LS(Graph): a constraint-based local search for constraint optimization on trees and paths

Abstract

Constrained optimum tree (COT) and constrained optimum path (COP) problems arise in many real-life applications and are ubiquitous in communication networks. They have been traditionally approached by dedicated algorithms, which are often hard to extend with side constraints and to apply widely. This paper proposes a constraint-based local search framework for COT/COP applications, bringing the compositionality, reuse, and extensibility at the core of constraint-based local search and constraint programming systems. The modeling contribution is the ability to express compositional models for various COT/COP applications at a high level of abstraction, while cleanly separating the model and the search procedure. The main technical contribution is a connected neighborhood based on rooted spanning trees to find high-quality solutions to COP problems. This framework is applied to some COT/COP problems, e.g., the quorumcast routing problem, the edge-disjoint paths problem, and the routing and wavelength assignment with delay side constraints problem. Computational results show the potential importance of the approach.

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

“…A comparison between the performances of the MP algorithm and those of alternative algorithms proposed in the literature [ 38 , 44 ] is reported in S1 Table . As benchmark instances we used: two internet-like topologies generated using the BRITE graph generator [ 65 ] with parameters set as in [ 44 ]; mesh graphs of sizes 15x15 and 25x25, Steiner and planar graphs as reported in [ 38 ]. For each of these graphs we used the same set of sender-receiver pairs of size M = 0.10 V ,0.25 V ,0.40 V used in [ 38 ].…”

“…Negative results on worst-case inapproximability did not stop progress on heuristic approaches. The problem has been studied intensely with a variety of classical techniques: heuristic greedy algorithms [ 13 , 14 , 18 , 31 ], elaborated strategies using bin packing [ 32 ], integer/linear programming relaxations [ 33 – 36 ], post-optimization [ 37 ], Montecarlo local search [ 38 ], genetic algorithms [ 39 – 42 ], particle swarm optimization [ 43 ] and ant colony optimization [ 44 ], among them.…”

“…The MP algorithm is tested on computer-generated instances of different classes of random graphs to study the scaling properties with the system size and to compare the performances against a greedy algorithm. We also considered the EDP problem on some benchmark instances found in the literature, for which we could compare the message-passing results with those obtained using other types of algorithms: greedy, ant colony optimization [ 44 ] and Montecarlo local search [ 38 ].…”

Survey of Scientific Programming Techniques for the Management of Data-Intensive Engineering Environments

“…Euler models Scientific computation [104] Statistical methods [105] [ 106,154] Graph theory Automata [124] Graph/complex network analysis [37,[108][109][110][111][112][113][114][115][116][117] Engineering methods…”

A constraint-based local search for designing tree networks with distance and disjoint constraints

“…CONSTRAINT-BASED LOCAL SEARCH Constraint-based local search has been recently introduced as an alternative solution to efficiently tackle many network design problems [7], [8] ranging from telecommunications to transportations, and VLSI circuit design.…”