Ronald W. Shonkwiler

Applications of random restart to genetic algorithms

In this paper, a new genetic algorithm is introduced in which the mutation operation has been replaced with random restart. The new genetic algorithm is applied to the problem of scheduling a set of tasks onto a multiprocessor system. This problem is known to be NP-complete. Using the Markov chain method, the expected time for the algorithm to reach an optimal solution is derived analytically and computed for several different problem sizes. These results indicate that the expected time to reach the goal for the mapping problem increases sublogarithmically as the size of the search spaces grows exponentially. It is also shown that the expected time to reach an optimal solution is proportional to the time the algorithm spends among the transient states.

Genetic algorithm/neural network synergy for nonlinearly constrained optimization problems

Michalewicz and Janikow (1991) proposed a methodology for applying genetic algorithms to constrained optimization problems in which the constraint equations are linear. They show that the set of feasible solutions can be more thoroughly searched by requiring the genetic population to remain in the set of feasible solutions and propose adopting a weighted average rule for combining parent gene strings in genetic crossover. Because the set of feasible solutions is convex, the population remains feasible. Unfortunately, this technique does not extend to the general case of nonlinear constraints. The purpose of this paper is to present a general technique by which a population can be restricted to a set of feasible solutions, even when the constraints are nonlinear. The technique combines the strengths of neural networks with the strengths of genetic algorithms by substituting a neural network operator for the usual method of genetic crossover.<<ETX>>

Finance with Monte Carlo

1. Geometric Brownian Motion and the Efficient Market Hypothesis.- 2. Return and Risk.- 3. Forward and Option Contracts and their Pricing.- 4. Pricing Exotic Options.- 5. Option Trading Strategies.- 6. Alternative to GBM Prices.- 7. Kellys Criterion.- Appendices.- A. Some Mathematical Background Topics.- B. Stochastic Calculus.- C. Convergence of the Binomial Method.- D. Variance Reduction Techniques.- E. Shell Sort.- F. Next Day Prices Program.- References.- List of Notation.- List of Algorithms.- Index.

Simulated annealing for throughput optimization in communication networks with window flow control

A queuing model of a multichain network is presented where the network is window flow controlled on its virtual channel of the communication network. Its performance is optimized based on simulated annealing. The solution space is assumed to be the set of all admissible service rates of all stations with the nonlinear cost constraint. The optimum total throughput of the network is determined for different chain packets. It is shown that the most desirable method against congestion in any region is to speed up the transmission rate of that channel, but since this costs too much, alternative methods should be considered which reduce the window size within the tolerable limit of throughputs.<<ETX>>

On age-dependent branching processes with immigration

Abstract We derive the probability generating function for the general Bellman—Harris age dependent branching process with immigration emphasizing the role of immigration parameters. The solution requires solving a single scalar-valued integral equation, namely the usual Bellman—Harris equation. Our results are applied to three particular examples. We derive the equations for the immigration of particles governed by a Bellman—Harris process into a second Bellman—Harris process. In the second example we study Poisson immigration of particles into a time continuous Markov branching process. In the third, we derive the equations for a one-time immigration into a Bellman—Harris process.

Annealing a Genetic Algorithm for Constrained Optimization

In this paper, we adapt a genetic algorithm for constrained optimization problems. We use a dynamic penalty approach along with some form of annealing, thus forcing the search to concentrate on feasible solutions as the algorithm progresses. We suggest two different general-purpose methods for guaranteeing convergence to a globally optimal (feasible) solution, neither of which makes any assumptions on the structure of the optimization problem. The former involves modifying the GA evolution operators to yield a Boltzmann-type distribution on populations. The latter incorporates a dynamic penalty along with a slow annealing of acceptance probabilities. We prove that, with probability one, both of these methods will converge to a globally optimal feasible state.

A validation study of a simulation model for common source epidemics

We consider an environment and a population of individuals who are susceptible to a disease caused by a pathogen spread from a common source. We view the sequence of events resulting in the illness of some individuals as consisting of three components: the introduction of the pathogens and their dispersion through the environment, the movement of susceptible individuals through the environment, and the physiological effects of exposure of susceptible individuals to various pathogen levels. We identify four important parameters: two for each of the first and third components. A computer simulation of a model with these features is developed and implemented to study a 1977 outbreak of toxoplasmosis. Questions of parameter estimation and model validation are considered in detail.

Classification power of multiple-layer artificial neural networks

Feedforward networks are artifical neural networks composed of successive layers of neurons. In this paper we use mathematical and geometric analysis to investigate properties of classifiers feedforward networks composed of neurons having threshold activation functions. The focus of this investigation is the relationship between the classification power of these networks and the number of layers composing them. We show that regions classifiable by simple twolayer classifiers also known as perceptrons are closed under region complementation and a limited form of region intersection. The proof of these results leads to a method for constructing twolayer classifiers for complicated regions. 1

A Model for Infection

There have been numerous mathematical studies on the spread of epidemics. Many useful and interesting results have been discovered thereby. However, to our knowledge all have treated the process beginning with an individual’s exposure to the causative agent and leading to incidence of disease in this individual on a purely empirical basis. Typically these models assume the aggregate number of new cases of illness to be proportional to the present number of cases. This may be completely appropriate in relation to the conclusion of the study but sheds no information on the processes of infection itself. It is known that illness among laboratory animals exposed to disease agents often result in only a fraction of the animals actually incurring the disease. Further it is known that mammals possess at least two defense mechanisms against disease organisms. Thus it is possible that some degree of exposure to the causative agent for a disease need not result in onset of illness. Indeed all organisms are constantly exposed to disease agents with frequently no ill effect.

Parallel simulated annealing for the n-queen problem

A parallel simulated annealing method, IIP, is applied to the n-queen problem. By this method, identical multiple copies of the single process algorithm are independently run in parallel. This technique gives superlinear speedup, in some cases on the order of 50 using only 8 processors. Convergence to the solution exceeds 99.96% for as few as 4 processors. In addition, simulated annealing was compared with a constant temperature version of itself since the resulting homogeneous Markov chain is amendable to Perron-Frobenius analysis. The two algorithms perform similarly.<<ETX>>