This paper presents an algorithm for solving a linear program LP (to a given tolerance) from a given prespecified starting point. The complexity of the algorithm is sensitive to and is dependent on the quality of the starting point, as assessed by suitable measures of the extent of infeasibility and the extent of nonoptimality of the starting point. Two new measures of the extent of infeasibili...

Much attention has been given in recent years to the problem of finding Minimally Unsatisfiable Subformulas (MUSes) of Boolean formulas. In this paper, we present a new view of the problem, strongly linking it to the maximal satisfiability problem. From this relationship, we have developed a novel technique for extracting all MUSes of a CNF formula, tightly integrating our implementation with a...

This paper provides an effective modification to the big-M method which leads to reducing the iterations of this method, when it is used to recognize the infeasibility of linear systems. 2008 Elsevier B.V. All rights reserved.

Methods for analyzing infeasible constraint sets have proliferated in the past decade, commonly focused on finding maximal satisfiable subsets (MSSes) or minimal unsatisfiable subsets (MUSes). Most common are methods for producing a single such subset (one MSS or one MUS), while a few algorithms have been presented for enumerating all of the interesting subsets of a constraint set. In the case ...

The problem of solving a multi-objective programming problem, by assuming that the decision maker has fuzzy goals for each of the objectives, is addressed. In this case a fuzzy goal programming problem has to be solved. But when we have several objectives it can be a difficult task for the decision maker to determine coherent aspiration levels, so it is possible that the tolerance thresholds be...

We study the complexity of combinatorial problems that consist of competing infeasibility and optimization components. In particular, we investigate the complexity of the connection subgraph problem, which occurs, e.g., in resource environment economics and social networks. We present results on its worst-case hardness and approximability. We then provide a typical-case analysis by means of a d...

This paper describes local probing, an algorithm hybridiza-tion form that combines backtrack search enhanced with local consistency techniques (BT+CS) with local search (LS) via probe backtrack-ing. Generally BT+CS can be eeective at nding solutions for (or proving the infeasibility of) tightly constrained problems with complex and overlapping constraints, but lacks good optimization characteri...