线性规划法确定用水网络最小用水量

水污染和水资源短缺是人类面临的重大问题。因此,改善用水过程以节约新鲜水,减少废水排放是值得认真研究的课题。本文提出了确定用水过程最小用水量的新方法一线性规划法。分别研究了单组分再利用、再生再利用、再生循环最小用水量问题,把它们归结为线性规划来求解,其中对于再生再利用和再生循环分别提出了两步线性规划法。对于再生再利用过程,第一步建立线性规划l,以确定整个过程的最小新鲜水和相应的最小再生水用量,第二步将第一步所获得的整个过程的最小用水量和相应的最小再生量以及最低再生浓度区间作为已知量,采用与线性规划l同样的约束建立线性规划2,再次求解即可得最低再生浓度c。。此外,本文发现再生再利用过程的最小用水量和再生浓度之间存在两种关系,这两种关系表明获得最小新鲜水用量和再生量的最低再生浓度存在两种可能：夹点处和夹点之上,从而得出了与文献“夹点处再生能获得最小新鲜水用量”不同的结论,即夹点处再生未必总能获得最小新鲜水用量。给出了一个实例,计算结果表明本文方法是有效和简便易行的。     

关于多污染因子用水网络的建模与优化方法

当前对大规模多污染因子水网络的研究尚未深入,故用水网络设计多缺乏实际意义。今利用用水过程污染物传质模型构造水回用网络模型,以配合法求解多污染因子情况下最小新鲜水用量的实现方法,每1用水过程入水以新鲜水、低污染回用水和高污染回用水配合获得,使各过程关键污染因子为依据的进水流量比尽可能趋近1。各过程按出口极限浓度之积由低到高依次运算。该方法以过程为运算单元,避免软件求解,不受用水网络规模的限制,此方法在用水网络优化技术方面有所创新。最后通过实例说明该方法有效,以其指导某石化企业,节水效率达到17.81%。     

非凸二次规划全局极小问题的新型分枝定界算法

针对求解多面集上二次函数的全局近似最优解问题,利用逐步缩小对偶间隙的处理办法,提出了一个新型分枝定界算法。新算法的主要改进之处是利用了Lagrange 对偶性获取下界。最后,用构造和随机产生的问题实例,对提出的新算法和传统的分枝定界算法做了初步的数值比较实验。计算实验表明算法对求解中大规模非凸二次规划问题的有效性。     

Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming

In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input–output data. In this study, two different input–output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.     

一种求解整数规划与混合整数规划非线性罚函数方法

证明了任何一个变量有界的整数规划问题（IP）和混合整数规划问题（MIP）都可以转化为一个等价的非整数（或连续化）规划问题（NIP），并给出一个用非线性精确罚函数法来求解该等价NIP的方法，从而达到求解IP或MIP的目的，数值实验表明了算法的可行性。该方法可广泛用于各应用领域里IP和MIP的求解，特别是为非线性IP和MIP问题提供了一条通用 的求解途径，对解决许多实际优化问题具有重要意义。     

Performance analysis of gradient neural network exploited for online time-varying quadratic minimization and equality-constrained quadratic programming

In this paper, the performance of a gradient neural network (GNN), which was designed intrinsically for solving static problems, is investigated, analyzed and simulated in the situation of time-varying coefficients. It is theoretically proved that the gradient neural network for online solution of time-varying quadratic minimization (QM) and quadratic programming (QP) problems could only approximately approach the time-varying theoretical solution, instead of converging exactly. That is, the steady-state error between the GNN solution and the theoretical solution can not decrease to zero. In order to understand the situation better, the upper bound of such an error is estimated firstly, and then the global exponential convergence rate is investigated for such a GNN when approaching an error bound. Computer-simulation results, including those based on a six-link robot manipulator, further substantiate the performance analysis of the GNN exploited to solve online time-varying QM and QP problems.     

New lower bounds based on column generation and constraint programming for the pattern minimization problem

The pattern minimization problem is a cutting and packing problem that consists in finding a cutting plan with the minimum number of different patterns. This objective may be relevant when changing from one pattern to another involves a cost for setting up the cutting machine. When the minimization of the number of different patterns is done by assuming that no more than the minimum number of rolls can be used, the problem is also referred to as the cutting stock problem with setup costs.     

多表达式程序设计的新型评估方法

多表达式程序设计(MEP)是应用十分广泛的自动程序设计方法。从MEP的染色体表示规则及种群演化方式来看,每个染色体中的任何基因都有可能多次被当前或其它后续种群中的其他基因引用,从而造成重复计算,耗费大量时空资源。由此提出并实现了一种新型评估方法,该新型评估方法在不改变传统MEP的染色体表示规则和种群演化方式的情况下,能够准确有效地识别演化过程中所有被重复引用的基因,从而避免了大量重复计算,显著提高了演化效率。     

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

This paper presents a new approach for the efficient solution of singular optimal control problems (SOCPs). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of solution. At first, the SOCP is converted into a binary optimal control problem. Then, by utilising the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the optimal control and to compute the approximating solution. The main advantages of the present method are that: (1) without a priori information, the structure of optimal control is detected; (2) it produces good results even using a small number of collocation points; (3) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples.     

多杂质用水网络设计方法的改进与比较

通过引入分配因子和最小限制流量对多杂质用水网络超结构模型进行改进,使模型更简捷高效;在逐步线性规划法中引入改进的超结构模型,提供了用水过程的排序依据,可代替枚举法直接排序,提高了求解效率。通过实例比较了改进前后的两种设计方法,找出了它们之间的优势和劣势,结果表明,本文的改进策略可以快速和准确地解决多杂质用水网络设计问题。