J. Chinneck and E. Dravnieks. Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing, 3:157--168, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Infeasible Subsystem (IIS) if every proper subsystem of # # is feasible. In order to help the modeler resolve infeasibility of large linear inequality systems, attention was first devoted to the problem of identifying IISs, with a small and possibly minimum number of inequalities [28] see [20, 22, 47] for some heuristics and [18] for implementations in commercial solvers such as CPLEX and MINOS. Clearly, in the presence of many overlapping IISs, this does not provide enough information to repair the original system. To achieve feasibility, one must delete at least one inequality from each IIS. ....

....m = n 1, then A has n 1 rows. Assuming A to be of full column rank, L = Ax = 0 = Q = conv( x 1 , xn 1 ) is an n simplex and Q. 2. 2 Minimum cardinality IISs We now consider the complexity status of the following problem for which heuristics have been proposed in [20, 22, 38, 39]. MIN IIS: Given an infeasible system # : b as above, find a minimum cardinality IIS. To settle the issue left open in [20, 22, 28, 39] we prove that MIN IIS is not only NP hard to solve optimally but also hard to approximate. If DTIME(T (m) denotes the class of problems solvable in ....

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J. W. CHINNECK AND E. DRAVNIEKS, Locating minimal infeasible constraint sets in linear programs, ORSA J. Comput. 3 (1991), pp. 157--168.

....a MUS within a formula is an NP hard problem, since it implies solving the SAT problem. Moreover, finding a MUS typically requires much more time than just solving the SAT problem, just like finding an IIS requires much more time than just solving the feasibility of a system of linear inequalities [6]. We therefore introduce the concept of approximation for an unsatisfiable subformula. Being m the number of clauses in , and the cardinality of any minMUS, an unsatisfiable subformula L of approximation e (with 0 e m ) of is an unsatisfiable subformula L having cardinality c = e. A ....

....a minMUS, or at least a MUS or a low approximation unsatisfiable subformula. Re design of that part is another issue, and, typically, requires the work of the original human designer. Postinfeasibility analysis, in fact, always requires the cooperation of algorithmic engine and human intelligence [6]. The process could need to be repeated until all MUS are removed from the formula. On the contrary, the set of clauses not satisfied by a Max SAT solution is not, in general, an unsatisfiable subset (although it may be) hence its location would not help in understanding the problem. In the case ....

J.W. Chinneck and E.W. Dravnieks. Locating Minimal Infeasible Constraint Sets in Linear Programs. ORSA Journal on Computing, 3:157-168, 1991.

....present, were treated as general constraints increasing the dimension of the tableau. Another drawback of Van Loon work is that no indication is given about how to lead an ecient search, in order to obtain a basis from which an IIS could be determined. The deletion ltering is a simple algorithm [ChDr91] that guarantees that an IIS is always found. This method consists in creating a set S, initiated as the set of all constraints from which constraints are deleted if their removal does not make the set S feasible. The importance of determining the IIS is that the model can be updated either by ....

....to IISs) upon the addition, to a set of feasible constraints, of a further constraint that makes the new set infeasible. A hierarchy manager of the system would then remove one of the constraints of the set, but the method does not guarantee minimality of the set of removed constraints. In [ChDr91], a presentation of previous work as well as the description of algorithms for the construction of all IIS is presented. In [Gree93] Harvey Greenberg describes the method of isolation , to detect the sources of infeasibility, and to conduct a diagnosis of the model, which he described in ....

J. W Chinneck and E. W Dravnieks, Locating Minimal Infeasible Constraint Sets in Linear Programs, ORSA Journal on Computing, Vol. 3, No. 2, pp. 157-168, 1991.

....(IIS) when 0 is infeasible, but every proper subsystem of 0 is feasible. In order to help the modeler resolve infeasibility of large linear inequality systems, attention was rst devoted to the problem of identifying IISs with a small and possibly minimum number of inequalities [19] see [14, 13] for several heuristics, now available in commercial solvers such as CPLEX and MINOS [11] Clearly, when there are many overlapping IISs, this does not provide enough information to repair the original system. To achieve feasibility, one must delete an inequality from each IIS. If all IISs were ....

....and let 2 be an arbitrary inequality of . Then the polyhedron corresponding to n , i.e. the subsystem obtained by removal of , is an ane convex cone. 2. 1 Minimum cardinality IISs We now determine the complexity status of the following problem for which heuristics have been proposed in [14, 13, 26, 27]. Min IIS: Given an infeasible system : fAx bg as above, nd a minimum cardinality IIS. To settle the issue left open in [19, 14, 27] we prove that Min IIS is not only NP hard to solve optimally but also hard to approximate. Note that, where DT IME(T (m) denotes the class of problems ....

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J. Chinneck and E. Dravnieks, Locating minimal infeasible constraint sets in linear programs, ORSA Journal on Computing, 3 (1991), pp. 157-168.

....AMPL session only if an unbounded problem is encountered. When a problem is infeasible, the modeler may want help in diagnosing the source(s) of infeasibility. One helpful technique offered by some solvers is to identify an irreducible infeasible subset (or IIS) of constraints and variable bounds (Chinneck and Dravnieks 1991). Since this computation may be time consuming, and since an IIS is not always wanted, the usual arrangement is that the solver only computes an IIS on request. When it does identify an IIS, the solver can return it to AMPL via a symbolic suffix on variables and constraints, conventionally named ....

