We study a less-than-truckload (LTL) transportation network and investigate the potential benefits of implementing an integrated solution approach for shipment routing throughout this network. In LTL transportation, shipments are first delivered to local hubs to be consolidated, then transferred to another hub, and finally sent to their destinations. This routing planning process involves three routing decisions: (i) from origins to hubs,(ii) between hubs, and (iii) from hubs to destinations. These decisions are usually handled in a sequential manner due to the complexity of these individual problems, which may result in suboptimal solutions. In this study, we develop an integrated framework for solving all of these decision problems simultaneously. We propose an optimization-driven approach that can efficiently handle large instances with thousands of loads and provides solutions with significant cost savings over the sequential approach.
34: Stability of probablisitic two-stage permutation flowshop problem
The Hamilton–Waterloo problem with uniform cycle sizes asks for a 2-factorization of the complete graph Kv (for odd v) or Kv minus a 1-factor (for even v) where r of the factors consist of n-cycles and s of the factors consist of m-cycles with r+s=⌊v−12⌋. In this paper, the Hamilton–Waterloo Problem with 4-cycle and m-cycle factors for odd m≥3 is studied and all possible solutions with a few possible exceptions are determined.
A multi-break rearrangement generalizes most of genome rearrangements, such as block-interchanges, transpositions and reversals.A k-break cuts k adjacencies over a permutation, and forms k new adjacencies by joining the extremities according to an arbitrary matching.Block-interchange distance is a polynomial problem, but the transposition and the reversal distances are both NP-hard problems.A FPT algorithm is known for the multi-break distance between two permutations.We propose the restricted multi-break rearrangement (rmb), where a restricted k-break cuts k adjacencies but forms k new adjacencies according to a fixed matching.By considering permutations graphs we are able to formulate a better way to represent the orders of a permutations.Cographs are P 4 -free graphs, a subclass of permutation graphs.The permutations that characterize cographs are the separable permutations, exactly the permutations which do not contain particular patterns that yield P 4 's.By using their cotree representation, we give an algorithm to sort by rmb the separable permutations.
The VIPAFLEET project consists in developing models and algorithms for man- aging a fleet of Individual Public Autonomous Vehicles (VIPA). Hereby, we consider a fleet of cars distributed at specified stations in an industrial area to supply internal transportation, where the cars can be used in different modes of circulation (tram mode, elevator mode, taxi mode). One goal is to develop and implement suitable algorithms for each mode in order to satisfy all the requests under an economic point of view by minimizing the total tour length or the makespan. The innovative idea and challenge of the project is to develop and install a dynamic fleet management system that allows the operator to switch between the differ- ent modes within the different periods of the day according to the dynamic transportation demands of the users. We model the underlying online transportation system and propose an according fleet management framework, to handle modes, demands and commands. We propose for each mode appropriate online algorithms and evaluate their performance.
In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated graph. We exploit the transformation proposed by Cornaz and Jost (2008), where given a graph G, an auxiliary graph (G) over cap is constructed, such that the family of all stable sets of (G) over cap is in one-to-one correspondence with the family of all feasible colorings of G. The transformation in Cornaz and Jost (2008) was originally proposed for the classical Vertex Coloring and the Max-Coloring problems; we extend it to the Equitable Coloring Problem and the Bin Packing Problem with Conflicts. We discuss the relation between the Maximum Weight Stable formulation and a polynomial-size formulation for the VCP, proposed by Campelo et al. (2008) and called the Representative formulation. We report extensive computational experiments on benchmark instances of the four problems, and compare the solution method with the state-of-the-art algorithms. By exploiting the proposed method, we largely outperform the state-of-the-art algorithm for the Max-coloring Problem, and we are able to solve, for the first time to proven optimality, 14 Max-coloring and 2 Equitable Coloring instances. (C) 2016 Elsevier B.V. All rights reserved.
We investigate Hunters & Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show that the minimum number of hunters required to win on an (n\times m)-grid is \lfloor min{n,m}/2\rfloor+1. We also show that the extremal value of this number on n-vertex trees is between \Omega(log n/log log n) and O(log n).
