Ejection chain methods, which include the classical Lin–Kernighan (LK) procedure and the Stem-and-Cycle (S&C) reference structure, have been the source of the currently leading algorithms for large scale symmetric traveling salesman problems (STSP). Although these methods proved highly effective in generating large neighborhoods for symmetric instances, their potential application to the asymmetric setting of the problem (ATSP) introduces new challenges that require special consideration. This article extends our studies on the single-rooted S&C to examine the more advanced doubly-rooted (DR) reference structure. The DR structure, which is allied both to metaheuristics and network optimization, allows more complex network-related (alternating) paths to transition from one tour to another, and offers special advantages for the ATSP. Computational experiments on an extensive testbed exhibits superior performance for the DR neighborhood over its LK counterpart for the ATSP. We additionally show that a straightforward implementation of a DR ejection chain algorithm outperforms the best local search algorithms and obtains solutions comparable to those obtained by the currently most advanced special-purpose algorithms for the ATSP, while requiring dramatically reduced computation time. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>We show that finding a subgraph realization with the minimum generalized Randić index for a given base graph and degree sequence is solvable in polynomial time by formulating the problem as the minimum weight perfect *b*-matching problem of Edmonds (J Res Natl Bur Stand 69B (1965), 125–130). However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight perfect *b*-matching problem subject to a connectivity constraint is shown to be NP-hard. For instances in which the optimal solution to the minimum Randić index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. Although we focus on finding graph realizations with minimum Randić index, our results extend to finding graph realizations with maximum Randić index as well. Applications of the Randić index are provided to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

Given a weighted undirected graph *G* with a set of pairs of terminals (*s*_{i}, *t*_{i}),
, and an integer
, the two node-disjoint hop-constrained survivable network design problem is to find a minimum weight subgraph of *G* such that between every *s*_{i} and *t*_{i} there exist at least two node-disjoint paths of length at most *L*. This problem has applications in the design of survivable telecommunication networks with QoS-constraints. We discuss this problem from a polyhedral point of view. We present several classes of valid inequalities along with necessary and/or sufficient conditions for these inequalities to be facet defining. We also discuss separation routines for these classes of inequalities, and propose a Branch-and-Cut algorithm for the problem when *L* = 3, as well as some computational results. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

We consider a multilayer network design model arising from a real-life telecommunication application where traffic routing decisions imply the installation of expensive nodal equipment. Customer requests come in the form of bandwidth reservations for a given origin destination pair. Bandwidth demands are expressed as multiples of nominal granularities. Each request must be single-path routed. Grooming several requests on the same wavelength and multiplexing wavelengths in the same optical stream allow a more efficient use of network capacity. However, each addition or withdrawal of a request from a wavelength requires optical to electrical conversion and the use of cross-connect equipment with expensive ports of high densities. The objective is to minimize the number of required ports of the cross-connect equipment. We deal with backbone optical networks, therefore with networks with a moderate number of nodes (14 to 20) but thousands of requests. Further difficulties arise from the symmetries in wavelength assignment and traffic loading. Traditional multicommodity network flow approaches are not suited for this problem. Instead, four alternative models relying on Dantzig–Wolfe and/or Benders' decomposition are introduced and compared. The formulations are strengthened using symmetry breaking restrictions, variable domain reduction, zero-one discretization of integer variables, and cutting planes. The resulting dual bounds are compared to the values of primal solutions obtained through hierarchical optimization and rounding procedures. For realistic size instances, our best approaches provide solutions with optimality gap of approximately 5% on average in around 2 h of computing time. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>Flow cover inequalities are among the most effective valid inequalities for capacitated fixed-charge network flow problems. These valid inequalities are based on implications for the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be obtained by collapsing a subset of nodes into a single node. In this article, we derive new valid inequalities for the capacitated fixed-charge network flow problem by exploiting additional information from the network. In particular, the new inequalities are based on a three partitioning of the nodes. The new three-partition flow cover inequalities include the flow cover inequalities as a special case. We discuss the constant capacity case and give a polynomial separation algorithm for the inequalities. Finally, we report computational results with the new inequalities for networks with different characteristics. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>We consider a content distribution network (CDN) in which data hubs or servers are established in multiple locations to cater to local demands. The distributions of data to these hubs along with related network design problems (such as hub location and user assignment) are the key decision problems to consider to minimize the total routing cost. A new model for allocation of segments is introduced in Sen, Krishnamoorthy, Rangaraj and Narayanan, Comput Oper 62 (2015), 282–295, in which local preferences guide the database partitioning process, and the servers are fully connected to each other. In this article, we develop a simulated annealing (SA) approach (referred to as SA-mesh) to solve this problem and compare its performance with the corresponding mixed-integer linear programming (MILP) formulation. We also formulate a much harder variant of the problem in which servers are interconnected by a tree. We develop a SA algorithm (referred to as SA-tree) for this variant, in which a local search is incorporated to find a suboptimal tree backbone. We use a customized data structure based on linked lists to represent a solution in our algorithms. This enables our algorithms to scale to much larger instances of the problem. We use optimal solutions and the benchmarks obtained by CPLEX to justify the performance of our algorithms. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>Suppose we have a graph *G* (finite and undirected) where the vertices of *G* are always operational, but the edges of *G* operate independently with probability . The *all-terminal reliability* of a graph *G* is the probability that every pair of vertices in *G* is connected by a path: that is, some spanning tree is operational. We prove that the points of inflections of all-terminal reliability polynomials are dense in [0,1]. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

The online shortest path problem is a type of stochastic shortest path problem in which certain arc costs are revealed *en route*, and the path is updated accordingly to minimize expected cost. This note addresses the open problem of determining whether a problem instance admits a finite optimal solution in the presence of negative arc costs. We formulate the problem as a Markov decision process and show ways to detect such instances in the course of solving the problem using standard algorithms such as value and policy iteration. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

