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2000 “The cost Minimizing Inverse Classification Problem: A Genetic Algorithm Approach”, Decision Support Systems 29,3
, 2000
"... We consider the inverse problem in classification systems described as follows. Given a set of prototype cases representing a set of categories, a similarity function, and a new case classified in some category, find the cost minimizing changes to the attribute values such that the case is reclassif ..."
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We consider the inverse problem in classification systems described as follows. Given a set of prototype cases representing a set of categories, a similarity function, and a new case classified in some category, find the cost minimizing changes to the attribute values such that the case is reclassified as a member of a (different) preferred category. The problem is “inverse ” because the usual mapping is from a case to its unknown category. The increased application of classification systems in business suggests that this inverse problem can be of significant benefit to decisionmakers as a form of sensitivity analysis. Analytic approaches to this inverse problem are difficult to formulate as the constraints are either not available or difficult to determine. To investigate this inverse problem, we develop several genetic algorithms and study their performance as problem difficulty increases. We develop a real genetic algorithm with feasibility control, a traditional binary genetic algorithm, and a steepest ascent hillclimbing algorithm. In a series of simulation experiments, we compare the performance of these algorithms to the optimal solution as the problem difficulty increases (more attributes and classes). In addition, we analyze certain algorithm effects (level of feasibility control, operator design, and fitness function) to determine the best approach. Our results indicate the viability of the real genetic algorithm and the importance of feasibility control as the problem difficulty increases.
Some Primality Testing Algorithms
 Notices of the AMS
, 1993
"... We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice. 1 Introduction In recent years, fast primality testing algorithms have been a popular subject of research and some of the modern methods are now i ..."
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We describe the primality testing algorithms in use in some popular computer algebra systems, and give some examples where they break down in practice. 1 Introduction In recent years, fast primality testing algorithms have been a popular subject of research and some of the modern methods are now incorporated in computer algebra systems (CAS) as standard. In this review I give some details of the implementations of these algorithms and a number of examples where the algorithms prove inadequate. The algebra systems reviewed are Mathematica, Maple V, Axiom and Pari/GP. The versions we were able to use were Mathematica 2.1 for Sparc, copyright dates 19881992; Maple V Release 2, copyright dates 19811993; Axiom Release 1.2 (version of February 18, 1993); Pari/GP 1.37.3 (Sparc version, dated November 23, 1992). The tests were performed on Sparc workstations. Primality testing is a large and growing area of research. For further reading and comprehensive bibliographies, the interested re...