This paper proposes a novel evolutionary algorithm called Epistocracy which
incorporates human socio-political behavior and intelligence to solve complex
optimization problems. The inspiration of the Epistocracy algorithm originates
from a political regime where educated people have more voting power than the
uneducated or less educated. The algorithm is a self-adaptive, and
multi-population optimizer in which the evolution process takes place in
parallel for many populations led by a council of leaders. To avoid stagnation
in poor local optima and to prevent a premature convergence, the algorithm
employs multiple mechanisms such as dynamic and adaptive leadership based on
gravitational force, dynamic population allocation and diversification,
variance-based step-size determination, and regression-based leadership
adjustment. The algorithm uses a stratified sampling method called Latin
Hypercube Sampling (LHS) to distribute the initial population more evenly for
exploration of the search space and exploitation of the accumulated knowledge.
To investigate the performance and evaluate the reliability of the algorithm,
we have used a set of multimodal benchmark functions, and then applied the
algorithm to the MNIST dataset to further verify the accuracy, scalability, and
robustness of the algorithm. Experimental results show that the Epistocracy
algorithm outperforms the tested state-of-the-art evolutionary and swarm
intelligence algorithms in terms of performance, precision, and convergence.
1,4 Dept. of Computer Science, Wayne State University, Detroit, MI 48202, USA
享年1,4。 コンピュータサイエンス、ウェイン州立大学、デトロイト、MI 48202、米国。
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2,3 Dept. of Radiology, Henry Ford Health System, Detroit, MI 48202, USA
2,3頁。 放射線学, ヘンリー・フォード健康システム, デトロイト, MI 48202, アメリカ
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Abstract. This paper proposes a novel evolutionary algorithm called Epistocracy which incorporates human socio-political behavior and intelligence to solve complex optimization problems.
The inspiration of the Epistocracy algorithm originates from a political regime where educated people have more voting power than the uneducated or less educated.
The algorithm is a selfadaptive, and multi-population optimizer in which the evolution process takes place in parallel for many populations led by a council of leaders.
To avoid stagnation in poor local optima and to prevent a premature convergence, the algorithm employs multiple mechanisms such as dynamic and adaptive leadership based on gravitational force, dynamic population allocation and diversification, variance-based step-size determination, and regression-based leadership adjustment.
The algorithm uses a stratified sampling method called Latin Hypercube Sampling (LHS) to distribute the initial population more evenly for exploration of the search space and exploitation of the accumulated knowledge.
To investigate the performance and evaluate the reliability of the algorithm, we have used a set of multimodal benchmark functions, and then applied the algorithm to the MNIST dataset to further verify the accuracy, scalability, and robustness of the algorithm.
Experimental results show that the Epistocracy algorithm outperforms the tested state-of-the-art evolutionary and swarm intelligence algorithms in terms of performance, precision, and convergence.
1 Introduction that Evolutionary computation (EC) encompasses methods mimicking mechanisms of biological evolution to solve various optimization problems.
An optimization problem essentially requires finding a set of parameters 𝑥⃗ = (𝑥1, … , 𝑥𝑛) 𝑆 of the current system, such that a certain quantity 𝑓: 𝑆 → ℝ is maximized (or minimized) ∀𝑥⃗ 𝑆 ∶ 𝑓(𝑥⃗) ≤ 𝑓(𝑥⃗∗).
最適化問題は、本質的には、ある量 f: S → R が最大化(または最小化)されるような、現在の系のパラメータ x* = (x1, ... , xn) の集合を見つける必要がある。 訳抜け防止モード: 最適化問題には基本的にパラメータのセットを見つける必要がある。 特定の量 f : s → r が最大となるように、現在の系の s は ..., xn) である。 or minimized ) ∀𝑥⃗ 𝑆 ∶ 𝑓(𝑥⃗ ) ≤ 𝑓(𝑥⃗∗ ) .
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is a subfield of artificial
人工のサブフィールドです
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intelligence
インテリジェンス
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Over the past few decades, many state-of-the-art evolutionary algorithms such as Genetic algorithm (GA) and Evolutionary Strategies (ES) have been proposed for applications where a well-defined or closed-form solution does not exist [1].
Genetic algorithm was developed by John Holland in the early 1970s [2]-[4] mimicking Darwinian theory of survival of the fittest and Evolutionary Strategies founded by Rechenberg and Schwefel in 1965 [5]-[7] based on the hypothesis that small mutations occur more commonly than large mutations.
Both Genetic algorithm and Evolutionary Strategies rely on the concept of population, representing potential solutions to the optimization problem which iteratively undergo genetic operators to improve their fitness score.
While Genetic algorithms use a binary string of digits to represent solutions and use both mutation and recombination as genetic operators, in Evolutionary Strategies a fixed-length real-valued vector is used for representation, and only mutation is used as a primary search operator.
In evolutionary algorithms, the recombination operator performs an information exchange, and the mutation operator generates variations of the solutions and increases the diversity among the population.
The selection operator, however, makes better individuals to survive and reproduce.
しかし、選択オペレーターは、生存と繁殖のためにより良い個人を作る。
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Another subset of nature-inspired algorithms is Swarm Intelligence (SI) which is based on collective behavior of a decentralized, self-organizing network of agents such as bird flocks or honeybees.
In SI algorithms, multiple agents can locally interact and exchange heuristic information which leads to the emergence of global behavior of adaptive search and optimization.
This algorithm is inspired by social behavior of bird flocking and fish schooling.
このアルゴリズムは、鳥の群れと魚の学業の社会的行動にインスパイアされている。
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Similar to GA, PSO is initialized with a population of random candidate solutions that are improved iteratively over time, however, unlike GA has no evolution operators such as recombination and mutation.
This algorithm is inspired by natural behavior of cuckoos who lay their eggs in other birds' nests for breeding.
このアルゴリズムは、他の鳥類の巣に卵を産むカクーの自然な行動にインスパイアされている。
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Compared to other approaches, Cuckoo requires fewer numbers of parameters to be fine-tuned.
他のアプローチと比較して、Cuckooは微調整されるパラメータの数が少ない。
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In 2018, Mareli et al.
2018年に、Mareliら。
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[18] developed three new Cuckoo search algorithms using linear, exponential and power increasing switching parameters to maintain an optimum balance between local and global exploration and increase the efficiency of CS algorithm.
[19] proposed a new variant of CSA called I-PKL-CS
[19]I-PKL-CSという新しいCSAの提案
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algorithm which employs self-adaptive knowledge learning strategies to mitigate premature convergence and poor balance between exploitation and exploration.
