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On the Impact of Migration Parameters on DIMEP for Designing Combinational Circuits
Abstract
This paper proposes an Island Model-based parallel linear genetic programming methodology: distributed multi expression programming (DMEP) to support the design of combinational logic circuits and investigates how the migration policy (the migration period, the number of migrants and the migration topology) affects the behavior of the evolutionary process in term of different statistics (computational effort, percentage of successful runs and average fitness) depending on the type and the size of the problems being solved. Two benchmark problems are considered: multiplier circuits and n-bit even parity circuits.
... The parameters used in [14] are given in table 12. According to [4] and [9] , the boolean even Parity problem appears to be extremely difficult to evolve using standard Fixed Population Size = 20 individuals 2−Bits adder with carry 2−Bits Multiplier MEP IMEP MEP IMEP A chromosome A chromosome A chromosome A chromosome length of 80 genes length of 50 length of 100 length of 50 yields over 90% genes yields over genes yields over genes yields successful runs. 100% successful 100%successful runs. ...
... According to [3], the Even Parity problem is a very hard classification problem for GP to solve; increasing rapidly in difficulty and solution size with N (N is the number of the problem inputs). Koza has shown that N = 5 represents, in effect, an upper limit for standard GP, even with a large population size of 8000 [4]. To solve the problem for N = 6 and higher, large populations and Automatically Defined Functions (ADF) [4] are required. ...
... Koza has shown that N = 5 represents, in effect, an upper limit for standard GP, even with a large population size of 8000 [4]. To solve the problem for N = 6 and higher, large populations and Automatically Defined Functions (ADF) [4] are required. In [14], two experiments have been done on both 3 and 4−bit parity problems. ...
Evolutionary Electronics is a research area which involves application of Evolutionary computation in the domain of electronics. It is seen as a quite promising alternative to overcome some drawbacks of conventional design. In this paper we propose a methodology based on an Improved Multi Expression Programming (IMEP) to automate the design of combinational logic circuits in which we aim to reach the functionality and to minimize the total num-ber of used gates. MEP is a genetic Programming variant that uses linear chromosomes for solution encoding. A unique MEP feature is its ability of encoding multiples solutions of a problem in a single chromosome. These solutions are handled in the same time complexity as other techniques that encode a single solution in a chromosome. This paper presents the main idea of an improved version of the MEP method, and shows positive preliminary experimental results.
... Migration topology affects the final solution quality and speed of convergence. In the [6]and [7]were investigated who must migrate from the source island to other island, selection of individuals is elitism or random and migration the elitism to other islands was suggested, hence, this migration method will have a greater impact on convergence. The migration and GA parameters were studied in articles [8]and [9], a fuzzy method for determining the migration rate, mutation rate and crossover rate was presented, The paper focuses on the convergence of each islands to determine the variables of IMPGA and the migration rate obtained of status of each island, determining the migration rate is only considered the convergence of each island that the obtaining convergence of each island is separate from the convergence of other islands , the convergence of the island (or subpopulation) is based on the global maximum fitness and the average individual fitness. ...
Parallel Genetic Algorithm (PGA) is used in many practical global optimizations to achieve high speed in convergence. The Island Model Parallel Genetic Algorithm (IMPGA) is very useful. Genetic Algorithms are one of the most powerful search and optimization method when we must solvecomplex and time consuming problems. IMPGA are more flexible than other PGA methods. There are several variables in the IMPGA that determining them are effective to enhance performance of the IMPGA. In this paper, we proposed a Migration method (Max-Min method). In our proposed method, according to status of subpopulation and comparing subpopulation with other subpopulations, the individuals for migrationare selected. In addition to enhancing the performance of PGA, we propose another method that embedding Hill-Climbing Algorithm within the structure of the PGA. As we know, creating an optimized structure for a Neural Network is a time consuming problem and costly one. The problem was studied in this paper is to determine the structure of a Neural Network forforecasting next day air quality. In addition, we used real data which was received from the Meteorological Organization and Tehran's Air Pollution Company. Output of the neural network is the value of Ozone Gas (o3) for the next 24 hours. The results of our two proposed methods are compared with conventional methods in other papers. Our algorithm has better performance than other papers.
Reversible logic is an emerging research area and has attracted significant attention in recent years. Developing systematic logic synthesis algorithms for reversible logic is still an area of research. Unlike other areas of application, there are relatively few publications on applications of genetic programming - (evolutionary algorithms in general) - to reversible logic synthesis. In this paper, we are introducing a new method; a variant of IMEP. The case of digital circuits for the even-parity problem is investigated. The type of gate used to evolve such a problem is the Fredkin gate.
This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.
A comparison between four evolutionary techniques for solving sym-bolic regression problems is presented in this paper. The compared methods are multi-expression programming, gene expression program-ming, grammatical evolution, and linear genetic programming. The comparison includes all aspects of the considered evolutionary algo-rithms: individual representation, fitness assignment, genetic opera-tors, and evolutionary scheme. Several numerical experiments using five benchmarking problems are carried out. Two test problems are taken from PROBEN1 and contain real-world data. The results reveal that multi-expression programming has the best overall behavior for the considered test problems.
