm for solving uncapacitated multilevel lot-sizing (MLLS) problems. The improvement is two-fold. First, we developed an effective local search method known as the Ancestors Depth-first Traversal Search (ADTS), which can be embedded in the VNS to significantly improve the solution quality. Second, we proposed a common and e...

We present a variable neighborhood search (VNS) for the 3-staged 2-dimensional cutting stock problem employing “ruin-and-recreate”-based very large neighborhood search in which parts of the incumbent solution are destroyed and rebuilt using construction heuristics and dynamic programming. Experimental results show that for instances where the sizes of the elements are not too small compared to ...

The Vertex Separation problem (VSP) is an NP-hard problem with practical applications in VLSI design, graph drawing and computer language compiler design. VSP belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. In this paper, we propose different heuristic methods and embed them into a Variable Neighborhood S...

Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on a systematic change of neighborhoods. In recent years, a large variety of VNS strategies have been proposed. However, we have only found limited experimental comparisons among different VNS variants. This paper reviews three VNS strategies for finding near-optimal solutions for vertex-cut minimizati...

This paper considers the application of a variable neighborhood search (VNS) algorithm for finite-horizon (H stages) Markov Decision Processes (MDPs), for the purpose of alleviating the ‘‘curse of dimensionality” phenomenon in searching for the global optimum. The main idea behind the VNSMDP algorithm is that, based on the result of the stage just considered, the search for the optimal solution...

The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products...

A set of vertices S in a graph G is a clique if any two of its vertices are adjacent. The clique number ω is the maximum cardinality of a clique in G. A series of best possible lower and upper bounds on the difference, sum, ratio or product of ω and some other common invariants of G were obtained by the system AGX 2, and most of them proved either automatically or by hand. In the present paper,...

In this paper, we compare three multi-objective algorithms based on Variable Neighborhood Search (VNS) heuristic. The algorithms are applied to solve the single machine scheduling problem with sequence dependent setup times and distinct due windows. In this problem, we consider minimizing the total weighted earliness/tardiness and the total flowtime criteria. We introduce two intensification pr...

We consider the generalized version of the classical Minimum Spanning Tree problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected. We present a Variable Neighborhood Search (VNS) approach which uses three different neighborhood types. Two of them work in complementary ways in order to maximize search effectivity. Both are large ...