Chinneck, J.W. and Dravnieks, E.W. (1991), "Locating Minimal Infeasible Constraint Sets in Linear Programs," ORSA Journal on Computing, vol. 3, pp. 157--168.

....of each system; their negations are summarised alongside their advantages in a later section which lists the characteristics of the ideal system. ffl In linear programming, Chinneck and Dravnieks have done some work on what they term IIS s (infeasible systems of linear equations and inequalities) [14, 15]. They relax each inequality i by adding a distinct new variable ffl i to it, and replace the original optimisation function with one which minimises the sum of the ffl s. Any non zero ffl in the answer indicates one member of the minimal infeasible subset. If that ffl is then removed and the ....

John Chinneck and Erik Dravnieks. Locating Minimal Infeasible Constraint Sets in Linear Programs. ORSA Journal on Computing, 3(2):157--168, Spring 1991.

....inspection. With the new software and hardware advances, dealing with infeasible programs is becoming a major bottleneck in linear programming. Several methods have been proposed in order to try to locate the source of infeasibility. While the first ones looked for minimal infeasible subsystems [28, 15], the later ones aim at removing as few constraints as possible to achieve feasibility [29, 53, 51, 50, 14] In fact, the more practical approach in which the modeler is allowed to weight the constraints according to their importance and flexibility leads to weighted versions of Min ULR [51, 50] ....

J. Chinneck and E. Dravnieks. Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing, 3:157--168, 1991.

....into an AMPL session only if an unbounded problem is encountered. When a problem is infeasible, the modeler may want help in diagnosing the source(s) of infeasibility. One helpful technique offered by some solvers is to identify an irreducible set of infeasible constraints and variable bounds [3], called an IIS. Since this computation may be time consuming, and since an IIS is not always wanted, the usual arrangement is that the solver only computes an IIS on request. When it does identify an IIS, the solver can return it to AMPL via a symbolic suffix on variables, conventionally named ....

Chinneck, J. W. and Dravnieks, E. W., "Locating Minimal Infeasible Constraint Sets in Linear Programs, " ORSA J. Computing 3 #2 (1991), pp. 157--168.

....by dropping any equality from it. It is useful to identify such systems (rather than just any infeasible sets of constraints) since these systems can be used to determine the smallest number of constraints that must be dropped (or modified) to result in a feasible model. Chinneck and Dravnieks [10] improve previous methods for finding IISs, and describe three filtering techniques for use in identifying IISs. In terms of the embedded languages framework, each of these three would be functions in an L language. The filtering techniques (analogous to the methods in PRESS) have different ....

Chinneck, John W., and Erik W. Dravnieks, "Locating Minimal Infeasible Constraint Sets in Linear Programs," ORSA Journal on Computing 3:4, pp. 157--168, 1991.

....constraints to be the set of constraints exclusive of all non negativity constraints. In some instances, we will wish to distinguish between non negativity constraints and functional constraints when we are identifying I ISs. We introduce the following definition due to Chinneck and Dravnieks [13]: An irreducible inconsistent set of functional constraints (I ISF) is the complete subset of functional constraints in an I IS. Suppose that S is infeasible. We define a maximum cardinality feasible subsystem of S as S(I mcf ) where I mcf = arg max I M fj I j j S(I) is a maximal feasible ....

....will provide a localization of the modeling error inconsistency. Thus, this approach provides a framework with which not only to isolate the infeasibility, but also to diagnose the infeasibility. To date, this approach had only been explored in the theoretical sense. Recently, Chinneck (e.g. [13], 10] 11] has developed a set of software tools to bring I IS isolation into practical use in LP infeasibility analysis. The goal of these algorithms is to identify a small cardinality I ISs, the idea being that the smaller the constraint set the infeasibility is isolated to the easier the ....

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Chinneck J., and Dravnieks E., Locating Minimal Infeasible Constraint Sets in Linear Programs, ORSA Journal on Computing, Vol. 3 (1991), pp. 157-168.

....of constraints frequently occur and cannot be repaired by simple inspection. With the new software and hardware advances, dealing with infeasible programs is becoming a major bottleneck in linear programming. Several methods have been proposed in order to try to locate the source of infeasibility [20, 11] and to remove as few constraints as possible to achieve feasibility [21, 37] There have recently been new substantial progresses in the study of the approximability of NP hard optimization problems. Various classes have been defined and different reductions preserving approximability have been ....

J. Chinneck and E. Dravnieks. Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing, 3:157--168, 1991.

....errors and to guarantee feasibility. Infeasible programs with thousands of constraints frequently occur and cannot be repaired by simple inspection. Several methods have been proposed in order to try to locate the source of infeasibility. While earlier ones look for minimal infeasible subsystems [28, 15], the later ones aim at removing as few constraints as possible to achieve feasibility [60, 57, 58, 13, 29] The more practical approach in which the modeler is allowed to weight the constraints according to their importance and flexibility leads to weighted versions of Min ULR [58, 57] The ....

J. Chinneck and E. Dravnieks. Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing, 3:157--168, 1991.

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J. Chinneck and E. Dravnieks. Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing, 3:157--168, 1991.

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J.W. Chinneck and E.W. Dravnieks. Locating Minimal Infeasible Constraint Sets in Linear Programs. ORSA Journal on Computing 3 (1991) 157-168.

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