Schema theory for genetic programming with one-point crossover and point mutation

We review the main results obtained in the theory of schemata in genetic programming (GP), emphasizing their strengths and weaknesses. Then we propose a new, simpler definition of the concept of schema for GP, which is closer to the original concept of schema in genetic algorithms (GAs). Along with a new form of crossover, one-point crossover, and point mutation, this concept of schema has been used to derive an improved schema theorem for GP that describes the propagation of schemata from one generation to the next. We discuss this result and show that our schema theorem is the natural counterpart for GP of the schema theorem for GAs, to which it asymptotically converges.     

Operator equalisation for bloat free genetic programming and a survey of bloat control methods

Bloat can be defined as an excess of code growth without a corresponding improvement in fitness. This problem has been one of the most intensively studied subjects since the beginnings of Genetic Programming. This paper begins by briefly reviewing the theories explaining bloat, and presenting a comprehensive survey and taxonomy of many of the bloat control methods published in the literature through the years. Particular attention is then given to the new Crossover Bias theory and the bloat control method it inspired, Operator Equalisation (OpEq). Two implementations of OpEq are described in detail. The results presented clearly show that Genetic Programming using OpEq is essentially bloat free. We discuss the advantages and shortcomings of each different implementation, and the unexpected effect of OpEq on overfitting. We observe the evolutionary dynamics of OpEq and address its potential to be extended and integrated into different elements of the evolutionary process.     

A comparison of bloat control methods for genetic programming

Genetic programming has highlighted the problem of bloat, the uncontrolled growth of the average size of an individual in the population. The most common approach to dealing with bloat in tree-based genetic programming individuals is to limit their maximal allowed depth. An alternative to depth limiting is to punish individuals in some way based on excess size, and our experiments have shown that the combination of depth limiting with such a punitive method is generally more effective than either alone. Which such combinations are most effective at reducing bloat? In this article we augment depth limiting with nine bloat control methods and compare them with one another. These methods are chosen from past literature and from techniques of our own devising. esting with four genetic programming problems, we identify where each bloat control method performs well on a per-problem basis, and under what settings various methods are effective independent of problem. We report on the results of these tests, and discover an unexpected winner in the cross-platform category.     

Dynamic limits for bloat control in genetic programming and a review of past and current bloat theories

Bloat is an excess of code growth without a corresponding improvement in fitness. This is a serious problem in Genetic Programming, often leading to the stagnation of the evolutionary process. Here we provide an extensive review of all the past and current theories regarding why bloat occurs. After more than 15 years of intense research, recent work is shedding new light on what may be the real reasons for the bloat phenomenon. We then introduce Dynamic Limits, our new approach to bloat control. It implements a dynamic limit that can be raised or lowered, depending on the best solution found so far, and can be applied either to the depth or size of the programs being evolved. Four problems were used as a benchmark to study the efficiency of Dynamic Limits. The quality of the results is highly dependent on the type of limit used: depth or size. The depth variants performed very well across the set of problems studied, achieving similar fitness to the baseline technique while using significantly smaller trees. Unlike many other methods available so far, Dynamic Limits does not require specific genetic operators, modifications in fitness evaluation or different selection schemes, nor does it add any parameters to the search process. Furthermore, its implementation is simple and its efficiency does not rely on the usage of a static upper limit. The results are discussed in the context of the newest bloat theory.

求解整数非线性规划结合正交杂交的离散PSO 算法

针对整数非线性规划问题,提出一种结合正交杂交的离散粒子群优化(PSO)算法.首先采用舍入取整方法,为了减少舍入误差,对PSO中的每个粒子到目前为止的最好位置进行随机修正,将基于正交实验设计的正交杂交算子引入离散PSO算法,以增强搜索性能;然后对PSO算法中的惯性权重和收缩因子采用动态调整策略,以提高算法的搜索效率;最后对一些不同维数的整数非线性规划问题进行数值仿真实验,实验结果表明了所提出算法的有效性.     

一类区间系数线性双层规划问题的遗传算法

针对一类上层目标函数带区间系数的线性双层规划问题,提出了一种基于双适应度函数评估的遗传算法(GA)。该算法的特点是在一次运算中同时获得最好最优解和最差最优解。首先,利用双层规划约束域的顶点进行个体编码,以上层目标函数中系数的上下端点构造两个适应度函数;其次,利用适应度函数排序种群中的个体,并按从好到差的次序验证个体的下层最优性,直到找到一个可行个体;最后,在算法运行中更新找到的可行个体。通过对4个算例的仿真实验,表明算法是可行且有效的。     

Genetic programming for prediction and control

The relatively new field of genetic programming has received a lot of attention during the last few years. This is because of its potential for generating functions which are able to solve specific problems. This paper begins with an extensive overview of the field, highlighting its power and limitations and providing practical tips and techniques for the successful application of genetic programming in general domains. Following this, emphasis is placed on the application of genetic programming to prediction and control. These two domains are of extreme importance in many disciplines. Results are presented for an oral cancer prediction task and a satellite attitude control problem. Finally, the paper discusses how the convergence of genetic programming can be significantly speeded up through bulk synchronous model parallelisation.     