自己適応型知識学習戦略を採用して、早期収束と搾取と探索の間のバランス不良を緩和するアルゴリズム。
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IPKL-CS exploits individual and population knowledge learning to improve the quality of solutions and convergence rate.
IPKL-CSは個人および人口の知識の学習を解決および収束率の質を改善するために利用します。
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There exist many real-world applications for EC.
ECには多くの実世界の応用がある。
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In [20], the genetic algorithm was used to decrease the dimension of the data and to optimize the weights and biases of the neural network in ECG signal classification.
The selection of an evolutionary approach can drastically reduce the amount of time needed for finding an optimal solution.
進化的アプローチの選択により、最適なソリューションを見つけるのに必要な時間を大幅に削減できます。
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According to several studies, evolutionary algorithms, in general, suffer from various problems such as limited searching ability [25]-[27], curse of dimensionality and scalability [28], [29], premature convergence and stagnation [30]-[33], and poor performance which usually occur in the absence of population diversity and adaptability [34]-[36], and due to unbalanced exploration-exploita tion capacities [37], [38].
The work reported in this paper was motivated by the fact that optimization algorithms require new explorative and exploitative capabilities along with a dynamic resource allocation technique and diversification strategies to help them converge to the optimal solution at the early stages of the optimization process.
There is a need for a new generation of evolutionary algorithms that can avoid entrapment in local optima and prevent premature convergence [39], [30].
In this paper, we propose a new hyper-heuristic algorithm based on a political regime called Epistocracy where educated people have more voting power (weight) than the uneducated or less educated.
The Epistocracy algorithm splits the population into Governors and Citizens based on the performance of the individuals.
エピストクラシーのアルゴリズムは、個人のパフォーマンスに基づいて、人口を知事と市民に分割する。
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The Citizens are assigned Governors based on the degree of similarity and the exercise of free will.
市民は類似度と自由意志の行使度に基づいて知事を任命される。
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Once a Citizen is assigned a Governor, they move towards their Governor in an attempt to mimic some of the traits which made their Governor successful.
Governors will also try to improve themselves and lead their population to collaboratively search for the optimal solution.
知事は自らを改良し、住民を協力して最適な解決策を探そうとする。
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The Epistocracy algorithm is a self-adaptive, and multi-population optimizer in which the evolution process takes place in parallel for many populations led by a council of leaders.
To avoid entrapment in poor local optima and to prevent a premature convergence, the algorithm employs multiple mechanisms such as dynamic and adaptive leadership based on gravitational force, dynamic population allocation and diversification, variance-based step-size determination, and regression-based leadership adjustment.
The algorithm uses a stratified sampling method called Latin
このアルゴリズムはラテンという層別サンプリング法を用いる
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Hypercube Sampling (LHS) to distribute the initial population more evenly for exploration of the search space and exploitation of the accumulated knowledge.
Section 2 describes the overall structure of the Epistocracy algorithm in detail.
第2節では、エピストクラシーアルゴリズムの全体構造を詳細に記述する。
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Experimental results and comparative studies on benchmark test functions along with Convolutional Neural Networks (CNNs) parameter optimization are presented in Section 3.
John Stuart Mill (1806-1873), the British philosopher and political economist in his book “Mill on Bentham and Coleridge” proposed to give more votes to the better educated [40].
ジョン・スチュアート・ミル(1806-1873)は、イギリスの哲学者であり、彼の著書「Mill on Bentham and Coleridge」で政治経済学者である。
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Jason Brennan believes that more competent or knowledgeable citizens must have slightly more political power than less competent citizens [41].
Jason Brennan氏は、より有能で知識のある市民は、より有能な市民よりもわずかに政治的権力を持つ必要があると考えている[41]。
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In fact, the problem with democracy is the elimination of the epistemic dimension of democracy.
実際、民主主義の問題は民主主義の認識論的な次元の排除である。
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While Democracy is more about the input aspect of the decision-making process, Epistocracy is concerned about the output.
Epistocracy algorithm is multi-population optimization algorithm which seeks to minimize the time taken to find an optimal value for the problem being solved.
As an adaptive, hyper-heuristic algorithm, Epistocracy employs problem-related knowledge, and globally aggregated statistics to automatically adjust itself during each run and search through a space of meta-heuristics to find the optimal solution.
Epistocracy attempts to incorporate human sociopolitical behavior and intelligence to improve the performance and convergence speed and reduce the probability of getting trapped in local optima compared to other meta-heuristic algorithms.
Information is systematically propagated among citizens and governors.
情報は市民と知事の間で体系的に伝達される。
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Fig. 2 shows the flowchart of the proposed algorithm.
フィギュア。 2は,提案アルゴリズムのフローチャートを示す。
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Fig. 2. Flowchart of the Epistocracy algorithm with all steps involved from the
フィギュア。 2. からのすべてのステップを含むエピストクラシーアルゴリズムのフローチャート。
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population generation until outputting the optimal solution.
最適なソリューションを出力するまでの人口発生。
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2.2 Generating the Initial Population
2.2 初期人口の生成
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The Epistocracy algorithm starts the optimization process by generating a population of random solutions, using a stratified sampling method called Latin Hypercube Sampling (LHS) which was originally proposed by McKay in 1979 [42].
Each individual solution has a set of genes or attributes known as chromosome which are defined using their corresponding upper and lower bounds in the search space.
各溶液は染色体と呼ばれる一連の遺伝子または属性を持ち、対応する上界と下界を探索空間で定義する。
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In this algorithm, the set of attributes represent the initial position and level of political knowledge of each individual in the society.
このアルゴリズムでは、属性のセットは、社会における各個人の政治的知識の初期位置とレベルを表します。
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2.3 Performance Evaluation The performance of an individual in the population is evaluated using a pre-defined fitness function.
2.3 性能評価 予め定義されたフィットネス機能を用いて、人口の個人のパフォーマンスを評価する。
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Given the individual’s current chromosome, the actual performance is calculated and stored as an individual’s “actual performance.” The previous actual performance is also recorded for future reference.
Individual solutions are then ranked based on their actual performance (fitness score).
個々のソリューションは、実際のパフォーマンス(適合度スコア)に基づいてランク付けされる。
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The adjusted performance is calculated based on the actual performance of each individual solution.
調整された性能は、各ソリューションの実際のパフォーマンスに基づいて算出される。
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The calculation steps will be explained in detail in the following sections.
計算手順は、以下のセクションで詳細に説明します。
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2.4 Population Separation
2.4 人口分離
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Different people demonstrate different understandings of patterns of change and achieve different levels of success and result upon the social hierarchy.
2.5 Governor Assignment Before evolving each individual and moving them around, about five percent of the top-performing individuals in each generation are selected as a set of governors to lead the population and help them improve their performance.
