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Effective production scheduling requires consideration of the dynamics and unpredictability of the manufacturing environment. An automated learning scheme, utilizing genetic search, is proposed for adaptive control in typical decentralized factory-floor decision making. A high-level knowledge representation for modeling production environments is developed, with facilities for genetic learning within this scheme. A multiagent framework is used, with individual agents being responsible for the dispatch decision making at different workstations. Learning is with respect to stated objectives, and given the diversity of scheduling goals, the efficacy of the designed learning scheme is judged through its response under different objectives. The behavior of the genetic learning scheme is analyzed and simulation studies help compare how learning under different objectives impacts certain aggregate measures of system performance.

Many studies have shown that decision tree induction methods could be used to determine rules for expert systems. Pruning techniques are often used to increase the accuracy of an induced decision tree over the instance space. While recent results of decision tree induction show that large samples may be required to induce a decision tree of small error, recent expository studies have used very small sample sizes. In such cases it is of value to obtain a posterior evaluation of the error of the induced concept. In this paper we give three methods to estimate the accuracy of a pruned decision tree. The first method assumes uniform prior distribution. For those cases where uniform prior is not appropriate, we develop a method to obtain appropriate prior using a beta distribution. Finally, we provide a general bound which requires no assumption over the instance space. These results can be used when a pruned decision tree is used to classify the original domain or another close domain.

A procedure is developed for determining two-group linear discriminant classifiers that misclassify the fewest number of observations in the training sample. An experimental study confirms the value of this approach.

The mathematical programming approach to linear disciminant analysis was first introduced in the early 1980's. Since then, numerous mathematical programming models have appeared in the literature. Some of these models were merely formulated while others were subjected to experimentation, in some cases rather extensively. The purpose of this paper is to present a unified survey of these models and their experimental results where applicable. Some mathematical programming (MP) models, unfortunately, have certain pathologies inherent in their structure which puts the degree of usefulness of these models in doubt. When known, such pathologies are also identified for the specific model in question.

This paper surveys problems that may appear in mathematical programming formulations for linear discriminant analysis. For some, there are known solutions. Other problems have not been adequately addressed. Specific problems and considerations include the choice of objective, unacceptable or improper solutions, side constraints, data translation and transformations, unbounded solutions, inconsistencies, gaps, and the balancing of misclassifications. Subject areas: Linear discriminant analysis, statistical methods, linear programming.

Characterization of unacceptable solutions of linear programming methods for linear discriminant problems have been studied by many researchers. This note shows that a recent correction was not a correction but a tightening of prior results.

In discounted Markov decision processes bounds on the optimal value function can be computed and used to eliminate suboptimal actions. In this paper we extend these procedures to the generalized Markov decision process. In so doing we forfeit the contraction property and must base our analysis on other procedures. Duality theory and the Perron-Frobenius theorem are the main tools.

The implications of constrained dependent and independent variables for model parameters are examined. In the context of linear model systems, it is shown that polyhedral constraints on the dependent variables will hold over the domain of the independent variables when a set of polyhedral constraints is satisfied by the model parameters. This result may be used in parameter estimation, in which case all predicted values of the dependent variables are consistent with constraints on the actual values. Also, the implicit constraints that define the set of parameters for many commonly used linear stochastic models with an error term yield values of the dependent variables consistent with the explicit constraints. Models possessing these properties are termed “logically consistent”.

Many linear programming models have been proposed for performing discriminant analysis. Partial characterizations for unacceptable solutions have been presented and new models proposed to circumvent these problems. In this paper those conditions leading to unacceptable solutions for all two-group models are characterized.

A new family of linear programming (LP) discriminant models, the hybrid discriminant model, was recently presented with claims that it avoids all the problems of its predecessor LP models. However, this note shows that it does not avoid unacceptable solutions.

BLACK AND SCHOLES [2] HAVE derived a model for the equilibrium price of a European Stock Purchase option. According to the Black and Scholes model, equilibrium option prices are a function of the time to maturity of the option, the exercise price, the current price of the underlying stock, the risk free rate of interest, and the instantaneous variance of the stock's rate of return. Of these five variables, only the first four can be directly observed; the instantaneous variance of the stock's return can only be estimated. Recently, severdl authors [3, 4, 5, 6, 10, 11], rather than estimating a variance from past data, have attempted to employ the Black-Scholes option pricing formula to derive an "implied variance." An implied variance is the value of the instantaneous variance of the stock's return which, when employed in the BlackScholes formula, results in a model price equal to the market price. U-nfortunately, the implied variance cannot be calculated explicitly, and previous researchers have used numerical methods such as the Newton-Raphson method and its variants [8]. However for many options, no values of implied variance could be found to justify the observed option prices. In this note, necessary and sufficient conditions for the existence of a positive implied variance are given. An algorithm is presented which converges monotonically and quadratically to the (unique) implied variance, when it exists. The most valuable feature of this algorithm is that it provides a starting value for the first iteration of the Newton-Raphson procedure. If one applies the Newton-Raphson procedure without the correct starting value, solutions that do exist can be overlooked. The option pricing formula of Black and Scholes is

This paper considers the problem of computing, by iterative methods, optimal policies for Markov decision processes. The policies computed are optimal for all sufficiently small interest rates.