Data processing: artificial intelligence – Knowledge processing system
Reexamination Certificate
2001-11-19
2002-11-05
Starks, Jr., Wilbert L. (Department: 2121)
Data processing: artificial intelligence
Knowledge processing system
C706S013000, C716S030000, C716S030000
Reexamination Certificate
active
06477519
ABSTRACT:
TECHNICAL FIELD OF THE INVENTION
This invention relates generally to the field of set merging, and more specifically to a method of implementing a set merging function as an array of cells for use in a genetic algorithm machine.
BACKGROUND
Although evolutionary computing has roots as far back as the 1950s, genetic algorithms (hereinafter referred to by the initials GA) were introduced in 1975 by John Holland as a method for finding an optimum or near optimum solution to complicated problems. As noted by another researcher, Grefenstette, the GA is a useful method for finding optimum or near optimum solutions to the Traveling Salesman Problem, a classic and well-known computationally intractable problem.
With reference now to
FIG. 1
, there is illustrated therein a conceptual model of a genetic algorithm and how a solution to a problem evolves in processing the GA, generally designated by the reference numeral
100
. As is understood in this art, in a genetic algorithm, an emulated chromosomal data structure is initially designed to represent a candidate or trial solution. A number of chromosomes of that data structure are then randomly generated and are registered in groups or populations of solutions. Parent chromosomes are selected from this population of generated chromosomes according to a given algorithm, e.g., selected chromosomes
105
and
110
in FIG.
1
. Each generated chromosome is assigned a unique problem-specific fitness which may or may not differ from other chromosomes in the population, identifying the solution quality of the chromosome. The problem-specific fitness is expressed by a fitness value, as is known in the art. In a true evolutionary, survival of the fittest manner, particular chromosomes are selected from the population of chromosomes in proportion to their fitness values with more-fit chromosomes having a higher probability of being selected.
As further illustrated in
FIG. 1
, when a pair of parent chromosomes, e.g., chromosomes
105
and
110
, are selected from the population, the parent chromosomes are combined using a probabilistically generated cut point, designated by the reference numeral
120
. In the case of having no cutpoint generated, either of the parent chromosomes is simply copied to provide a new chromosome as a child chromosome. Thus, a child chromosome is created and outputted. The child chromosome, therefore, contains portions of each parent or the whole portion of a parent, e.g., a child chromosome
125
contains portion
105
A of parent chromosome
105
and portion
110
B of parent chromosome
110
, as illustrated in FIG.
1
. The child chromosome may then be mutated in a controlled manner, preferably having a low probability. In the evolutionary example illustrated in
FIG. 1
, the mutation is performed through inversion of a bit
130
in the child chromosome
125
, e.g., 0 to 1 or 1 to 0. A mutated child chromosome
125
′ is then evaluated to be assigned its fitness value. An evaluated child chromosome along with its fitness value is then stored as a member of the next generation in the population, perhaps replacing one or both of the associated parent chromosomes
105
and
110
.
After repeated iteration of this evolutionary process, the general fitness of chromosomes in the population improves toward the optimal solution. Thus, a solution to the problem emerges in the population, and is acquired with highly-fit chromosomes concentrated in the population.
In the conventional approach, a GA is emulated by software and the algorithm used for computing the fitness of a GA-based candidate solution to the combinatorial problem is also emulated by software. Due to such a software-based emulation on conventional computers, however, the execution speed of the algorithm for finding an optimum solution to the combinatorial problem is extremely slow.
Thus, a major drawback of conventional machines is the slow execution speed of a GA when emulated by software on conventional general-purpose computers.
A hardware-based implementation of a GA has been addressed for offsetting the drawback but only with a limited success in its execution speed. U.S. Pat. No. 5,970,487 to Shackleford, et al. solved some of the drawbacks and disadvantages of prior art techniques, particularly speed of operation, by the utilization of a hardware-based framework for accelerated used of genetic algorithms. The advantages and usages of the Shackleford et al. invention, Shackleford being the sole inventor in the instant application, are fully described in U.S. Pat. No. 5,970,487, which is incorporated by reference herein.
A common problem that is generally solved using a genetic algorithm is a combinatorial problem, also called a routing or ordering problem. A combinatorial problem is deemed to be a non-deterministic polynomial hard (NP-hard) problem, which is intractable to solve using brute force computations, e.g., finding solutions to such problems may take longer than the life of the universe. Indeed, such difficult problems must be solved by other paradigms, i.e., the genetic algorithm approach. A resource selection from among many resources by an applied form of a GA, minimizing the hardware architecture of a logic circuit, for example, will most efficiently solve an NP-hard combinatorial problem.
An example of a combinatorial problem is the Traveling Salesman Problem (or TSP), as is known in the art, which can be used to model many combinatorial, routing and ordering problems. The TSP seeks to find the shortest route between n cities, and while any solution which contains all n cities once and only once is valid, some solutions are better than others. A solution to the problem describes the order of travel between cities, which determines the distance of the route traveled, so the order of travel between cities having the shortest route is the best solution. It should be understood that the TSP is an NP-hard combinatorial problem with n! potential solutions and (n−1)! unique solutions.
With reference now to
FIG. 2
, there is illustrated a series of examples of solutions to a Traveling Salesman Problem. In an 8-city problem, having a particular arrangement of cities, any route that includes all cities once and only once is valid. In the first solution of
FIG. 2
, designated by the reference numeral
210
, one possible solution to the Traveling Salesman Problem is illustrated. However, it is apparent that solution
210
is not the best solution for the problem. The route depicted in solution
210
is clearly not the shortest possible route needed to cover all 8 cities. Another example, referenced by the numeral
220
, depicts another possible solution to the Traveling Salesman Problem although, again, solution
220
is not the best solution. The solution illustrated by the example referenced by the numeral
230
depicts the best solution, which is readily apparent as the solution having the shortest distance and, thus, the best order.
Because of the large number of possible solutions to a Traveling Salesman Problem, e.g., a 32-city TSP has over 2.5*10
35
solutions, heuristic and non-deterministic solving methods must be used to solve this type of problem. The TSP can be solved through a optimal solution-finding approach that aims at attaining an optimal solution through a screening process of candidate or trial solutions created through a GA, based upon a fitness evaluation of the candidate solutions. In this approach, more-fit candidate solutions are selected with less-fit candidate solutions screened out to concentrate highly-fit solutions or chromosomes and in the end to reach an optimal or near optimal solution.
The Shackleford et al. invention achieves significant increase in execution speed in its hardware implementation. The hardware implementation of a GA machine, such as that set forth in Shackleford et al., requires fast hardware-based implementations of the various steps of a GA machine, the parent selection step, the crossover step, the mutation step, the evaluation step, and the survival step.
However, the Shacklefo
Hewlett--Packard Company
Starks, Jr. Wilbert L.
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