多智能体遗传算法用于线性系统逼近

Optimal Approximation of Linear Systems by Multi-agent Genetic Algorithm

提出了一种新的参数优化方法——多智能体遗传算法，来求解线性系统逼近问题．该方法中每个智能体代表一个候选解，即搜索空间中的一个实值向量．所有智能体生存在一个网格状的环境中，且每个智能体占据一个格点不能移动．为了增加能量，它们将与其邻域进行合作或竞争，也可以利用自身的知识．因此，设计了4个进化算子来模拟智能体间的竞争、合作、自学习等行为．该方法利用这些智能体与智能体间的相互作用来达到优化逼近模型中参数的目的；此外，还采用了一种动态扩展搜索空间的方法以解决算法所需的搜索空间难以确定的问题．实验中，利用一个稳定和一个非稳定的线性系统逼近问题来验证算法的性能，并与两种新近提出的方法作了比较．结果表明，该文方法优于其它方法，能够用较少的计算量找到高质量的逼近模型，具有良好的性能和实际应用价值．

The problem of optimally approximating linear systems is solved by the multi-agent genetic algorithm (MAGA). In MAGA, each possible solution, a real-valued vector in the search space, is considered as an agent, and all agents live in a latticelike environment, with each agent being fixed at a lattice-point. In order to increase energies, they compete or cooperate with their neighbors, and they can also use knowledge. Therefore, four evolutionary operators are designed for simulating the intelligent behaviors of agents, such as competition, cooperation, self-learning and so on. Making use of these agent-agent interactions, MAGA realizes minimizing the objective function value. At the same time, a search-space expansion scheme is adopted to find the regions where the optimal parameters locate. In experiments, two linear systems, a stable one and an unstable one, are used to test the performance of MAGA, and a comparison is made between MAGA and two recent algorithms. The results show that MAGA can find high quality approximate models with low computational cost.