Maximum Satisfiability: Anatomy of the Fitness Landscape for a Hard Combinatorial Optimization Problem

Backbone Guided Extremal Optimization for the Hard Maximum Satisfiability Problem

The original Extremal Optimization (EO) algorithm and its modified versions have been successfully applied to a variety of NP-hard optimization problems. However, there exists a problem that almost all existing EO-based algorithms have overlooked the inherent structural properties behind the optimization problems, e.g., the backbone information. This paper proposes a novel stochastic search met...

Combinatorial Optimization Solutions for the Maximum Quartet Consistency Problem

Given a set of taxa S and a complete set of quartet topologies Q over S, the problem of determining a phylogeny that satisfies the maximum number of topologies is called the Maximum Quartet Consistency (MQC) problem. The MQC problem is an NP-problem. MQC has been solved both heuristically and exactly. Exact solutions for MQC include Constraint Programming, Answer Set Programming and Pseudo-Bool...

Statistical physics of hard combinatorial optimization: The vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper we use the vertex cover probl...

Handbook of Combinatorial Optimization the Maximum Clique Problem

The Maximum Clique Problem Handbook Of Combinatorial Optimization

The maximum clique problem (MCP) is to determine a sub graph of maximum cardinality. A clique is a The corresponding optimization problem i.e. finding the maximum Maximum Clique Problem. in Handbook of Combinatorial. Common theme of every optimization problem: of semidefinite programming, A module on combinatorial optimization, Selected topics: The largest clique (i.e., complete subgraph)! In “...