Transcending traditional societies, in Epistocracy, governments have no obvious borders, and individuals can follow or vote for any governor anywhere expressing the idea of “Global Village”.
In the Epistocracy algorithm, each individual is assigned to a governor based on their phenotypic characteristics, and the degree of influence and impact of the governor on the citizen.
To that end, the Gravitational Force (1) is used to calculate the magnitude of attraction between each citizen and every governor.
この目的のために、重力(1)は、各市民と各知事の間の引力の大きさを計算するために用いられる。
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A governor with a larger gravitational force has a higher probability to attract a citizen and form a larger territory.
大きな重力力を持つ知事は、市民を引き寄せ、より大きな領域を形成する確率が高い。
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However, some citizens may act as rebels and resist against the orders of the befitting authorities and may follow different governors.
しかし、一部の市民は反乱者として行動し、適格な当局の命令に抵抗し、異なる総督に従うことができる。
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𝐹 = 𝐺 × ( 𝑚1 × 𝑚2
𝐹 = 𝐺 × ( 𝑚1 × 𝑚2
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𝑟2 ) (1)
𝑟2 ) (1)
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In the above equation of the Gravitational Force, G is a constant, and m1, and m2, are the adjusted performances of the governor and citizen respectively.
The Euclidean distance (3) is used to calculate the distance r between a governor
ユークリッド距離(3)は、知事間の距離rを計算するために使用される
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and a citizen. 𝑑𝑖𝑠𝑡(𝒙𝒊, 𝒙𝒋) = ‖𝒙𝒊 − 𝒙𝒋‖ = √∑(𝑥𝑖𝑘 − 𝑥𝑗𝑘)
そして市民だ 𝑑𝑖𝑠𝑡(𝒙𝒊, 𝒙𝒋) = ‖𝒙𝒊 − 𝒙𝒋‖ = √∑(𝑥𝑖𝑘 − 𝑥𝑗𝑘)
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2 𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠
2 𝑛 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠
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𝑘=1 (3) To imitate the rebelliousness of citizens, a roulette wheel with the governors' calculated gravitational forces is used to give citizens a freedom of selecting other governors with even a greater dissimilarity (distance).
This will help the algorithm to explore the interspace between the governors by moving a citizen across the governments.
これは、市民を政府に移動させることで、知事間の空間を探索するアルゴリズムに役立つだろう。
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The selection probability is defined using the following equation:
選択確率は次の式で定義されます。
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𝑃𝑗 = 𝐺(𝑆𝑗) 𝑛 𝑖=1
𝑃𝑗 = 𝐺(𝑆𝑗) 𝑛 𝑖=1
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∑ 𝐺(𝑆𝑖) (4)
∑ 𝐺(𝑆𝑖) (4)
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In (4), n is the number of governors.
(4)では、nは知事の数である。
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G is the gravitational force of solution Sj.
G は解 Sj の重力力である。
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In the next generation, if the assigned governor is overthrown or resigned due to their poor performance or their own population votes, the surviving citizen will choose a new governor from the updated list of governors.
In this case, the governor will lose his popularity regardless of his own performance at the time of being selected.
この場合、知事は選出された時点で自分の業績に関係なく、その人気を失うことになる。
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In fact, a governor's popularity rests on his credibility and competence, and his performance in leading his population and improving their lives.
実際、知事の人気は、その信任性と能力と、その人口をリードし、その生活を改善する業績にかかっている。
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By adjusting the actual performance of the governor, the governor's rank in the governors list will change.
知事の実際の業績を調整することによって、知事リストの知事のランクは変わります。
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Given that, this governor will have a lower chance to be selected by new citizens who do not have any governor yet.
それを考えると、この知事は、まだ知事を持っていない新しい市民によって選ばれる機会が低くなります。
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2.6 Leading the Population
2.6 人口を先導する
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In the next step, the Epistocracy algorithm allows governors to lead their own population.
次のステップでは、エピストクラシー・アルゴリズムによって知事が自身の人口を導くことができる。
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Each citizen will take a step of variable length (5) toward his governor to improve his performance and become similar and even better than their governor.
step size is proportional to the distance between the governor and citizen and inversely proportional to the self-improvement of the citizen under the rule of the governor.
ステップサイズは、知事と市民の間の距離に比例し、総督の統治下での市民の自己改善に逆比例する。
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The following formula is used to calculate the next step of each citizen:
以下の式は、各市民の次のステップを計算するために使われる。
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𝑆𝑖 = ( 𝐼𝑎𝑣𝑔 𝐼𝑚𝑖𝑛
𝑆𝑖 = ( 𝐼𝑎𝑣𝑔 𝐼𝑚𝑖𝑛
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) × 𝜎2 × 𝑑𝑖,𝑔 × 𝜑
) × 𝜎2 × 𝑑𝑖,𝑔 × 𝜑
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(5) where Si is the individual’s new step size, and Iavg is the average improvement of the governor’s sub-population (7).
Imin is the minimum improvement in the population.
イミンは人口の最小限の改善である。
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σ2 is the variance of the sub-population, and di,g is the Euclidean distance between the individual and its designated governor.
σ2はサブ人口の分散であり、di,gは個人と指定された知事の間のユークリッド距離である。
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φ is the rate of change equal to 0.1.
φ は 0.1 に等しい変化率である。
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The selfimprovement is calculated as follows:
自己改善は次のように計算される。
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𝐼𝑖 = (𝑃𝑜𝑙𝑑 𝑖 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖)
𝐼𝑖 = (𝑃𝑜𝑙𝑑 𝑖 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖)
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(6) The self-improvement is the difference between the old and the current actual performance of the citizen.
(6) 自己改善とは、高齢者と現在の市民のパフォーマンスの違いである。
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The average improvement is then calculated by:
平均的な改善は次のようになります。
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𝐼𝑎𝑣𝑔 = 1 𝑛
𝐼𝑎𝑣𝑔 = 1 𝑛
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𝑛 × ∑ 𝐼𝑖 𝑖=1
𝑛 × ∑ 𝐼𝑖 𝑖=1
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(7) In (7), n is the size of the governor’s sub-population.
(7) 7)では、nは知事のサブ人口の大きさである。
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The average improvement is an important factor for the step size determination.
平均的な改善はステップ サイズ決定のための重要な要因です。
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To avoid missing any minima or maxima, a smaller step will be taken when a larger improvement is achieved, and a larger step will be taken when a smaller improvement is obtained.
The population variance is given by the following formula:
人口変動は以下の式によって与えられる。
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𝜎2 = ∑(𝑥𝑖 − 𝜇)2
𝜎2 = ∑(𝑥𝑖 − 𝜇)2
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𝑛 (8) To reflect the diversity of the society, if a citizen by taking a new step becomes exactly similar to his governor or another citizen in the same population, the citizen will be mutated to save the system resources.