Mixed method for solving the general convex programming problem

Conclusion Let us return to the claim that we made at the beginning: given the existing level of computers, computational mathematics must not ignore new opportunities for finding results that have been impossible until very recently. In our view, the proposed mixed method is consistent with technological progress: all known problems have been solved in acceptable time, and not in a single case has the method failed to produce a solution. Although we can always dispute claims of the kind made above, our calculations nevertheless convince that the algorithms proposed in this article may be used to solve a fairly broad class of problems, and in particular semidefinite programming problems [7, 17]. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 121–134, July–August, 1998.     

A method for solving a problem of possibilistic programming

The models of possibilistic programming considered in [1–3] are generalized to the case when the binary relations that relate the left and right sides in the model of constraints are fuzzy. The corresponding mathematical formalism for describing models of this class is developed. A method for solving the problem is proposed. The capabilities of the approach are demonstrated in numerical examples.     

Genetic production systems for intelligent problem solving

The paper discusses an evolutionary knowledge approach to intelligent problem solving. A rule-based production system is used to model the problem and the means by which the problem space should be searched. Search heuristics are modelled as production rules. These rules are redundant as there may be more than one view on the best method for building solutions. Some rules may have complex reasoning for their actions, others have none. Deciding which rule is most appropriate is solved by a genetic algorithm and ultimately only the fitter rules will survive. The approach eliminates the necessity of designing problem specific search or variation operators, leaving the genetic algorithm to process patterns independent of the problem at hand. Learning methods and how they aid evolution is also discussed: they are Lamarckian learning and the Baldwin effect. The approach is tested on a scheduling problem.     

Teaching problem solving and structured programming in FORTRAN

This paper describes an approach to teaching problem solving in an introductory programming course using the FORTRAN language. The course is oriented around a set of problems which are used to illustrate a problem solving methodology. Three pedagogic aids (data table, flow diagram, and program system chart) and two control structure extensions to the FORTRAN language are used in order to provide a more convenient framework in which students can practice good problem solving and programming techniques. The control structure extensions facilitate structured programming in FORTRAN. The use of the control structures and the pedagogic aids is illustrated in the solution of a simple statistics problem: the benefits derived from using these aids are also discussed.     

基于偏好矩阵遗传算法求解长期车辆合乘问题

针对长期车辆合乘问题（LTCPP）,提出带有偏好矩阵的遗传算法（PMGA）,将拥有私家车且目的地相同的用户群体分配到产生总花费最少的合乘小组。首先,建立计算基于全体用户费用成本的目标函数,构建以用户时间窗和车容量为约束的长期车辆合乘模型;然后,结合模型特点,在传统遗传算法（GA）的基础上,通过在交叉算子与变异算子中添加偏好矩阵记录并更新用户间的偏好信息来提高可行解的数量和质量。实验结果表明,在相同计算环境下,当用户数量小于200时,通过PMGA所获得的20个解中的最优解的值与最优化算法相同;而处理大规模的实例时,PMGA可以获得更高质量的解。所提算法可以明显提高长期车辆合乘问题的求解质量,在降低汽车尾气污染和减少交通拥挤等方面具有重要作用。     

线性线性分式型区间系数双层规划问题的遗传算法

针对一类上层为线性规划、下层为线性分式规划的区间系数双层规划问题,提出了一种基于系数取值区间搜索的遗传算法。首先,对下层目标系数进行个体编码,使得对每一编码个体,原问题被转化为确定的双层规划问题;其次,利用分式规划的最优性条件求解得到确定性问题;最后,算法通过不断进化下层目标系数找到最好最优解和最差最优解。数值仿真结果表明,该算法是可行并有效的。     

求解双层规划优化问题的层次风驱动优化算法

针对双层规划的求解问题, 提出一种层次风驱动优化算法. 初始化上层优化变量后, 首先对下层规划进行求解, 满足约束条件的同时, 更新下层规划中的空气质点速度和位置; 然后, 利用风驱动优化算法对上层规划问题进行求解; 最后, 在优化解集合中, 选择上下层规划目标值次序之和最小的解作为最终优化解. 实验结果表明, 所提出的层次风驱动算法是一种有效的求解双层规划问题的方法.

     

A neural network approach for solving linear bilevel programming problem

A novel neural network approach is proposed for solving linear bilevel programming problem. The proposed neural network is proved to be Lyapunov stable and capable of generating optimal solution to the linear bilevel programming problem. The numerical result shows that the neural network approach is feasible and efficient.     

A neural network approach for solving nonlinear bilevel programming problem

A neural network model is presented for solving nonlinear bilevel programming problem, which is a NP-hard problem. The proposed neural network is proved to be Lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem. The asymptotic properties of the neural network are analyzed and the condition for asymptotic stability, solution feasibility and solution optimality are derived. The transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples.     

The hybrid algorithm for solving the three-level linear programming problem

Several algorithms have been developed to solve two-level programming problem during the past years. In this paper, we will develop an algorithm for solving three-level programming problem. The hybrid algorithm is coded and used to test a group of problems. Computational experience and comparisons will be presented.