Multi-objective integrated optimization based on evolutionary strategy with a dynamic weighting schedule

The evolutionary strategy with a dynamic weighting schedule is proposed to find all the compromised solutions of the multi-objective integrated structure and control optimization problem, where the optimal system performance and control cost are defined by H2 or H∞ norms. During this optimization process, the weights are varying with the increasing generation instead of fixed values. The proposed strategy together with the linear matrix inequality （LMI） or the Riccati controller design method can find a series of uniformly distributed nondominated solutions in a single run. Therefore, this method can greatly reduce the computation intensity of the integrated optimization problem compared with the weight-based single objective genetic algorithm. Active automotive suspension is adopted as an example to illustrate the effectiveness of the proposed method.

Handling Error Propagation in Sequential Data Assimilation Using an Evolutionary Strategy

An evolutionary strategy-based error parameterization method that searches for the most ideal error adjustment factors was developed to obtain better assimilation results. Numerical experiments were designed using some classical nonlinear models （i.e., the Lorenz-63 model and the Lorenz-96 model）. Crossover and mutation error adjustment factors of evolutionary strategy were investigated in four aspects： the initial conditions of the Lorenz model, ensemble sizes, observation covarianee, and the observation intervals. The search for error adjustment factors is usually performed using trial-and-error methods. To solve this difficult problem, a new data assimilation system coupled with genetic algorithms was developed. The method was tested in some simplified model frameworks, and the results are encouraging. The evolutionary strategy- based error handling methods performed robustly under both perfect and imperfect model scenarios in the Lorenz-96 model. However, the application of the methodology to more complex atmospheric or land surface models remains to be tested.

Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.

On the minimum cost of an evolutionary strategy response to environment stress

Two revised drafts about a simple evolution trade off function studied by Mitchell(Mitchell, 2000) were put up first. Considering the complex of the environment, or the nonlinear interaction of the environment and species, we put up two new cost functions:c(u,z)=c 0+c 1u+k(z+az 2)u,u>0;c(u,z)=c 0+c 1u+kz du,u>0,d>0. In the first case, if the environment is adverse to species ( a >0), the region of low stress which is more suitable for the intolerant species is very small, and at the same environment stress z , the tolerant species will pay the more cost than it will paid in the normal environment. However the tolerant species will pay more cost but low strategies in the environment of a <0 than that it will paid in the environment of a =0 or a >0. In the second case, the results showed that the greater the stress of the environment is, or the more complex the environment is, the lower cost the intolerant species will pay in the region of z <1. In order to exist or to evolve from an environment of high stress, the organisms must possess a higher u , or a better means of mitigating of the stress of environment. Meanwhile in the region d >1, when d decrease, the intolerant species will pays more lower cost of exploiting a habitat in the low stress environment while the tolerant one will pays more lower cost in the high stress environment. This means that scale d describes the selection character of the species system in the evolution process, the smaller the d(d <1) is, the better the selection or the mitigation the system will possesses.

Meta-Learning of Evolutionary Strategy for Stock Trading

Meta-learning algorithms learn about the learning process itself so it can speed up subsequent similar learning tasks with fewer data and iterations. If achieved, these benefits expand the flexibility of traditional machine learning to areas where there are small windows of time or data available. One such area is stock trading, where the relevance of data decreases as time passes, requiring fast results on fewer data points to respond to fast-changing market trends. We, to the best of our knowledge, are the first to apply meta-learning algorithms to an evolutionary strategy for stock trading to decrease learning time by using fewer iterations and to achieve higher trading profits with fewer data points. We found that our meta-learning approach to stock trading earns profits similar to a purely evolutionary algorithm. However, it only requires 50 iterations during test, versus thousands that are typically required without meta-learning, or 50% of the training data during test.

Evolutionary Games in Two-Layer Networks with the Introduction of Dominant Strategy

We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.

SPECTRUM SHARING IN ITERATED PRISONER'S DILEMMA GAME BASED ON EVOLUTIONARY STRATEGIES FOR COGNITIVE RADIOS

We study a spectrum sharing problem where multiple systems coexist and interfere with each other. First, an analysis is proposed for distributed spectrum sharing based on Prisoners' Dilemma (PD) in Cognitive Radios (CRs). In one-shot game, selfish and rational CRs greedily full spread their own spectrum space in order to maximize their own rates, which leads to Nash Equilibrium (N.E.). But with long term interaction, i.e., Iterated Prisoner's Dilemma (IPD), CRs can come to cooperate and acquire the social optimal point by using different evolutionary strategies such as Tit For Tat (TFT), Generous TFT (GTFT), etc. Also we compare the performances of the different evolutionary strategies in noise-free and noisy environments for two-player games. Finally, N-player IPD (N-IPD) is simulated to verify our conclusions that TFT is a good strategy for spectrum sharing in CRs.

Practical Meta-Reinforcement Learning of Evolutionary Strategy with Quantum Neural Networks for Stock Trading

We show the practicality of two existing meta-learning algorithms Model- Agnostic Meta-Learning and Fast Context Adaptation Via Meta-learning using an evolutionary strategy for parameter optimization, as well as propose two novel quantum adaptations of those algorithms using continuous quantum neural networks, for learning to trade portfolios of stocks on the stock market. The goal of meta-learning is to train a model on a variety of tasks, such that it can solve new learning tasks using only a small number of training samples. In our classical approach, we trained our meta-learning models on a variety of portfolios that contained 5 randomly sampled Consumer Cyclical stocks from a pool of 60. In our quantum approach, we trained our quantum meta-learning models on a simulated quantum computer with portfolios containing 2 randomly sampled Consumer Cyclical stocks. Our findings suggest that both classical models could learn a new portfolio with 0.01% of the number of training samples to learn the original portfolios and can achieve a comparable performance within 0.1% Return on Investment of the Buy and Hold strategy. We also show that our much smaller quantum meta-learned models with only 60 model parameters and 25 training epochs have a similar learning pattern to our much larger classical meta-learned models that have over 250,000 model parameters and 2500 training epochs. Given these findings, we also discuss the benefits of scaling up our experiments from a simulated quantum computer to a real quantum computer. To the best of our knowledge, we are the first to apply the ideas of both classical meta-learning as well as quantum meta-learning to enhance stock trading.

