GENETIC ALGORITHMS AND GAME THEORY FOR HIGH LIFT DESIGN PROBLEMS IN AERODYNAMICS

A multi-objective evolutionary optimization method (combining genetic algorithms(GAs)and game theory(GT))is presented for high lift multi-airfoil systems in aerospace engineering.Due to large dimension global op-timization problems and the increasing importance of low cost distributed parallel environments,it is a natural idea to replace a globar optimization by decentralized local sub-optimizations using GT which introduces the notion of games associated to an optimization problem.The GT/GAs combined optimization method is used for recon-struction and optimization problems by high lift multi-air-foil desing.Numerical results are favorably compared with single global GAs.The method shows teh promising robustness and efficient parallel properties of coupled GAs with different game scenarios for future advanced multi-disciplinary aerospace techmologies.

Research on Different Heuristics for Minimax Algorithm Insight from Connect-4 Game

Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.

NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES

The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.

Billiards Optimization Algorithm:A New Game-Based Metaheuristic Approach

Metaheuristic algorithms are one of themost widely used stochastic approaches in solving optimization problems.In this paper,a new metaheuristic algorithm entitled Billiards Optimization Algorithm(BOA)is proposed and designed to be used in optimization applications.The fundamental inspiration in BOA design is the behavior of the players and the rules of the billiards game.Various steps of BOA are described and then its mathematical model is thoroughly explained.The efficiency of BOA in dealing with optimization problems is evaluated through optimizing twenty-three standard benchmark functions of different types including unimodal,high-dimensional multimodal,and fixed-dimensionalmultimodal functions.In order to analyze the quality of the results obtained by BOA,the performance of the proposed approach is compared with ten well-known algorithms.The simulation results show that BOA,with its high exploration and exploitation abilities,achieves an impressive performance in providing solutions to objective functions and is superior and far more competitive compared to the ten competitor algorithms.

Development of Algorithm of Traditional Kei-Yen Game

Manipuri traditional game Kei-Yen, which originates from the ancient Meitei mythological story, is a mind game between two players of different mindsets, one has the mindset of killing (Kei), whereas the other (Yen) has the mindset of protecting itself and block the moves of Kei. We propose and develop an algorithm of this game by incorporating various possible logical tactics and strategies for a possible computer software of this game. Since this game involves various logical mind games, playing this game can improve our way of thinking, strategies, tricks and other skills related to mind game. In this play there is not the case of draw which means one has to win over the other at the end of the game. This game could become one of most interesting indoor national or international game.

Solving the Balance Problem of On-Line Role-Playing Games Using Evolutionary Algorithms

In on-line role-playing games (RPG), each race holds some attributes and skills. Each skill contains several abilities such as physical damage, hit rate, etc. Parts of the attributes and all the abilities are a function of the character’s level, which are called Ability-Increasing Functions (AIFs). A well-balanced on-line RPG is characterized by having a set of well-balanced AIFs. In this paper, we propose an evolutionary design method, including integration with an improved Probabilistic Incremental Program Evolution (PIPE) and a Cooperative Coevolutionary Algorithm (CCEA), for on-line RPGs to maintain the game balance. Moreover, we construct a simplest turn-based game model and perform a series of experiments based on it. The results indicate that the proposed method is able to obtain a set of well-balanced AIFs efficiently. They also show that in this case the CCEA outperforms the simple genetic algorithm, and that the capability of PIPE has been significantly improved through the improvement work.

A Competitive Markov Approach to the Optimal Combat Strategies of On-Line Action Role-Playing Game Using Evolutionary Algorithms

In the case of on-line action role-playing game, the combat strategies can be divided into three distinct classes, Strategy of Motion(SM), Strategy of Attacking Occasion (SAO) and Strategy of Using Skill (SUS). In this paper, we analyze such strategies of a basic game model in which the combat is modeled by the discrete competitive Markov decision process. By introducing the chase model and the combat assistant technology, we identify the optimal SM and the optimal SAO, successfully. Also, we propose an evolutionary framework, including integration with competitive coevolution and cooperative coevolution, to search the optimal SUS pair which is regarded as the Nash equilibrium point of the strategy space. Moreover, some experiments are made to demonstrate that the proposed framework has the ability to find the optimal SUS pair. Furthermore, from the results, it is shown that using cooperative coevolutionary algorithm is much more efficient than using simple evolutionary algorithm.

Dynamic constraint and objective generation approach for real-time train rescheduling model under human-computer interaction

Real-time train rescheduling plays a vital role in railway transportation as it is crucial for maintaining punctuality and reliability in rail operations.In this paper,we propose a rescheduling model that incorporates constraints and objectives generated through human-computer interaction.This approach ensures that the model is aligned with practical requirements and daily operational tasks while facilitating iterative train rescheduling.The dispatcher’s empirical knowledge is integrated into the train rescheduling process using a human-computer interaction framework.We introduce six interfaces to dynamically construct constraints and objectives that capture human intentions.By summarizing rescheduling rules,we devise a rule-based conflict detection-resolution heuristic algorithm to effectively solve the formulated model.A series of numerical experiments are presented,demonstrating strong performance across the entire system.Furthermore,theflexibility of rescheduling is enhanced through secondary analysis-driven solutions derived from the outcomes of humancomputer interactions in the previous step.This proposed interaction method complements existing literature on rescheduling methods involving human-computer interactions.It serves as a tool to aid dispatchers in identifying more feasible solutions in accordance with their empirical rescheduling strategies.