This also helps the algorithm to avoid division by zero in calculating the gravitational force when the distance between a citizen and his governor becomes zero.
Similar to citizens, governors will also improve themselves by taking a step in a direction that hopefully increases their performance.
市民と同様に、知事は自分のパフォーマンスを高める方向に一歩踏み出すことで、自らを改善する。
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To that end, the variance of governors’ population is calculated, helping governors converge toward a location with the highest possibility of finding the optimal solution.
The next step size of the governor is calculated like that of a citizen.
知事の次のステップサイズは、市民のステップのように計算される。
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However, instead of calculating the distance between the governor and citizen, this time the governor’s previous step is considered according to the following formula:
Since the governor is in charge of leading his population and pushing them to the right direction, the algorithm will let the governor take a step only if that step improves his overall performance, otherwise, the governor will stay in his previous place without making any movement.
Since for computing the new step the variance of all governors is used, in the next iterations for the same governor the step size might be different and might help the governor to get improved and consequently positively contribute to the improvement of his population.
The following piecewise function (11) shows the conditional step that must be taken by each governor, provided that the step improves the governor’s actual performance:
This formula is designed for a minimization optimization problem.
この式は最小化最適化問題のために設計されている。
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2.8 Governor’s Performance Adjustment
2.8 知事のパフォーマンス調整
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When a population performs well or poorly under a leadership of a governor, the algorithm will adjust the governor’s actual performance to allocate the right amount of resources (individuals) to the governor.
For example, if a population is performing well, that must increase the trust of the population in the governor.
例えば、人口がうまく機能している場合、それは知事の人口の信頼を高める必要があります。
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In this case, generally more individuals will be following the governor to help him accomplish the task of finding the optimal solution.
この場合、より多くの個人が知事に従い、最適な解決策を見つけるタスクを遂行する手助けをするでしょう。
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If a governor is performing poorly, the governor’s actual performance will be lowered accordingly, and eventually, some individuals will leave the governor and follow another governor to improve their quality of life.
In other words, like the Epistocratic societies, when a population is under-performing, this will eventually affect the popularity and credibility of the governor.
The Epistocracy algorithm will compute the average improvement per each population, giving higher weights to individuals who are closer to the governor (and
more educated) and lower weights to citizens who are farther away (and less educated) before using the following formula:
より教育された)と、以下の式を使用する前に遠く(かつ教育の少ない)市民への体重を減らす。
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𝐼𝑎𝑣𝑔 = 1 ∑ 𝑤𝑖
𝐼𝑎𝑣𝑔 = 1 ∑ 𝑤𝑖
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𝑛 𝑖=1 𝑛 × ∑ 𝑤𝑖𝐼𝑖
𝑛 𝑖=1 𝑛 × ∑ 𝑤𝑖𝐼𝑖
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𝑖=1 (12) In (12), n is the size of the sub-population and Ii is the individual’s self-improvement given by:
𝑖=1 (12) 12) では、n はサブ人口の大きさであり、ii は次の個人の自己改善である。
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𝐼𝑖 = (𝑃𝑜𝑙𝑑𝑎𝑐𝑡𝑢𝑎𝑙𝑖 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖)
𝐼𝑖 = (𝑃𝑜𝑙𝑑𝑎𝑐𝑡𝑢𝑎𝑙𝑖 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖)
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(13) In (13), Pi is the individual’s performance.
(13) 13)では、Piは個人のパフォーマンスです。
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The weight of an individual’s vote, wi is calculated as follows:
個人の投票の重量、wiは次のように計算されます。
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𝑤𝑖 = − log
wi = − ログ。
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𝑑𝑖,𝑔 ∑ 𝑛 𝑘=0
𝑑𝑖,𝑔 ∑ 𝑛 𝑘=0
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𝑑𝑘,𝑔 × 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖
𝑑𝑘,𝑔 × 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖
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(𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑔 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖) + 𝜀
(𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑔 − 𝑃𝑎𝑐𝑡𝑢𝑎𝑙 𝑖) + 𝜀
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(14) 𝑛 𝑘=0
(14) 𝑛 𝑘=0
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where 𝑑𝑖,𝑔 is the Euclidean distance between the individual and their governor.
ここでdi,gは個人と総督の間のユークリッド距離である。
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∑ is the total distance between a governor and every individual in their subpopulation.
は、知事とそのサブ人口における各個人の間の合計距離である。
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P is the performance, and 𝜀 is a very small positive number.
P は性能であり、ε は非常に小さい正の数である。
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In (14), the log scale is used to mitigate the impact of extreme changes in distance calculation.
14)では、ログスケールは距離計算の極端な変化の影響を軽減するために用いられる。
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𝑑𝑘,𝑔 In the next step, a linear regression is used to compute the adjusted performance of each governor based on their population average performance and votes.
We have also used 5 state-of-the-art evolutionary algorithms to compare the consistency and reliability of the Epistocracy algorithm using these benchmark functions.
In order to make a fair comparison between Epistocracy and other state-of-the-art algorithms, we have selected a set of optimization problems, and tested each algorithm with a population size of 100, for 100 runs and 100 iterations in each run.
The results of comparison among Epistocracy, Genetic Algorithm, Evolutionary Strategies, Artificial Bee Colony, Cuckoo Search, and Particle Swarm Optimization on different functions are given in Table 1, where “Mean” indicates the average fitness obtained from 100 runs and “Std.” is the standard deviation.
The results of Comparison between Epistocracy, Genetic Algorithm, Evolutionary Strategies, Artificial Bee Colony, Cuckoo Search, and Particle Swarm Optimization on different function were given in Table 1, where “Mean” indicate the average fitness obtained from 100 run and “Std.” is the standard deviation。
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“Min” and “Max” are the best and worst fitness values, found throughout 100 runs, respectively.
Min” と “Max” は、それぞれ100回のランで見つかった、最高の、最悪のフィットネス値だ。
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As shown in Table 1, the Epistocracy algorithm demonstrates higher reliability and consistency compared to other algorithms due to lower variation and dispersion in the outcome of the objective function.
As illustrated in Fig. 3, The absence of outliers and smaller standard deviation represented by a tinier boxplot are the most significant advantages of the Epistocracy algorithm.
For Schaffer-4 2D, Epistocracy algorithm shows a higher reliability than other algorithms by producing results within a narrower range depicted in its corresponding boxplot.
Among all other algorithms, for Griewank 2D, the Epistocracy algorithm has produced a narrower range of optimal solutions which is represented by its tiny boxplot.
