An oil pipeline design problem

Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574

Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

A note on the data-driven capacity of P2P networks

We consider two capacity problems in P2P networks. In the first one, the nodes have an infinite amount of data to send and the goal is to optimally allocate their uplink bandwidths such that the demands of every peer in terms of receiving data rate are met. We solve this problem through a mapping from a node-weighted graph featuring two labels per node to a max flow problem on an edge-weighted bipartite graph. In the second problem under consideration, the resource allocation is driven by the availability of the data resource that the peers are interested in sharing. That is a node cannot allocate its uplink resources unless it has data to transmit first. The problem of uplink bandwidth allocation is then equivalent to constructing a set of directed trees in the overlay such that the number of nodes receiving the data is maximized while the uplink capacities of the peers are not exceeded. We show that the problem is NP-complete, and provide a linear programming decomposition decoupling it into a master problem and multiple slave subproblems that can be resolved in polynomial time. We also design a heuristic algorithm in order to compute a suboptimal solution in a reasonable time. This algorithm requires only a local knowledge from nodes, so it should support distributed implementations. We analyze both problems through a series of simulation experiments featuring different network sizes and network densities. On large networks, we compare our heuristic and its variants with a genetic algorithm and show that our heuristic computes the better resource allocation. On smaller networks, we contrast these performances to that of the exact algorithm and show that resource allocation fulfilling a large part of the peer can be found, even for hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio

Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

Efficient edge filtering of directly-follows graphs for process mining

Automated process discovery is a process mining operation that takes as input an event log of a business process and generates a diagrammatic representation of the process. In this setting, a common diagrammatic representation generated by commercial tools is the directly-follows graph (DFG). In some real-life scenarios, the DFG of an event log contains hundreds of edges, hindering its understandability. To overcome this shortcoming, process mining tools generally offer the possibility of filtering the edges in the DFG. We study the problem of efficiently filtering the DFG extracted from an event log while retaining the most frequent relations. We formalize this problem as an optimization problem, specifically, the problem of finding a sound spanning subgraph of a DFG with a minimal number of edges and a maximal sum of edge frequencies. We show that this problem is an instance of an NP-hard problem and outline several polynomial-time heuristics to compute approximate solutions. Finally, we report on an evaluation of the efficiency and optimality of the proposed heuristics using 13 real-life event logsWe thank Luciano García-Baíuelos for proposing the idea of combining the results of Chu-Liu-Edmonds’ algorithm to filter a DFG. We also thank Adriano Augusto for providing us with the implementation of the Split Miner filtering technique. This research was funded by the Spanish Ministry of Economy and Competitiveness (TIN2017-84796-C2-1-R) and the Galician Ministry of Education, Culture and Universities (ED431G/08). These grants are co-funded by the European Regional Development Fund (ERDF/FEDER program). D. Chapela-Campa is supported by the Spanish Ministry of Education, under the FPU national plan (FPU16/04428 and EST19/00135). This research is also funded by the Estonian Research Council (grant PRG1226)S

Robust capacitated trees and networks with uniform demands

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes called terminals, and a bound k on the number of edge failures. We first study the problem where k = 1 and the network that we want to design must be a tree covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Second, we consider the problem of computing a minimum-cost survivable network, i.e., a network that covers the root and terminals even after the removal of any k edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set based formulation, a flow based one, and a bilevel one (with an attacker and a defender). We propose algorithms to solve each formulation and compare their efficiency

Subjectively interesting connecting trees and forests

Consider a large graph or network, and a user-provided set of query vertices between which the user wishes to explore relations. For example, a researcher may want to connect research papers in a citation network, an analyst may wish to connect organized crime suspects in a communication network, or an internet user may want to organize their bookmarks given their location in the world wide web. A natural way to do this is to connect the vertices in the form of a tree structure that is present in the graph. However, in sufficiently dense graphs, most such trees will be large or somehow trivial (e.g. involving high degree vertices) and thus not insightful. Extending previous research, we define and investigate the new problem of mining subjectively interesting trees connecting a set of query vertices in a graph, i.e., trees that are highly surprising to the specific user at hand. Using information theoretic principles, we formalize the notion of interestingness of such trees mathematically, taking in account certain prior beliefs the user has specified about the graph. A remaining problem is efficiently fitting a prior belief model. We show how this can be done for a large class of prior beliefs. Given a specified prior belief model, we then propose heuristic algorithms to find the best trees efficiently. An empirical validation of our methods on a large real graphs evaluates the different heuristics and validates the interestingness of the given trees