Given an edge-colored graph, an internal vertex of a path experiences a reload cost if it lies between two consecutive edges of different colors. The value of the reload cost depends only on the colors of the traversed edges. The reload cost concept has important applications in dynamic networks, such as transportation networks and dynamic spectrum access networks. In the minimum changeover cost arborescence (MinCCA) problem, we seek a spanning tree of an edge-colored graph, in which the sum of reload costs of all internal vertices, starting from a given root, is minimized. In general, MinCCA is known to be hard to approximate within factor n 1 - , for any 0 , on a graph of n vertices.We first show that MinCCA can be optimally solved in polynomial-time on cactus graphs. Our main result is an optimal polynomial-time algorithm for graphs of bounded treewidth, thus establishing the solvability of our problem on a fundamental subclass of graphs. Our results imply that MinCCA is fixed parameter tractable when parameterized by treewidth and the maximum degree of the input graph.
Several problems in optimization and control involve a matrix of decision variables to be subject to a rank constraint. Although semidefinite programming is used as a generalpurpose tool to provide strong relaxations of such problems, finding feasible solutions mostly relies on algorithmic techniques specific to the problem at hand. We present models for expressing rank constraints using mathematical programming, that provide a general-purpose method to find feasible solutions. Our models were tested against the classical Distance Geometry Problem.
A \textit{locally identifying coloring} ($lid$-coloring) of a graph is a proper coloring such that the sets of colors appearing in the closed neighborhoods of any pair of adjacent vertices having distinct neighborhoods are distinct. Our goal is to study a \textit{relaxed locally identifying coloring} ($rlid$-coloring) of a graph that is similar to locally identifying coloring for which the coloring is not necessary proper.We denote by $\chi_{rlid}(G)$ the minimum number of colors used in a relaxed locally identifying coloring of a graph $G$ In this paper, we prove that the problem of deciding that $\chi_{rlid}(G)=3$ for a $2$-degenerate planar graph $G$ is $NP$-complete. We give several bounds of $\chi_{rlid}(G)$ and construct graphs for which some of these bounds are tightened. Studying some families of graphs allows us to compare this parameter with the minimum number of colors used in a locally identifying coloring of a graph $G$ ($\chi_{lid}(G)$), the size of a minimum identifying code of $G$ ($\gamma_{id}(G)$) and the chromatic number of $G$ ($\chi(G)$).
The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem, and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is among the best algorithms in practice and performs very well in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis to NS and MMCC. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here, $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$.
The problem of maximizing non-negative submodular functions has been studied extensively in the last few years. However, most papers consider submodular set functions. Recently, several advances have been made for the more general case of submodular functions on the integer lattice. In this paper, we present a deterministic $\frac{1}{3}$-approximation for maximizing a submodular function on a bounded integer lattice $\{0, \ldots, C\}^n$ using a Double Greedy framework. Moreover, we show that the analysis is tight and that other ideas used for approximating set functions cannot easily be extended. In contrast to set functions, submodularity on the integer lattice does not imply the so-called diminishing returns property. Assuming this property, it was shown that many results for set functions can also be obtained for the integer lattice. In this paper, we consider a further generalization. Instead of the integer lattice, we consider a distributive lattice as the function domain and assume the diminishing returns (DR) property. On the one hand, we show that some approximation algorithms match the set functions setting. In particular, we can obtain a $\frac{1}{2}$-approximation for unconstrained maximization, a $(1-\frac{1}{e})$-approximation for monotone functions under a cardinality constraint and a $\frac{1}{2}$-approximation for a poset matroid constraint. On the other hand, for a knapsack constraint, the problem becomes significantly harder: even for monotone DR-submodular functions, we show that there is no $2^{(\log (n^{1/2} - 1))^\delta - 1}$-approximation for every $\delta > 0$ under the assumption that $3-SAT$ cannot be solved in time $2^{n^{3/4 + \epsilon}}$.
We introduce the non-unit count of an interval graph as the minimum number of intervals in an interval representation whose lengths deviate from one. We characterize a variant of the non-unit count (where all interval lengths are required to be at least one) and graphs with non-unit count 1.