For Griewank 5D, the Epistocracy algorithm, again,
Griewank 5Dの場合、エピストクラシーアルゴリズムは再び。
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shows a better result than other algorithms, and reconfirms the reliability and consistency of the algorithm working in different environments with different characteristics.
From the robustness aspect, the Epistocracy algorithm is more robust with respect to the existence of multiple minima.
堅牢性の観点から、エピストクラシーアルゴリズムは複数のミニマの存在に関してより堅牢である。
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For large scale search space, the Epistocracy algorithm performs more efficiently than other algorithms.
大規模検索空間では、エピストクラシーアルゴリズムは他のアルゴリズムよりも効率的に処理する。
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In terms of convergence, the Epistocracy algorithm showed a decent rate of convergence compared to other algorithms.
収束の点では、エピストクラシーアルゴリズムは他のアルゴリズムと比較してまともな収束率を示した。
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3.2 Evaluation of Epistocracy Algorithm Using the MNIST Dataset
3.2 mnistデータセットを用いたエピスクラシーアルゴリズムの評価
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To further evaluate the performance of our method, we tasked the Epistocracy algorithm to find the optimal set of hyper-parameters to build the best CNN model for “MNIST” handwritten digit recognition.
The MNIST dataset is a set of hand-written digit images ranging from 0-9.
MNISTデータセットは、0から9までの手書きの数字画像のセットです。
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This dataset contains size-normalized, gray-scale examples of digits written by 500 writers that were centered in a 28x28 image and associated with a label from 10 classes.
MNIST consists of a training set of 60,000 examples, and a test set of 10,000 examples and was constructed from NIST's (the US National Institute of Standards and Technology) Special Database 3 and Special Database 1 which contain binary images.
The end goal is to classify the handwritten digits based on a 28x28 black and white image.
最終目標は、28x28の黒と白の画像に基づいて手書きの数字を分類することです。
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MNIST dataset is commonly used for training classification algorithms and benchmarking purpose.
MNISTデータセットは、分類アルゴリズムとベンチマークの目的のトレーニングに一般的に使用される。
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Optimization of Hyper-parameters.
ハイパーパラメータの最適化
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The problem of finding the optimal value for hyper-parameter λ is called hyper-parameter optimization.
ハイパーパラメータλの最適値を見つける問題はハイパーパラメータ最適化と呼ばれる。
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The main technique for finding such a value is to choose a value 𝜆𝑖 from the trial set {𝜆1, 𝜆2, … , 𝜆𝑛}, to evaluate the response function Ψ(𝜆) for each one, and return the 𝜆𝑖 that worked the best as 𝜆̂.
The optimization of hyper-parameters can be expressed as follow:
ハイパーパラメータの最適化は次のように表現できる。
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𝜆̂ ≈ argmin
argmin (複数形 argmins)
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𝜆∈Λ 𝔼~𝒢𝑥 [ℒ (𝑥; 𝒜𝜆(𝑋𝑡𝑟𝑎𝑖𝑛))] ≡ argmin
𝜆∈Λ 𝔼~𝒢𝑥 [ℒ (𝑥; 𝒜𝜆(𝑋𝑡𝑟𝑎𝑖𝑛))] ≡ argmin
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Ψ(𝜆) 𝜆∈Λ (21)
Ψ(𝜆) 𝜆∈Λ (21)
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In the above formula, λ is the hyper-parameter that should be selected in a way that the generalization error (loss function) 𝔼~𝒢𝑥 [ℒ (𝑥; 𝒜𝜆(𝑋𝑡𝑟𝑎𝑖𝑛))] minimized.
𝒜 is the learning algorithm that maps the training dataset 𝑋𝑡𝑟𝑎𝑖𝑛 from a natural distribution 𝒢𝑥 to the function f, 𝑓 = 𝒜𝜆(𝑋𝑡𝑟𝑎𝑖𝑛) The hyper-parameter optimization can be denoted as the minimization of the response function Ψ(𝜆) over 𝜆 ∈ Λ where Λ is the search space.
a は、自然分布 gx から関数 f へのトレーニングデータセット xtrain を写像する学習アルゴリズムであり、f = aλ(xtrain) ハイパーパラメータ最適化は、λ が探索空間である λ ∈ λ 上の応答関数 ψ(λ) の最小化として表すことができる。
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MNIST CNNs as a Proof of Concept.
概念実証としてのMNIST CNN。
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Epistocracy as a multivariate optimization algorithm can be adapted for use in the automated discovery of CNN architectures, however, its effectiveness in doing so would be difficult to test.
A regular multivariate optimization problem might have a known minimum or maximum while the accuracy of a CNN does not.
正規の多変量最適化問題は既知の最小値または最大値を持つが、cnnの精度は低い。
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In addition, the exact answer of most problems can be obtained through mathematical proof or exhaustive search.
さらに、ほとんどの問題の正確な答えは、数学的証明や徹底的な探索によって得られる。
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A full exhaustive search, however, is both time-consuming and computationally expensive, and there is no way to know what the best possible architecture of a model is.
unique models were generated, using all possible values of the hyper-parameters shown in Table 2.
表2に示すハイパーパラメータのすべての可能な値を使用して、ユニークなモデルが生成される。
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Every permutation of these hyper-parameters was used to create a distinct model.
これらのハイパーパラメータの全ての置換は、異なるモデルを作成するために使われた。
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More hyper-parameters were not used since each model takes a considerable amount of time to train and test.
各モデルがトレーニングとテストにかなりの時間を要するため、ハイパーパラメータは使用されなかった。
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Adding more options would make the amount of time needed to create all permutations of models unreasonable, and we must know the accuracy of all permutations in order to use MNIST as a proof of concept.
Each set is a unique set of hyperparameters for a single model.
各集合は単一のモデルに対する一意なハイパーパラメータの集合である。
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Given a set of hyper-parameters, a 16-layer equivalent CNN model is created in Keras using Google’s sample code to train an “MNIST” handwritten digit recognition model.
To evaluate the performance and robustness of the Epistocracy algorithm, we compared our proposed algorithm with two state-of-the-art algorithms: Particle Swarm Optimization and Genetic Algorithm.
Fig. 4. Performance comparison of GA, PSO, and Epistocracy.
フィギュア。 4. GA, PSO, エピストクラシーのパフォーマンス比較
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Fig. 4 shows that the Epistocracy algorithm initially has a higher accuracy than PSO and GA. After around 20 iterations, the Epistocracy algorithm asymptotically converges to the same fitness score of PSO, and eventually after about 92 iterations it defeats the PSO and shows higher accuracy.
