Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover

CSM-467: Quotient Geometric Crossovers

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In previous work we have started studying how metric transformations of the distance associated with geometric crossover affect the original geometric crossover. In particular, we focused on the product of metric spaces. This metric transformation gives rise to the notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way. In this paper, we study another metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many examples of application of the quotient geometric crossover

A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover

Accounting for Recent Changes of Gain in Dealing with Ties in Iterative Methods for Circuit Partitioning

In iterative methods for partitioning circuits, there is often a choice among several modules which will all produce the largest available reduction in cut size if they are moved between subsets in the partition. This choice, which is usually made by popping modules off a stack, has been shown to have a considerable impact on performance. By considering the most recent change in the potential reduction in cut size associated with moving each module between subsets, the performance of this LIFO (last-in first-out) approach can be significantly improved

A New Adaptive Hungarian Mating Scheme in Genetic Algorithms

In genetic algorithms, selection or mating scheme is one of the important operations. In this paper, we suggest an adaptive mating scheme using previously suggested Hungarian mating schemes. Hungarian mating schemes consist of maximizing the sum of mating distances, minimizing the sum, and random matching. We propose an algorithm to elect one of these Hungarian mating schemes. Every mated pair of solutions has to vote for the next generation mating scheme. The distance between parents and the distance between parent and offspring are considered when they vote. Well-known combinatorial optimization problems, the traveling salesperson problem, and the graph bisection problem are used for the test bed of our method. Our adaptive strategy showed better results than not only pure and previous hybrid schemes but also existing distance-based mating schemes

유전 알고리즘에서의 적응적 짝짓기 제도

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 문병로.짝짓기 제도는 자식 해를 만들기 위하여 두 부모를 선택하는 방법을 말한다. 이는 유전 알고리즘의 동작 전반에 영향을 끼친다. 본 논문에서 는,헝가리안방법을사용한짝짓기제도에대해연구하였다.그제도들은 대응되는 거리의 합을 최소화하는 방법, 최대화하는 방법, 그리고 비교를 위해 랜덤하게 대응시키는 방법들을 가리킨다. 본 논문에서는 이 제도들 을잘알려진문제인순회판매원문제와그래프분할문제에적용하였다. 또한 세대별로 가장 좋은 해가 어떻게 변화하는지 분석하였다. 이러한 분 석에 기초하여, 본 논문에서는 간단히 결합된 짝짓기 제도를 제안하였다. 제안된 제도는 결합되지 않은 제도에 비해 더 좋은 결과를 보였다. 본 논문에서는 또한, 본 논문의 핵심 방법인 짝짓기 제도를 결합하는 방법을 제안한다. 본 논문의 적응적인 짝짓기 방법은 세 헝가리안 제도 중하나를선택한다.모든짝지어진쌍은다음세대를위한짝짓기방법을 결정할 투표권을 갖게 된다. 각각의 선호도는 부모해간 거리와 부모해와 자식해의 거리의 비율을 통해 결정된다. 제안된 적응적 방법은 모든 단일 헝가리안짝짓기제도,비적응적으로결합된방법,전통적인룰렛휠선택, 기존의다른거리기준방법들보다좋은결과를보였다.제안된적응적방 법은정기적인해집단의유입과지역최적화와결합된환경에서도적절한 제도를 선택했다. 본 논문에서는 헝가리안 방법을 최대 혹은 최소의 지역 최적점을찾는방법으로교체했다.이방식역시지역최적점을찾는단일 방법들보다 좋은 결과를 보였다I. Introduction 1 1.1 Motivation 1 1.2 Related Work 2 1.3 Contribution 4 1.4 Organization 6 II. Preliminary 7 2.1 Hungarian Method 7 2.2 Geometric Operators 10 2.2.1 Formal Definitions 10 2.3 Exploration Versus Exploitation Trade-off 11 2.4 Test Problems and Distance Metric 13 III. Hungarian Mating Scheme 15 3.1 Proposed Scheme 15 3.2 Tested GA 18 3.3 Observation 18 3.3.1 Traveling Salesman Problem 18 3.3.2 Graph Bisection Problem 21 IV. Hybrid and Adaptive Scheme 28 4.1 Simple Hybrid Scheme 28 4.2 Adaptive Scheme 30 4.2.1 Significance of Adaptive Scheme 30 4.2.2 Proposed Method 31 4.2.3 Theoretical Support 34 4.2.4 Experiments 36 4.2.5 Traveling Salesman Problem 36 4.2.6 Graph Bisection Problem 40 4.2.7 Comparison with Traditional Method 41 4.2.8 Comparison with Distance-based Methods 42 V. Tests in Various Environments 50 5.1 Hybrid GA 50 5.1.1 Experiment Settings 50 5.1.2 Results and Discussions 51 5.2 GA with New Individuals 52 5.2.1 Experiment Settings 52 5.2.2 Results and Discussions 53 VI. A Revised Version of Adaptive Method 62 6.1 Hungarian Mating Scheme 62 6.2 Experiment Settings 62 6.3 Results and Discussions 63 VII. Conclusion 67 7.1 Summary 67 7.2 Future Work 68Docto