Showing papers by "Christian Blum published in 2001"
01 Jan 2001
TL;DR: This paper proposes a new way of implementing ACO algorithms, which explicitly defines the hyperspace for the pheromone values as the convex hull of the set of 0-1 coded feasible solutions of the combinatorial optimization problem under consideration.
Abstract: Ant Colony Optimization (ACO) [2] is a recently proposed metaheuristic approach for solving hard combinatorial optimization problems. The inspiring source of ACO is the foraging behavior of real ants. In most ACO implementations the hyperspace for the pheromone values used by the ants to build solutions is only implicitly limited. In this paper we propose a new way of implementing ACO algorithms, which explicitly defines the hyperspace for the pheromone values as the convex hull of the set of 0-1 coded feasible solutions of the combinatorial optimization problem under consideration. We call this new implementation the hyper-cube framework for ACO algorithms. The organization of this extended abstract is as follows. In section 2 we briefly present the original Ant System [3] for static combinatorial optimization problems. In section 3 we propose the hyper-cube framework for ACO algorithms and we present pheromone updating rules for Ant System (AS) and MAX -MIN Ant System (MMAS). In section 4 we discuss some of the advantages involved with the hyper-cube framework for ACO algorithms, while Section 5 outlines future work.
88 citations
01 Jan 2001
TL;DR: The maximal-CSP is defined, defined as the problem of finding an assignment that satisfies the greatest number of constraints, which is to maximize the sum of the weights belonging to satisfied constraints.
Abstract: A CSP is formally defined as a triple (X,D,C), where X = {x1, . . . , xn} is the set of variables, D = {D1, . . . , Dn} is the set of domains which define the values a variable can assume and C = {C1, . . . , Cm} is the set of constraints among the variables. The CSP is a decision problem: a solution of the problem is a complete assignment which satisfies all the constraints (see [12] for an overview of CSPs). Here we are interested in solving the maximal-CSP, defined as the problem of finding an assignment that satisfies the greatest number of constraints. Often, weights are associated to constraints and the goal is to maximize the sum of the weights belonging to satisfied constraints.
43 citations
25 Sep 2001
TL;DR: Empirical evidence is shown for the existence of a critical level of parallelism which leads to the best performance of a local search algorithm for MAX-SAT.
Abstract: In this work we investigate the effects of the parallelization of a local search algorithm for MAX-SAT. The variables of the problem are divided in subsets and local search is applied to each of them in parallel, supposing that variables belonging to other subsets remain unchanged. We show empirical evidence for the existence of a critical level of parallelism which leads to the best performance. This result allows to improve local search and adds new elements to the investigation of criticality and parallelism in combinatorial optimization problems.
11 citations