フィギュア。 The Epistocracy algorithm has a higher accuracy than PSO and GA. After around 20 iterations, the Epistocracy algorithm issymptotically to the same fitness score of PSO, and finally after 92 iterations that defeat the PSO and higher accuracy。
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In this figure, the Epistocracy algorithm converges to the optimal solution faster than GA.
この図では、エピストクラシーアルゴリズムは、GAよりも速く最適なソリューションに収束します。
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However, even though PSO has a faster convergence rate of accuracy, it eventually fell behind Epistocracy.
Overall, the Epistocracy algorithm shows better performance than the other algorithms.
概して、エピスクラシーアルゴリズムは他のアルゴリズムよりも優れた性能を示す。
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4 Conclusion and Future Work
4 結論と今後の課題
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Evolutionary algorithms, in general, suffer from different types of problems such as premature convergence and stagnation which is closely related to the diversity of the population, curse of dimensionality and scalability, and a random, limited searching ability which usually occur in the absence of a guided change and due to unbalanced exploration-exploita tion capacities.
Governors can be promoted or demoted based on their population performance and votes.
知事は人口パフォーマンスと投票に基づいて昇進または降格することができる。
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Individuals with better performance have votes of greater weights.
より良いパフォーマンスを持つ個人は、より大きな体重の票を持っています。
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The Epistocracy algorithm was tested using several benchmark functions.
エピスクラシーアルゴリズムはいくつかのベンチマーク関数を用いてテストされた。
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The experimental results show that the Epistocracy algorithm can achieve superior results compared to other evolutionary and swarm-intelligence algorithms.
The Epistocracy algorithm uses the idea of rebels, dynamic resource management, gravitational force, and population variance to conduct an efficient explorative and exploitative search.
For future works, a number of research directions can be envisioned.
今後の研究には、様々な研究の方向性が考えられます。
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First, the exploration-exploita tion strategies can be enhanced to achieve a better convergence rate.
第一に、より優れた収束率を達成するために探索・探索戦略を強化することができる。
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Second, a multi-objective version of the algorithm can be implemented.
第二に、アルゴリズムの多目的バージョンを実装することができる。
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Third, a more comprehensive test set with high dimensionality can be utilized, and the results compared with more evolutionary and swarm intelligence algorithms.
Finally, the Epistocracy algorithm can be adapted for the discovery of optimal architectures of Convolutional Neural Networks and their hyper-parameters.
References 1. F. Ong, P. Milanfar, and P. Getreuer, "Local kernels that approximate Bayesian regularization and proximal operators," IEEE Transactions on Image Processing, vol.
参考文献 1. F. Ong, P. Milanfar, P. Getreuer, "Local kernels that almost Bayesian regularization and proximal operator", IEEE Transactions on Image Processing, vol.
0.79
28, no. 6, pp.
28歳。 6, pp。
0.64
3007-3019, 2019.
3007-3019, 2019.
0.84
2. J. H. Holland, Adaptation in natural and artificial systems : an introductory analysis with applications to biology, control, and artificial intelligence.
2. J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with application to biological, control, and Artificial Intelligence
0.85
Ann Arbor: University of Michigan Press, 1975, pp.
Ann Arbor: University of Michigan Press, 1975, pp。
0.83
viii, 183 p.
viii, 183p。
0.74
3. J. H. Holland, "Genetic algorithms and the optimal allocation of trials," SIAM Journal on
3. J.H.ホランド, "ジェネティックアルゴリズムと試験の最適配置", SIAM Journal on
0.77
Computing, vol.
コンピューター、Vol。
0.63
2, no. 2, pp.
2、いいえ。 2、p。
0.67
88-105, 1973.
88-105, 1973.
0.84
4. J. H. Holland, "Outline for a logical theory of adaptive systems," Journal of the ACM
4. J. H. Holland, "Outline for a logical theory of Adaptive systems" Journal of the ACM
0.87
(JACM), vol. 9, no.
(JACM)。 9、いいえ。
0.61
3, pp. 297-314, 1962.
3、p。 297-314, 1962.
0.74
5. I. Rechenberg, Cybernetic Solution Path of an Experimental Problem: Kybernetische
5. I. Rechenberg, Cybernetic Solution Path of a Experimental Problem: Kybernetische
0.88
Lösungsansteuerung Einer Experiméntellen Forschungsaufgabe.
Lösungsansteuerung Einer Experiméntellen Forschungsaufgabe。
0.76
RAE, 1965.
1965年、RAE。
0.79
6. H.-G. Beyer and H.-P. Schwefel, "Evolution strategies – A comprehensive introduction," doi:
6. H.-G. Beyer and H.-P. Schwefel, "Evolution Strategy – A comprehensive introduction, doi:
0.86
2002/03/01
2002/03/01
0.39
2002, 3-52,
2002, 3-52,
0.78
vol. no. pp.
Vol. ダメよ pp.
0.69
Natural Computing, 10.1023/A:1015059928 466.
10.1023/A:1015059928 466。
0.54
1, 1, 7. H. P. Schwefel, "Kybernetische evolution als strategie der experimentellen forschung in
1, 1, 7. H. P. Schwefel, "Kybernetische evolution als strategie der experimentellen forschung"
0.88
der strömungstechnik. Dipl.-Ing," thesis, 1965.
技術系。 原著『Dip.-Ing』、1965年。
0.47
8. R. Eberhart and J. Kennedy, "Particle swarm optimization," in Proceedings of the IEEE
8. R. Eberhart and J. Kennedy, "Particle swarm optimization" in the Proceedings of the IEEE
0.90
international conference on neural networks, 1995, vol.
ニューラルネットワークに関する国際会議 1995年、Vol.
0.70
4: Citeseer, pp.
4: citeseer, pp。
0.69
1942-1948.
1942-1948.
0.71
9. X. Pan, L. Xue, Y. Lu, and N. Sun, "Hybrid particle swarm optimization with simulated annealing," Multimedia Tools and Applications, vol.
9. X. Pan, L. Xue, Y. Lu, N. Sun, "Hybrid Particle swarm optimization with simulated annealing", Multimedia Tools and Applications, vol。
0.84
78, no. 21, pp. 29921-29936, 2019/11/01 2019, doi: 10.1007/s11042-018-6 602-4.
10. S. Wang, G. Liu, M. Gao, S. Cao, A. Guo, and J. Wang, "Heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer with two mutation operators," Information doi: https://doi.org/10.1 016/j.ins.2020.06.02 7.
10. S. Wang, G. Liu, M. Gao, S. Cao, A. Guo, J. Wang, "heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizationr with two mutation operator", Information doi: https://doi.org/10.1 016/j.ins.2020.06.02 7.