The optimal design of water distribution networks is a complex non-linear combinatorial optimization problem. It consists in finding the least-cost pipe configuration that satisfies hydraulic laws and customer requirements, using a limited set of available pipe types. In a previous paper (De Corte and Sörensen, Eur J Oper Res 228 (2013), 1–10), we have argued that state-of-the-art optimization algorithms proposed in this domain are unduly complicated and poorly tested. The main contribution of this article is a straightforward, fast, transparent, and effective iterated local search (ILS) algorithm that has at least equivalent performance when compared to the best approaches in the literature, but has a much simpler algorithmic structure. A full-factorial experiment is conducted to obtain the heuristic's best parameter settings. Contrary to existing algorithms, the ILS algorithm is additionally shown to perform well on a broad set of much more challenging HydroGen (De Corte and Sörensen, Water Resour Manage 28 (2014), 333–350) test instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 187–198 2016

]]>Vasko et al., Comput Oper Res 29 (2002), 441–458 defined the cable-trench problem (CTP) as a combination of the Shortest Path and Minimum Spanning Tree Problems. Specifically, let be a connected weighted graph with specified vertex (referred to as the *root*), length for each , and positive parameters and . The CTP is the problem of finding a spanning tree of such that is minimized, where is the total length of the spanning tree and is the total path length in from to all other vertices of . Recently, Jiang et al., Proceedings of MICCAI 6893 (2011), 528–536 modeled the vascular network connectivity problem in medical image analysis as an extraordinarily large-scale application of the generalized cable-trench problem (GCTP). They proposed an efficient solution based on a modification of Prim's algorithm (MOD_PRIM), but did not elaborate on it. In this article, we formally define the GCTP, describe MOD_PRIM in detail, and describe two linearly parallelizable metaheuristics which significantly improve the performance of MOD_PRIM. These metaheuristics are capable of finding near-optimal solutions of very large GCTPs in quadratic time in . We also give empirical results for graphs with up to 25,001 vertices. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 199–208 2016

We present two metaheuristics for the Critical Node Problem, that is, the maximal fragmentation of a graph through the deletion of nodes. The two metaheuristics are based on the Iterated Local Search and Variable Neighborhood Search frameworks. Their main characteristic is to exploit two smart and computationally efficient neighborhoods which we show can be implemented far more efficiently than the classical neighborhood based on the exchange of any two nodes in the graph, and which we prove is equivalent to the classical neighborhood in the sense that it yields the same set of neighbors. Solutions to improve the overall running time without deteriorating the quality of the solution computed are also illustrated. The results of the proposed metaheuristics outperform those currently available in literature. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 209–221 2016

]]>In the multi-depot ring star problem (MDRSP), a set of customers has to be connected to a set of given depots by ring stars. Such a ring star is a cycle graph, also called a ring, with some additional nodes assigned to its nodes by single star edges. Optional Steiner nodes can be used in the network as intermediate nodes on the rings. Depot dependent capacity limits apply to both, the number of customers in each ring star and the number of ring stars connected to a depot. The MDRSP asks for a network such that the sum of the edge costs is minimized. In this article, we present a matheuristic that iteratively refines a solution network in a locally exact fashion. In contrast to existing approaches, we define an *equi-model matheuristic*. That is a refinement method in which the subproblems are modeled as smaller instances of the global problem. Hence the optimization model that is used to explore the various structural multi-exchange neighborhoods in our algorithm is the MDRSP itself. A first class of neighborhoods considers local subnetworks for optimal improvements. Through an advanced modeling technique, we are able to refine arbitrary subnetworks of suitable size induced by simple node sets. A second class aims at globally restructuring the current network after the application of different contraction techniques. For both purposes, we develop an exact branch & cut algorithm for the MDRSP that efficiently solves the local optimization problems to optimality, if they are chosen reasonably in terms of size and complexity. The efficiency of the approach is shown by computational results improving known upper bounds for instance classes from the literature containing up to 1000 nodes. Ninety-one percent of the known best objective values are improved up to 13% in competitive computational time. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 222–237 2016

In this article, a heuristic is said to be *provably best* if, assuming
, no other heuristic always finds a better solution (when one exists). This extends the usual notion of “best possible” approximation algorithms to include a larger class of heuristics. We illustrate the idea on several problems that are somewhat stylized versions of real-life network optimization problems, including the maximum clique, maximum *k*-club, minimum (connected) dominating set, and minimum vertex coloring problems. The corresponding provably best construction heuristics resemble those commonly used within popular metaheuristics. Along the way, we show that it is hard to recognize whether the clique number and the *k*-club number of a graph are equal, yet a polynomial-time computable function is “sandwiched” between them. This is similar to the celebrated Lovász function wherein an efficiently computable function lies between two graph invariants that are
-hard to compute. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 238–245 2016

We study a new multiobjective job scheduling problem on nonidentical machines with applications in the car industry, inspired by the problem proposed by the car manufacturer Renault in the ROADEF 2005 Challenge. Makespan, smoothing costs and setup costs are minimized following a lexicographic order, where smoothing costs are used to balance resource utilization. We first describe a mixed integer linear programming (MILP) formulation and a network interpretation as a variant of the well-known vehicle routing problem. We then propose and compare several solution methods, ranging from greedy procedures to a tabu search and an adaptive memory algorithm. For small instances (with up to 40 jobs) whose MILP formulation can be solved to optimality, tabu search provides remarkably good solutions. The adaptive memory algorithm, using tabu search as an intensification procedure, turns out to yield the best results for large instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 246–261 2016

]]>