82,670 research outputs found
Maximally Disjoint Solutions of the Set Covering Problem
This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, extensive computational tests are given demonstrating the nature of these algorithms. These tests are carried out both on randomly generated problems and on problems found in the literature
A Novel SAT-Based Approach to the Task Graph Cost-Optimal Scheduling Problem
The Task Graph Cost-Optimal Scheduling Problem consists in scheduling a certain number of interdependent tasks onto a set of heterogeneous processors (characterized by idle and running rates per time unit), minimizing the cost of the entire process. This paper provides a novel formulation for this scheduling puzzle, in which an optimal solution is computed through a sequence of Binate Covering Problems, hinged within a Bounded Model Checking paradigm. In this approach, each covering instance, providing a min-cost trace for a given schedule depth, can be solved with several strategies, resorting to Minimum-Cost Satisfiability solvers or Pseudo-Boolean Optimization tools. Unfortunately, all direct resolution methods show very low efficiency and scalability. As a consequence, we introduce a specialized method to solve the same sequence of problems, based on a traditional all-solution SAT solver. This approach follows the "circuit cofactoring" strategy, as it exploits a powerful technique to capture a large set of solutions for any new SAT counter-example. The overall method is completed with a branch-and-bound heuristic which evaluates lower and upper bounds of the schedule length, to reduce the state space that has to be visited. Our results show that the proposed strategy significantly improves the blind binate covering schema, and it outperforms general purpose state-of-the-art tool
Asynchronous Teams for probe selection problems
AbstractThe selection of probe sets for hybridization experiments directly affects the efficiency and cost of the analysis. We propose the application of the Asynchronous Team (A-Team) technique to determine near-optimal probe sets. An A-Team is comprised of several different heuristic algorithms that communicate with each other via shared memories. The A-Team method has been applied successfully to several problems including the Set Covering Problem, the Traveling Salesman Problem, and the Point-to-Point Connection Problem, and lends itself well to the Probe Selection Problem. We designed and developed a C + + program to run instances of the Minimum Cost Probe Set and Maximum Distinguishing Probe Set problems. A program description and our results are presented in the paper
Unifying Parsimonious Tree Reconciliation
Evolution is a process that is influenced by various environmental factors,
e.g. the interactions between different species, genes, and biogeographical
properties. Hence, it is interesting to study the combined evolutionary history
of multiple species, their genes, and the environment they live in. A common
approach to address this research problem is to describe each individual
evolution as a phylogenetic tree and construct a tree reconciliation which is
parsimonious with respect to a given event model. Unfortunately, most of the
previous approaches are designed only either for host-parasite systems, for
gene tree/species tree reconciliation, or biogeography. Hence, a method is
desirable, which addresses the general problem of mapping phylogenetic trees
and covering all varieties of coevolving systems, including e.g., predator-prey
and symbiotic relationships. To overcome this gap, we introduce a generalized
cophylogenetic event model considering the combinatorial complete set of local
coevolutionary events. We give a dynamic programming based heuristic for
solving the maximum parsimony reconciliation problem in time O(n^2), for two
phylogenies each with at most n leaves. Furthermore, we present an exact
branch-and-bound algorithm which uses the results from the dynamic programming
heuristic for discarding partial reconciliations. The approach has been
implemented as a Java application which is freely available from
http://pacosy.informatik.uni-leipzig.de/coresym.Comment: Peer-reviewed and presented as part of the 13th Workshop on
Algorithms in Bioinformatics (WABI2013
Shareability Network Based Decomposition Approach for Solving Large-scale Multi-modal School Bus Routing Problems
We consider the classic School Bus Routing Problem (SBRP) with a multi modal
generalization, where students are either picked up by a fleet of school buses
or transported by an alternate transportation mode, subject to a set of
constraints. The constraints that are typically imposed for school buses are a
maximum fleet size, a maximum walking distance to a pickup point and a maximum
commute time for each student. This is a special case of the Vehicle Routing
Problem (VRP) with a common destination. We propose a decomposition approach
for solving this problem based on the existing notion of a shareability
network, which has been used recently in the context of dynamic ridepooling
problems. Moreover, we simplify the problem by introducing the connection
between the SBRP and the weighted set covering problem (WSCP). To scale this
method to large-scale problem instances, we propose i) a node compression
method for the shareability network based decomposition approach, and ii)
heuristic-based edge compression techniques that perform well in practice. We
show that the compressed problem leads to an Integer Linear Programming (ILP)
of reduced dimensionality that can be solved efficiently using off-the-shelf
ILP solvers. Numerical experiments on small-scale, large-scale and benchmark
networks are used to evaluate the performance of our approach and compare it to
existing large-scale SBRP solving techniques.Comment: 41 pages, 27 figure
A distance-limited continuous location-allocation problem for spatial planning of decentralized systems
We introduce a new continuous location-allocation problem where the facilities have both a fixed opening cost and a coverage distance limitation. The problem has wide applications especially in the spatial planning of water and/or energy access networks where the coverage distance might be associated with the physical loss constraints. We formulate a mixed integer quadratically constrained problem (MIQCP) under the Euclidean distance setting and present a three-stage heuristic algorithm for its solution: In the first stage, we solve a planar set covering problem (PSCP) under the distance limitation. In the second stage, we solve a discrete version of the proposed problem where the set of candidate locations for the facilities is formed by the union of the set of demand points and the set of locations in the PSCP solution. Finally, in the third stage, we apply a modified Weiszfeld's algorithm with projections that we propose to incorporate the coverage distance component of our problem for fine-tuning the discrete space solutions in the continuous space. We perform numerical experiments on three example data sets from the literature to demonstrate the performance of the suggested heuristic method. © 2017 Elsevier Lt
The Subtour Centre Problem
The subtour centre problem is the problem of finding a closed trail S of bounded length on a connected simple graph G that minimises the maximum distance from S to any vertex ofG. It is a central location problem related to the cycle centre and cycle median problems (Foulds et al., 2004; Labbé et al., 2005) and the covering tour problem (Current and Schilling, 1989). Two related heuristics and an integer linear programme are formulated for it. These are compared numerically using a range of problems derived from tsplib (Reinelt, 1995). The heuristics usually perform substantially better then the integer linear programme and there is some evidence that the simpler heuristics perform better on the less dense graphs that may be more typical of applications
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