A Graphic Algorithm of＂Track＂ Effect in 3D Games

In 3D games, a lot of weapons in the movement will drag a ＂follow the shadow＂ effect, which is called the ＂track＂. In this paper, we first analyze the change rule of the ＂track＂, and then put forward a kind of algorithm to realize the ＂track＂. The calculation of this algorithm is small, but the effect is very real, has been successfully applied to a variety of 3D games.

Distributed Optimal Variational GNE Seeking in Merely Monotone Games

In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.

基于Stackelberg Game诱导策略的网络调度算法

首先建立了网络Stackelberg Game模型,分析了该模型下Nash均衡的存在性,给出了网络的队最优解。在网络资源管理中,引入基于Stackelberg Game的网络诱导策略,利用动态博弈和多次逐步诱导的方法,提出了一种网络由一般状态到最优运行状态的动态调度算法。队最优解保证了网络在最优运行状态下的稳定性。数值仿真验证了该算法的有效性。

Dynamic Multi-team Antagonistic Games Model with Incomplete Information and Its Application to Multi-UAV

At present, the studies on multi-team antagonistic games (MTAGs) are still in the early stage, because this complicated problem involves not only incompleteness of information and conflict of interests, but also selection of antagonistic targets. Therefore, based on the previous researches, a new framework is proposed in this paper, which is dynamic multi-team antagonistic games with incomplete information (DMTAGII) model. For this model, the corresponding concept of perfect Bayesian Nash equilibrium (PBNE) is established and the existence of PBNE is also proved. Besides, an interactive iteration algorithm is introduced according to the idea of the best response for solving the equilibrium. Then, the scenario of multiple unmanned aerial vehicles (UAVs) against multiple military targets is studied to solve the problems of tactical decision making based on the DMTAGII model. In the process of modeling, the specific expressions of strategy, status and payoff functions of the games are considered, and the strategy is coded to match the structure of genetic algorithm so that the PBNE can be solved by combining the genetic algorithm and the interactive iteration algorithm. Finally, through the simulation the feasibility and effectiveness of the DMTAGII model are verified. Meanwhile, the calculated equilibrium strategies are also found to be realistic, which can provide certain references for improving the autonomous ability of UAV systems. © 2014 Chinese Association of Automation.

Diffusion mechanism simulation of cloud manufacturing complex network based on cooperative game theory

Cloud manufacturing is a specific implementation form of the "Internet + manufacturing" strategy. Why and how to develop cloud manufacturing platform(CMP), however, remains the key concern of both platform operators and users. A microscopic model is proposed to investigate advantages and diffusion forces of CMP through exploration of its diffusion process and mechanism. Specifically, a three-stage basic evolution process of CMP is innovatively proposed. Then, based on this basic process, a more complex CMP evolution model has been established in virtue of complex network theory, with five diffusion forces identified. Thereafter, simulations on CMP diffusion have been conducted. The results indicate that, CMP possesses better resource utilization,user satisfaction, and enterprise utility. Results of simulation on impacts of different diffusion forces show that both the time required for CMP to reach an equilibrium state and the final network size are affected simultaneously by the five diffusion forces. All these analyses indicate that CMP could create an open online cooperation environment and turns out to be an effective implementation of the "Internet + manufacturing" strategy.

Cooperative driving model for non-signalized intersections with cooperative games

Cooperative driving around intersections has aroused increasing interest in the last five years.Meanwhile,driving safety in non-signalized intersections has become an issue that has attracted attention globally.In view of the potential collision risk when more than three vehicles approach a non-signalized intersection from different directions,we propose a driving model using cooperative game theory.First,the characteristic functions of this model are primarily established on each vehicle’s profit function and include safety,rapidity and comfort indicators.Second,the Shapley theorem is adopted,and its group rationality,individual rationality,and uniqueness are proved to be suitable for the characteristic functions of the model.Following this,different drivers’characteristics are considered.In order to simplify the calculation process,a zero-mean normalization method is introduced.In addition,a genetic algorithm method is adopted to search an optimal strategy set in the constrained multi-objective optimization problem.Finally,the model is confirmed as valid after simulation with a series of initial conditions.

Understanding the Nature of Predatory Pricing in Large-Scale Market Economy with Genetic Algorithms

In this paper the nature of predatory pricing is analyzed with genetic algorithms. It is found that, even under the same payoff structure, the results of the coevolution of weak monopolists and entrants are sensitive to the representationof the decisionmaking process. Two representations are studied in this paper. One is the actionbased representation and the other the strategybased representation. The former is to represent a naive mind and the latter is to capture a sophisticated mind. For the actionbased representation, the convergence results are easily obtained and predatory pricing is only temporary in all simulations. However, for the strategybased representation, predatory pricing is not a rare phenomenon and its appearance is cyclical but not regular. Therefore, the snowball effect of a little craziness observed in the experimental game theory wins its support from this representation. Furthermore, the nature of predatory pricing has something to do with the evolution of the sophisticated rather than the naive minds.