EVOLUTIONARY GAME OF DYNAMIC KNOWLEDGE EXCHANGING IN KNOWLEDGE INTERACTION

Characteristics of knowledge exchanging behavior among individual agents in a knowledge dynamic interaction system are studied by using the game theory. An analytic model of evolutionary game of continuous dynamic knowledge interaction behavior is founded based on the structure of the evolutionary game chain. Possible evolution trends of the model are discussed. Finally, evolutionary stable strategies （ESSs） of knowledge transactions among individual agents in the knowledge network are identified by simulation data. Stable charicteristics of ESS in a continuous knowledge exchanging team help employee to communicate and grasp the dynamic regulation of shared knowledge.

Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2 × 2 games in a well-mixed population with a finite size is investigated. In the model, the individuals＇ payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength β and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when s is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the ＇Hawk-Dove＇ game and the ＇Coordinate＇ game are used to illustrate our model. We give the evolutionary stable strategy （ESS） of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.

Evolutionary Game Dynamics in a Fitness-Dependent Wright-Fisher Process with Noise

Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player＇s rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy （ESS） of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner＇s dilemma games （PDG） and the snowdrift games （SG）. We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.

Networked Evolutionary Model of Snow-Drift Game Based on Semi-Tensor Product

This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.

Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network

This paper proposes a co-evolutionary recurrent neural network （CERNN） for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by coevolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets： the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series.

A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

In this study,we propose a spatial prisoner＇s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of- 3〈 β 〈-1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.

A new evolutionary algorithm for constrained optimization problems

To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.

Exploring the dynamic evolutionary mechanism of game model on the protection of traditional villages

With the rapid improvement of urbanization and industrialization in countries around the world,how to effectively solve the rapid demise of traditional villages is a social dilemma faced by all countries,which is why a series of relevant protection regulations have been promulgated in different historical periods.However,the formulation of relevant policies is still not scientific,universal,and long-term.In this study,we constructed an evolutionary game model of local governments and residents based on the evolutionary game theory(EGT),which is used to explore the evolutionary stability strategy(ESS)and stability conditions of stakeholders under the premise of mutual influence and restriction.Besides,the study also included the analysis about the impacts of different influence factors on the evolution tendency of the game model.At the same time,numerical simulation examples were used to verify the theoretical results and three crucial conclusions have been drawn.Firstly,the strategic evolution of stakeholders is a dynamic process of continuous adjustment and optimization,and its results and speed show consistent interdependence.Secondly,the decision-making of stakeholders mainly depends on the basic cost,and the high cost of investment is not conducive to the protection of traditional villages.Thirdly,the dynamic evolutionary mechanism composed of different influence factors will have an impact on the direction and speed of decision-making of stakeholders,which provides the basis for them to effectively restrict the decision-making of each other.This study eliminates the weaknesses of existing research approaches and provides scientific and novel ideas for the protection of traditional villages,which can contribute to the formulation and improvement of the relevant laws and regulations.

Research on the Strategy of Information Resource Sharing between Governments in the Perspective of Game Theory

In order to improve the operational efficiency, the government can realize the streamlining policy through the mode of government information resource sharing. By building government information resources sharing, the government breaks the inter-departmental data island. The government realizes the development direction and trend of “Internet government”. This paper also takes the information resource sharing as the game process between the government management department and the information resource sharing body, and analyzes the policy and suggestion of the information resource sharing in the perspective of game theory by constructing the sharing model of the government information resource in the perspective of game theory.

Multi-Knapsack Model of Collaborative Portfolio Configurations in Multi-Strategy Oriented

Aiming at constructing the multi-knapsack model of collaborative portfolio configurations in multi-strategy oriented, the hybrid evolutionary algorithm was designed based on greedy method, combining with the organization of the multiple strategical guidance and multi-knapsack model. Furthermore, the organizing resource utility and risk management of portfolio were considered. The experiments were conducted on three main technological markets which contain communication, transportation and industry. The results demonstrated that the proposed model and algorithm were feasible and reliable.

Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms

Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.

New Solution Generation Strategy to Improve Brain Storm Optimization Algorithm for Classification

As a new intelligent optimization method,brain storm optimization(BSO)algorithm has been widely concerned for its advantages in solving classical optimization problems.Recently,an evolutionary classification optimization model based on BSO algorithm has been proposed,which proves its effectiveness in solving the classification problem.However,BSO algorithm also has defects.For example,large-scale datasets make the structure of the model complex,which affects its classification performance.In addition,in the process of optimization,the information of the dominant solution cannot be well preserved in BSO,which leads to its limitations in classification performance.Moreover,its generation strategy is inefficient in solving a variety of complex practical problems.Therefore,we briefly introduce the optimization model structure by feature selection.Besides,this paper retains the brainstorming process of BSO algorithm,and embeds the new generation strategy into BSO algorithm.Through the three generation methods of global optimal,local optimal and nearest neighbor,we can better retain the information of the dominant solution and improve the search efficiency.To verify the performance of the proposed generation strategy in solving the classification problem,twelve datasets are used in experiment.Experimental results show that the new generation strategy can improve the performance of BSO algorithm in solving classification problems.