David Harlan Wood

On a Feasible–Infeasible Two-Population (FI-2Pop) Genetic Algorithm for Constrained Optimization: Distance Tracing and no Free Lunch

We explore data-driven methods for gaining insight into the dynamics of a two-population genetic algorithm (GA), which has been effective in tests on constrained optimization problems. We track and compare one population of feasible solutions and another population of infeasible solutions. Feasible solutions are selected and bred to improve their objective function values. Infeasible solutions are selected and bred to reduce their constraint violations. Interbreeding between populations is completely indirect, that is, only through their offspring that happen to migrate to the other population. We introduce an empirical measure of distance, and apply it between individuals and between population centroids to monitor the progress of evolution. We find that the centroids of the two populations approach each other and stabilize. This is a valuable characterization of convergence. We find the infeasible population influences, and sometimes dominates, the genetic material of the optimum solution. Since the infeasible population is not evaluated by the objective function, it is free to explore boundary regions, where the optimum is likely to be found. Roughly speaking, the No Free Lunch theorems for optimization show that all blackbox algorithms (such as Genetic Algorithms) have the same average performance over the set of all problems. As such, our algorithm would, on average, be no better than random search or any other blackbox search method. However, we provide two general theorems that give conditions that render null the No Free Lunch results for the constrained optimization problem class we study. The approach taken here thereby escapes the No Free Lunch implications, per se.

A PCR-based Protocol for In Vitro Selection of Non-crosshybridizing Oligonucleotides

DNA computing often requires oligonucleotides that do not produce erroneous cross-hybridizations. By using in vitro evolution, huge libraries of non-crosshybridizing oligonucleotides might be evolved in the test tube. As a first step, a fitness function that corresponds to noncrosshybridization has to be implemented in an experimental protocol. Therefore, a modified version of PCR that selects non-crosshybridizing oligonucleotides was designed and tested. Experiments confirmed that the PCR-based protocol did amplify maximally mismatched oligonucleotides selectively over those that were more closely matched. In addition, a reaction temperature window was identified in which discrimination between matched and mismatched might be obtained. These results are a first step toward practical manufacture of very large libraries of non-crosshybridizing oligonucleotides in the test tube.

Characterization of Non-crosshybridizing DNA Oligonucleotides Manufactured in vitro

Libraries of DNA oligonucleotides manufactured by an in vitro selection protocol were characterized for their non-crosshybridizing properties. Cloning and sequencing after several iterations of the protocol showed that the sequences, in general, became more non-crosshybridizing. Gel electrophoresis of protocol product, also, indicated non-crosshybridization, and showed evolution in the population of molecules under the non-crosshybridization selection pressure. Melting curves of protocol product also indicated non-crosshybridization when compared to control samples. Thus, it appears that the protocol does select populations of non-crosshybridizing sequences.

Test Tube Selection of Large Independent Sets of DNA Oligonucleotides

Self-assembly of nanostructures through template-matching hybridization reactions is potentially an important technique in nanotechnology. Given the possibility of errors in hybridization and the difficulty of designing DNA sequences on conventional computers, a viable alternative is to manufacture libraries of oligonucleotides for nanotechnology applications in the test tube. Thus, a protocol has been designed and tested to select mismatched oligonucleotides from a random starting material. Experiments indicate that the selected oligonucleotides are independent, and that there are about 10 000 distinct sequences. Such manufactured libraries are a potential enabling resource for DNA self-assembly in nanotechnology.

DNA Starts to Learn Poker

DNA is used to implement a simplified version of poker. Strategies are evolved that mix bluffing with telling the truth. The essential features are (1) to wait your turn, (2) to default to the most conservative course, (3) to probabilistically override the default in some cases, and (4) to learn from payoffs. Two players each use an independent population of strategies that adapt and learn from their experiences in competition.

Characterization of non-crosshybridizing DNA oligonucleotides manufactured In Vitro

Libraries of DNA oligonucleotides manufactured by an In Vitro selection protocol were characterized for their non-crosshybridizing properties. Cloning and sequencing after several iterations of the protocol showed that the sequences, in general, became more non-crosshybridizing. Gel electrophoresis of protocol product, also, indicated non-crosshybridization, and showed evolution in the population of molecules under the non-crosshybridization selection pressure. Melting curves of protocol product also indicated non-crosshybridization when compared to control samples. Thus, it appears that the protocol does select populations of non-crosshybridizing sequences.

In vitro selection of non-cross hybridizing oligonucleotides for computation

Since they minimize errors from cross-hybridizations, DNA oligonucleotides that annealas designed are beneficial to DNA computing. By in vitro selection, huge libraries of non-crosshybridizing oligonucleotides might be evolved in the test tube. As a first step, a fitness function corresponding to non-crosshybridization was based upon the duplex stability of randomly matched oligonucleotides. By melting pairs that have a low thermal stability, a protocol based on DNA polymerization selectively amplifies maximally mismatched oligonucleotides over those that were more closely matched. Experiments confirmed this property of the protocol, and in addition, a reaction temperature window was identified in which discrimination between matched and mismatched might be obtained. The protocol was iterated on a set of random starting material, and there was evidence that non-crosshybridizing libraries were in fact being created. These results are a step toward practical manufacture of very large libraries of non-crosshybridizing oligonucleotides in the test tube.

Universal Biochip Readout of Directed Hamiltonian Path Problems

Auni versal design for a biochip that reads out DNAe ncoded graphs is enhanced by a readout technique that may resolve multiple solutions of Hamiltonian path problems. Asin gle laboratory step is used. DNAen coded graphs are labeled with many quantum dot barcodes and then hybridized to the universal biochip. Optical readouts, one for each barcode, yield multiple partial readouts that may isolate individual paths. Computer heuristics then seek additional individual paths.

Product rules for the displacement of near-Toeplitz matrices

Abstract We consider displacements which are linear operations mapping a near-Toeplitz matrix into a low-rank matrix. The objective is to use this low-rank representation in solving matrix equations in place of using the full matrix. Two formulas for the displacement of the product of two matrices are presented and applied. Applications include multiplication of Toeplitz matrices, inversion of near-Toeplitz matrices, and finding the eigenvectors of a special class of matrices.

Exploring the Evolutionary Details of a Feasible-Infeasible Two-Population GA

A two-population Genetic Algorithm for constrained optimization is exercised and analyzed. One population consists of feasible candidate solutions evolving toward optimality. Their infeasible but promising offspring are transferred to a second, infeasible population. Four striking features are illustrated by executing challenge problems from the literature. First, both populations evolve essentially optimal solutions. Second, both populations actively exchange offspring. Third, beneficial genetic materials may originate in either population, and typically diffuse into both populations. Fourth, optimization vs. constraint tradeoffs are revealed by the infeasible population.