0.80
2020/11/01/
2020/11/01/
0.34
Sciences, 175-201,
科学 175-201,
0.56
2020, 540,
2020, 540,
0.85
vol. pp. 11.
Vol. pp. 11.
0.79
A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, "Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients," IEEE Transactions on evolutionary computation, vol.
A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, "Self-organizing Hierarchical Particle Swarm Optimizationr with time-variant acceleration coefficients", IEEE Transactions on Evolution calculation, vol。
0.87
8, no. 3, pp.
8、いいえ。 3、p。
0.69
240-255, 2004.
240-255, 2004.
0.84
12. P. N. Suganthan, "Particle swarm optimiser with neighbourhood operator," in Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat.
12. P. N. Suganthan, "Particle swarm optimiser with neighborhood operator" in Proceedings on the Congress on Evolutionary Computation-CEC99 (Cat)
0.85
No. 99TH8406), 1999, vol.
いいえ。 99TH8406), 1999年, vol。
0.81
3: IEEE, pp.
3:IEEE, pp。
0.63
1958-1962.
1958-1962.
0.71
英語（論文から抽出）
日本語訳
スコア
13. S. Kumar, A. Nayyar, and R. Kumari, "Arrhenius artificial bee colony algorithm," in International conference on innovative computing and communications, 2019: Springer, pp.
13. S. Kumar, A. Nayyar, R. Kumari, "Arrhenius artificial bee colony algorithm" in International conference on innovative computing and communication, 2019: Springer, pp。
0.85
187-195. 14.
187-195. 14.
0.78
D. Karaboga, "An idea based on honeybee swarm for numerical optimization," Technical
16. S. Xiao, W. Wang, H. Wang, and X. Zhou, "A New Artificial Bee Colony Based on Multiple Search Strategies and Dimension Selection," IEEE Access, vol.
16. S. Xiao, W. Wang, H. Wang, X. Zhou, "A New Artificial Bee Colony based on multiple search Strategies and Dimension Selection", IEEE Access, vol.
0.87
7, pp. 133982133995, 2019, doi: 10.1109/ACCESS.2019. 2941247.
adaptive knowledge learning," Neural Computing and Applications, pp.
適応的知識学習」 ニューラルコンピューティングと応用, pp。
0.70
1-31, 2019.
1-31, 2019.
0.84
20. H. Li, D. Yuan, X. Ma, D. Cui, and L. Cao, "Genetic algorithm for the optimization of features and neural networks in ECG signals classification," ; Scientific reports, vol.
20. H. Li, D. Yuan, X. Ma, D. Cui, L. Cao, “ECG信号分類における特徴とニューラルネットワークの最適化のためのジェネティックアルゴリズム”, Scientific Report, vol。
0.88
7, p. 41011, 2017.
7、p.41011、2017。
0.78
21. W. Xi, G. Li, H. Moayedi, and H. Nguyen, "A particle-based optimization of artificial neural network for earthquake-induced landslide assessment in Ludian county, China," Geomatics, Natural Hazards and Risk, vol.
21. W. Xi, G. Li, H. Moayedi, H. Nguyen, “A Particle-based optimization of Artificial Neural Network for earthquake-induced Landlide Assessment in Ludian County, China, Geomatics, Natural Hazards and Risk, vol.”。
0.90
10, no. 1, pp.
10、いいえ。 1、p。
0.70
1750-1771, 2019.
1750-1771, 2019.
0.84
22. T. S. Kim, J. C. Na, and K. J. Kim, "Optimization of an autonomous car controller using a self-adaptive evolutionary strategy," International Journal of Advanced Robotic Systems, vol.
22. T.S. Kim, J. C. Na, K. J. Kim, “Optimization of a autonomous car controller using a self-adaptive evolution strategy”. International Journal of Advanced Robotic Systems, Vol.
0.90
9, no. 3, p. 73, 2012.
9、いいえ。 3, p. 73, 2012。
0.80
23. M. Prakash, R. Saranya, K. R. Jothi, and A. Vigneshwaran, "An optimal job scheduling in grid using cuckoo algorithm," International Journal of Computer Science and Telecommunications, vol.
23. M. Prakash, R. Saranya, K. R. Jothi, A. Vigneshwaran, “A optimal job schedule in grid using cuckoo algorithm”. International Journal of Computer Science and Telecommunications, vol.
0.89
3, no. 2, pp.
3、いいえ。 2、p。
0.68
65-69, 2012.
65-69, 2012.
0.84
24. W.-C. Yeh, J. C. Su, T.-J.
24. W.C. Yeh, J.C. Su, T.-J
0.77
Hsieh, M. Chih, and S.-L. Liu, "Approximate reliability function based on wavelet latin hypercube sampling and bee recurrent neural network," IEEE Transactions on Reliability, vol.
Hsieh、M. Chih、S.-L. Liuは「ウェーブレットラチンハイパーキューブサンプリングと蜂の再発ニューラルネットワークに基づく近似信頼性関数」とIEEE Transactions on Reliability, vol。 訳抜け防止モード: Hsieh, M. Chih, S.-L. Liu, "Wavelet latin hypercube sampleとbee recurrent neural networkに基づく近似信頼性関数" IEEE Transactions on Reliability , vol。
0.82
60, no. 2, pp. 404-414, 2011.
60だ 2、p。 404-414, 2011.
0.63
25. R. C. Contreras, O. M. Junior, and M. S. Viana, "A New Local Search Adaptive Genetic Algorithm for the Pseudo-Coloring Problem," in International Conference on Swarm Intelligence, 2020: Springer, pp.
25. R. C. Contreras, O. M. Junior, and M. S. Viana, "A New Local Search Adaptive Genetic Algorithm for the Pseudo-Coloring Problem" in International Conference on Swarm Intelligence, 2020: Springer, pp.
0.92
349-361. 26.
349-361. 26.
0.78
S. Rahmani and N. Amjady, "Non-deterministic optimal power flow considering the uncertainties of wind power and load demand by multi-objective information gap decision theory and directed search domain method," IET Renewable Power Generation, vol.
S. Rahmani と N. Amjady は「多目的情報ギャップ決定理論と有向探索領域法による風力・負荷需要の不確実性を考慮した非決定論的最適電力流」と述べている。
0.82
12, no. 12, pp.
12、いいえ。 12、p。
0.70
1354-1365, 2018.
1354-1365, 2018.
0.84
27. M. Han, C. Liu, and J. Xing, "An evolutionary membrane algorithm for global numerical
27. M. Han, C. Liu, J. Xing, "グローバル数値のための進化膜アルゴリズム"
0.85
optimization problems," Information Sciences, vol.
