人工记忆优化算法

为了求解复杂函数优化问题,根据人类记忆原理构造出了具有全局收敛性的人工记忆优化算法. 在该算法中,每个记忆元对应着一个试探解; 将记忆原理的记忆和遗忘规律用于控制每个记忆元的状态转移; 记忆元的状态由与试探解相关的状态描述量以及记忆残留值构成,该值分为瞬时记忆、短时记忆和长时记忆三种状态类型,并依据记忆元接受刺激的强度被加强或衰减; 处在瞬时记忆、 短时记忆和长时记忆状态的记忆残留值衰减速度由快到慢,记忆残留值低于某个阈值的记忆元要被遗忘,不再被处理. 在记忆元状态转变过程中,记忆元从一个状态转移到另一个状态实现了对优化问题最优解的搜索. 该算法将试探解与记忆关联,使得试探解依据其质量好坏被自动分类; 处于长时记忆状态的试探解因其质量好,其部分变量的状态值将被传给其它质量差的试探解对应的变量,使其质量得到改善; 处于不同记忆状态的试探解交换信息时,只有很少部分变量进行状态信息交换,这样既可以使试探解的大部分变量的状态保持不变,又能使其质量得到改善,且可大幅减少变量处理个数,对于高维优化问题此举可大幅提高算法收敛速度; 随着演化的进行,质量差的试探解会不断被遗忘,被处理的试探解的数量会不断减少,因此,随着时间的推移,本算法的收敛速度将越来越快. 应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性. 测试结果表明本算法的性能与现有的群智能优化算法相比,具有收敛速度快,求解精度高的优势.

Artificial memory-based optimization

To solve complicated optimization problems (OP), the artificial memory-based optimization (AMO) with global convergence is constructed based on memory principles (MP). In the algorithm, each memory cell is just an alternative solution of OP; the memorizing and forgetting rules of MP are used to control transition of states of each memory cell; a memory cell's state consists of the state describing index associated with an alternative solution and the residual memory which is divided into three memory states such as instantaneous, short and long-term memory, each of which is strengthened or weakened by accepted stimulus strength; attenuation speed of instantaneous, short and long-term memory is from quick to slow, a memory cell that its residual memory is lower than a threshold is forgotten and then discarded. During evolution process, a memory cell's transferring from one state to another realizes the search for the optimum solution. The algorithm associates alternative solutions with memory, enabling alternative solutions to be classified automatically based on their quality; because the alternative solutions staying at long-term memory state have good quality, they transfer state values of some variables to the corresponding variables of the alternative solutions with poor quality, making their quality be improved; when alternative solutions staying at different states exchange state information of variables, only a small part of variables are dealt with, both the states of a large part of variables in these alternative solutions keep unchanged, and their quality can be improved, and also the number of variables to be processed decreases greatly, it can substantially improve convergence speed of the algorithm for high-dimensional optimization problems; as evolution proceeds, the alternative solutions with poorer quality will continue to be forgotten, the number of the alternative solutions to be processed will continue to decrease, therefore the convergence speed of the algorithm will become faster and faster as time lapses. The stability condition of a reducible stochastic matrix is applied to prove the global convergence of the algorithm. The case study shows that the algorithm has advantages of high speed of convergence and high accuracy of optimum solutions when comparing with the existed population-based intelligent optimization algorithms.