The island model genetic algorithm shows promise as a superior formulation based on considerations from theories of natural evolution and from the efficiencies of coarse- grained parallel computer architectures. The theory of punctuated equilibria calls for the population to be partitioned into several distinct subpopulations. These subpopulations have extensive periods of isolated evolution, i.e. computation, occasionally interspersed with migration, i.e. communication. It is precisely for this sort of process with its alternating phases of extended computation and limited communication that message- passing multiprocessors (implementing coarse-grained parallelism) are best suited. We validate this promise of the island model and illustrate the effects of varying configuration attributes through experiments with a difficult very large-scale integration (VLSI) design problem.
Migration of individuals between populations may increase the selection pressure. This has the desirable consequence of speeding up convergence, but it may result in an excessively rapid loss of variation that may cause the search to fail. This paper investigates the effects of migration on the distribution of fitness. It considers arbitrary migration rates and topologies with different number of neighbors, and it compares algorithms that are configured to have the same selection intensity. The results suggest that migration preserves more diversity as the number of neighbors of a deme increases.
Evolutionary Electronics is a research area which involves application of Evolutionary computation in the domain of electronics. It is seen as a quite promising alternative to overcome some drawbacks of conventional design. In this paper we propose a methodology based on an Improved Multi Expression Programming (IMEP) to automate the design of combinational logic circuits in which we aim to reach the functionality and to minimize the total num-ber of used gates. MEP is a genetic Programming variant that uses linear chromosomes for solution encoding. A unique MEP feature is its ability of encoding multiples solutions of a problem in a single chromosome. These solutions are handled in the same time complexity as other techniques that encode a single solution in a chromosome. This paper presents the main idea of an improved version of the MEP method, and shows positive preliminary experimental results.
A need for solving more and more complex problems drives the Evolutionary Computation community towards advanced models of Evolutionary Algorithms. One such model is the island model which, although the subject of a variety of studies, still needs additional fundamental research. In this paper we have experimentally studied the influence of various migrations sizes and intervals on island models using a set of special functions. One of the surprising observations from these experiments is that the migration interval seems to be a dominating factor, with migration size generally playing a minor role with regard to the best solution found. Additional experiments measuring genetic diversity show that too frequent migrations cause islands to dominate others and lose global diversity before they are able to exchange solutions to produce better results. Also, we observe that even small migrations already make a significant impact on the behavior of an island model and therefore the effects are comparable to those of bigger migrations. On the other hand rare migrations cause a degraded performance due to the slow convergence. Collectively, these observations provide useful guidance for island model applications.
Evolutionary Electronics (EE) is a research area which involves application of Evolutionary Computation in the domain of electronics. EE algorithms are generally able to find good solutions to rather small problems in a reasonable amount of time, but the need for solving more and more complex problems increases the time required to find adequate solutions. This is due to the large number of individuals to be evaluated and to the large number of generations required until the convergence process leads to the solution. As a consequence, there have been multiple efforts to make EE faster, and one of the most promising choices is to use distributed implementations. In this paper, we propose a cluster-based evolutionary design of digital circuits using a distributed improved multi expression programming method (DIMEP). DIMEP keeps, in parallel, several sub-populations that are processed by Impoved Multi-Expression Programming algorithms, with each one being independent from the others. A migration mechanism produces a chromosome exchange between the subpopulations using MPI (Message Passing Interface) on a dedicated cluster of workstations (Lido Cluster, Dortmund University). This paper presents the main ideas and shows preliminary experimental results.
This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.
Parallel genetic algorithms (PGAs) have been traditionally used to overcome the intense use of CPU and memory that serial GAs show in complex problems. Non-parallel GAs can be classified into two classes: panmictic and structured-population algorithms. The difference lies in whether any individual in the population can mate with any other one or not. In this work, they are both considered as two reproductive loop types executed in the islands of a parallel distributed GA. Our aim is to extend the existing studies from more conventional sequential islands to other kinds of evolution. A key issue in such a coarse grain PGA is the migration policy, since it governs the exchange of individuals among the islands. This paper investigates the influence of migration frequency and migrant selection in a ring of islands running either steady-state, generational, or cellular GAs. A diversity analysis is also offered from an entropy point of view. The study uses different problem types, namely easy, deceptive, multimodal, NP-Complete, and epistatic search landscapes in order to provide a wide spectrum of problem difficulties to support the results. Large isolation values and random selection of the migrants are demonstrated as providing a larger probability of success and a smaller number of visited points. Also, interesting observations on the relative performance of the different models are offered, as well as we point out the considerable benefits that can accrue from asynchronous migration.