最適化問題 (Information Sciences, vol.)。
0.65
276, pp. 219-241, 2014.
276, pp。 219-241, 2014.
0.82
28. M. Kheshti, X. Kang, J. Li, P. Regulski, and V. Terzija, "Lightning flash algorithm for solving non-convex combined emission economic dispatch with generator constraints," IET Generation, Transmission & Distribution, vol.
28. M. Kheshti, X. Kang, J. Li, P. Regulski, V. Terzija, “Lightning flash algorithm for solve non-convex combined emission economic dispatch with generator constraints”. IET Generation, Transmission & Distribution, vol.
0.91
12, no. 1, pp.
12、いいえ。 1、p。
0.69
104-116, 2017.
104-116, 2017.
0.84
29. K. Zhang and B. Li, "Cooperative coevolution with global search for large scale global optimization," in 2012 IEEE Congress on Evolutionary Computation, 2012: IEEE, pp.
29. K. Zhang, B. Li, "Cooperative coevolution with global search for large scale global optimization" in 2012 IEEE Congress on Evolutionary Computation, 2012: IEEE, pp。
0.85
1-7.
1-7.
0.71
英語（論文から抽出）
日本語訳
スコア
30. C. Vanaret, J.-B.
30. C. Vanaret、J.-B。
0.79
Gotteland, N. Durand, and J.-M. Alliot, "Preventing premature convergence and proving the optimality in evolutionary algorithms," in International Conference on Artificial Evolution (Evolution Artificielle), 2013: Springer, pp.
Gotteland, N. Durand, and J.-M. Alliot, "Preventing premature convergence and proving the optimality in Evolution algorithm" in International Conference on Artificial Evolution (Evolution Artificielle), 2013: Springer, pp。
0.87
29-40. 31.
29-40. 31.
0.78
E. L. Dolson, A. E. Vostinar, M. J. Wiser, and C. Ofria, "The MODES toolbox: Measurements of open-ended dynamics in evolving systems," Artificial life, vol.
E. L. Dolson, A. E. Vostinar, M. J. Wiser, C. Ofria, "The MODES toolbox: Measurements of open-ended dynamics in evolution systems", Artificial life, vol。
0.94
25, no. 1, pp. 50-73, 2019.
25だ 1、p。 50-73, 2019.
0.62
32. A. Rajan and T. Malakar, "Optimal reactive power dispatch using hybrid Nelder–Mead simplex based firefly algorithm," International Journal of Electrical Power & Energy Systems, vol.
32. A. Rajan, T. Malakar, “Optimal Reactive Power dispatch using hybrid Nelder–Mead simplex based firefly algorithm”. International Journal of Electric Power & Energy Systems, Vol.
0.89
66, pp. 9-24, 2015.
66, pp。 9-24, 2015.
0.82
33. S. Sreejith, H. K. Nehemiah, and A. Kannan, "Clinical Data Classification Using an Enhanced SMOTE and Chaotic Evolutionary Feature Selection," Computers in Biology and Medicine, p. 103991, 2020.
33. S.Sreejith, H.K. Nehemiah, A. Kannan, "Clinical Data Classification Using an Enhanced SMOTE and Chaotic Evolutionary Feature Selection", Computers in Biology and Medicine, p. 103991, 2020.
0.88
34. M. Bardeen, "Survey of methods to prevent premature convergence in evolutionary algorithms," in Workshop of Natural Computing, J. Chilenas de Computation, 2013, pp.
34. M. Bardeen, "Survey of methods to prevent premature convergence in evolution algorithm" in Workshop of Natural Computing, J. Chilenas de Computation, 2013 pp。
0.83
13-15. 35.
13-15. 35.
0.78
T. Jansen, Analyzing evolutionary algorithms: The computer science perspective.
T. Jansen, Analyzing evolutionary algorithm: the computer science perspective。
0.88
Springer Science & Business Media, 2013.
ばね 2013年、Science & Business Mediaに入社。
0.57
36. M. Tahir, A. Tubaishat, F. Al-Obeidat, B. Shah, Z. Halim, and M. Waqas, "A novel binary chaotic genetic algorithm for feature selection and its utility in affective computing and healthcare," Neural Computing and Applications, pp.
36. m. tahir, a. tubaishat, f. al-obeidat, b. shah, z. halim, and m. waqas, "a novel binary chaotic genetic algorithm for feature selection and its utility in affective computing and healthcare", neural computing and applications, pp.
0.87
1-22, 2020.
1-22, 2020.
0.84
37. S. S. Jadon, R. Tiwari, H. Sharma, and J. C. Bansal, "Hybrid artificial bee colony
37. S.S. Jadon、R. Tiwari、H. Sharma、J. C. Bansal、「ハイブリッド人工ミツバチコロニー」
0.79
algorithm with differential evolution," Applied Soft Computing, vol.
微分進化型アルゴリズム」応用ソフトコンピューティング, vol.
0.62
58, pp. 11-24, 2017.
58, pp。 11-24, 2017.
0.82
38. R. Murugan, M. Mohan, C. C. A. Rajan, P. D. Sundari, and S. Arunachalam, "Hybridizing bat algorithm with artificial bee colony for combined heat and power economic dispatch," Applied Soft Computing, vol.
38. R. Murugan, M. Mohan, C. C. A. Rajan, P. D. Sundari, S. Arunachalam, “Hybridizing bat algorithm with artificial bee colony for combination heat and power economic dispatch”. Applied Soft Computing, vol.
0.91
72, pp. 189-217, 2018.
72, pp。 189-217, 2018.
0.83
39. O. Kramer, "Premature convergence in constrained continuous search spaces," in International Conference on Parallel Problem Solving from Nature, 2008: Springer, pp.
39. O. Kramer, "Premature convergence in constrained continuous search space" in International Conference on Parallel Problem Solving from Nature, 2008: Springer, pp. (英語)
0.87
6271. 40. J. S. Mill, "Mill on Bentham and Coleridge, ed," FR Leavis, London: Chatto and Windus,
6271. 40. J.S.ミル, "Mill on Bentham and Coleridge, ed", FR Leavis, London: Chatto and Windus,
0.85
1950. 41. J. Brennan, Against democracy: New preface.
1950. 41. J. Brennan、民主主義に反対:新しい序文。
0.82
Princeton University Press, 2017.
プリンストン大学出版局、2017年。
0.67
42. M. D. McKay, R. J. Beckman, and W. J. Conover, "Comparison of three methods for selecting values of input variables in the analysis of output from a computer code," Technometrics, vol.
42. M.D. McKay, R. J. Beckman, W. J. Conover, "Comparison of three method for selecting input variables in the analysis of output from a computer code", Technometrics, vol。