Optimization of project payment schedules with Nash equilibrium model and genetic algorithm

To minimize the deviations of the net present values of project payment for both the owner and the client and optimize project payment schedules, a Nash equilibrium model based on game theory was set up and a genetic algorithm was developed to work out the Nash equilibrium solution with a two-stage backward inductive approach that requires the client responds to the owner’s payment schedule with an activity schedule so as to maximize the client’s net present value of cash flows. A case study demonstrated that a payment schedule at the Nash equilibrium position enables both the owner and the client to gain their desirable interests, thus is a win-win solution for both parties. Despite the computation time of the proposed algrithm in need of improving, combining Nash equilibrium and genetic algorithm into a complete-information dynamic-game model is a promising method for project management optimization.

Strategy Selection for Moving Target Defense in Incomplete Information Game

As a core component of the network,web applications have become one of the preferred targets for attackers because the static configuration of web applications simplifies the exploitation of vulnerabilities by attackers.Although the moving target defense(MTD)has been proposed to increase the attack difficulty for the attackers,there is no solo approach can cope with different attacks;in addition,it is impossible to implement all these approaches simultaneously due to the resource limitation.Thus,the selection of an optimal defense strategy based on MTD has become the focus of research.In general,the confrontation of two players in the security domain is viewed as a stochastic game,and the reward matrices are known to both players.However,in a real security confrontation,this scenario represents an incomplete information game.Each player can only observe the actions performed by the opponent,and the observed actions are not completely accurate.To accurately describe the attacker’s reward function to reach the Nash equilibrium,this work simulated and updated the strategy selection distribution of the attacker by observing and investigating the strategy selection history of the attacker.Next,the possible rewards of the attacker in each confrontation via the observation matrix were corrected.On this basis,the Nash-Q learning algorithm with reward quantification was proposed to select the optimal strategy.Moreover,the performances of the Minimax-Q learning algorithm and Naive-Q learning algorithm were compared and analyzed in the MTD environment.Finally,the experimental results showed that the strategy selection algorithm can enable defenders to select a more reasonable defensive strategy and achieve the maximum possible reward.

Optimizing Polynomial-Time Solutions to a Network Weighted Vertex Cover Game

Weighted vertex cover(WVC)is one of the most important combinatorial optimization problems.In this paper,we provide a new game optimization to achieve efficiency and time of solutions for the WVC problem of weighted networks.We first model the WVC problem as a general game on weighted networks.Under the framework of a game,we newly define several cover states to describe the WVC problem.Moreover,we reveal the relationship among these cover states of the weighted network and the strict Nash equilibriums(SNEs)of the game.Then,we propose a game-based asynchronous algorithm(GAA),which can theoretically guarantee that all cover states of vertices converging in an SNE with polynomial time.Subsequently,we improve the GAA by adding 2-hop and 3-hop adjustment mechanisms,termed the improved game-based asynchronous algorithm(IGAA),in which we prove that it can obtain a better solution to the WVC problem than using a the GAA.Finally,numerical simulations demonstrate that the proposed IGAA can obtain a better approximate solution in promising computation time compared with the existing representative algorithms.

Path Planning of the Multiple Mobile Robot System Applied in Chinese Chess Game

The article presents the path planning algorithm to be applied in the Chinese chess game, and uses multiple mobile robots to present the experimental scenario. Users play the Chinese chess game using the mouse on the supervised computer. The supervised computer programs the motion paths using A＊ searching algorithm, and controls mobile robots moving on the grid based chessboard platform via wireless radio frequency （RF） interface. The A＊ searching algorithm solves shortest path problems of mobile robots from the start point to the target point, and avoids the obstacles on the chessboard platform. The supervised computer calculates the total time to play the game, and computes the residual time to play chess in the step for each player. The simulation results can fired out the shortest motion paths of the mobile robots （chesses） moving to target points from start points in the monitor, and decides the motion path to be existence or not. The eaten chess can moves to the assigned position, and uses the A＊ searching algorithm to program the motion path, too. Finally, the authors implement the simulation results on the chessboard platform using mobile robots. Users can play the Chinese chess game on the supervised computer according to the Chinese chess game rule, and play each step of the game in the assigned time. The supervised computer can suggests which player don＇t obey the rules of the game, and decides which player to be a winner. The scenario of the Chinese chess game feedback to the user interface using the image system.

基于Gur Game的LEACH改进算法

在LEACH中引入了Gur Game算法,来实现对无线传感网络中工作节点总数的控制。在节点密度较高的网络中,当算法满足它的节点密度要求时,允许部分节点进入低能耗状态同时也减少了簇头节点个数。仿真实验证明改进算法与LEACH相比能有效延长了系统的生存时间。