Multi Expression Programming (MEP) is a new evolutionary paradigm intended for solving computationally difficult problems. MEP individuals are linear entities that encode complex computer programs. MEP chromosomes are represented in the same way as C or Pascal compilers translate mathematical expressions into
machine code. MEP is used for solving some difficult problems like symbolic regression and game strategy discovery. MEP is compared with Gene Expression Programming (GEP) and Cartesian Genetic Programming (CGP) by using several well-known test problems. For the considered problems MEP outperforms GEP and CGP. For these examples, MEP is two magnitude orders better than CGP.
A new evolutionary technique, called Infix Form Genetic Programming (IFGP) is proposed in this paper. The IFGP individuals are strings encoding complex mathematical expressions. The IFGP technique is used for solving several classification problems. All test problems are taken from PROBEN1 and contain real world data. IFGP is compared to Linear Genetic Programming (LGP) and Artificial Neural Networks (ANNs). Numerical experiments show that IFGP is able to solve the considered test problems with the same (and sometimes even better) classification error than that obtained by LGP and ANNs.
The island model genetic algorithm shows promise as a superior formulation based on considerations from theories of natural evolution and from the efficiencies of coarse-grained parallel computer architectures. The theory of "punctuated equilibria" calls for the population to be partitioned into several distinct subpopulations. These subpopulations have extensive periods of isolated evolution, i.e., computation, occasionally interspersed with migration, i.e., communication.
. This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node functions are also separately numbered. The genotype is just a list of node connections and functions. The genotype is then mapped to an indexed graph that can be executed as a program. Evolutionary algorithms are used to evolve the genotype in a symbolic regression problem (sixth order polynomial) and the Santa Fe Ant Trail. The computational effort is calculated for both cases. It is suggested that hit effort is a more reliable measure of computational efficiency. A neutral search strategy that allows the fittest genotype to be replaced by another equally fit genotype (a neutral genotype) is examined and compared with non-neutral search for the Santa Fe ant problem. The neutral search...
In this paper we present a systematic experimental study of some of the parameters influencing parallel and distributed genetic
programming (PADGP) by using three benchmark problems. We first present results on the system’s communication topology and
then we study the parameters governing individual migration between subpopulations: the number of individuals sent and the
frequency of exchange. Our results suggest that fitness evolution is more sensitive to the migration factor than the communication
topology.
An abstract is not available.
We describe a Genetic Algorithm that can evolve complete programs. Using a variable length linear genome to govern the mapping of a Backus Naur Form grammar definition to a program, expressions and programs of arbitrary complexity may be evolved. Our system, Grammatical Evolution, has been applied to problems such as a Symbolic Regression problem, and finding Trigonometric Identities. In this paper we describe how we applied GE to a Symbolic Integration problem, that being finding a function which is an integral of Cos(X)+2X +1. We also show how a Steady State selection mechanism was found to improve the performance of Grammatical Evolution.
Gene expression programming, a genotype/phenotype genetic algorithm (linear and ramified), is presented here for the first time as a new technique for the creation of computer programs. Gene expression programming uses character linear chromosomes composed of genes structurally organized in a head and a tail. The chromosomes function as a genome and are subjected to modification by means of mutation, transposition, root transposition, gene transposition, gene recombination, and one- and two-point recombination. The chromosomes encode expression trees which are the object of selection. The creation of these separate entities (genome and expression tree) with distinct functions allows the algorithm to perform with high efficiency that greatly surpasses existing adaptive techniques. The suite of problems chosen to illustrate the power and versatility of gene expression programming includes symbolic regression, sequence induction with and without constant creation, block stacking, cellular automata rules for the density-classification problem, and two problems of boolean concept learning: the 11-multiplexer and the GP rule problem.
Genetic Programming with Context-Sensitive Grammars
- N Patterson
Patterson, N., Genetic Programming with Context-Sensitive Grammars, Ph.D. Thesis, School of Computer Science, University of Scotland, 2002
Grammatical Evolution : A Steady State Approach, Late Breaking Paper, Genetic Programming
- C Ryan
- O Neill
Ryan, C., O'Neill, M., Grammatical Evolution : A Steady State Approach, Late Breaking Paper, Genetic Programming, Edited by J.R. Koza (University of Wisconsin, Madison, Wisconsin, 1998).
Evolutionary Design of Digital Circuits Using Distributed Linear Genetic Programming on Graphs under the structural model of " Islands
- F Z Hadjam
- C Moraga
Hadjam F. Z., Moraga C., Evolutionary Design of Digital Circuits Using Distributed Linear Genetic Programming on Graphs under the structural model of " Islands ". Research Report, European Centre for Soft Computing, Mieres, Asturias, Spain, 2007.
The influence of migration sizes and intervals on island models
- Z Skoliki
- De Jong
Skoliki, Z., De Jong, K., The influence of migration sizes and intervals on island models, In: Proceedings of the Conference on Genetic and Evolutionary Computation, 2005, 1295-1302.