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The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

The optimization algorithm's objection function was the normalized production intensity.

该优化方法中将归一化的生产强度取最大值作为目标函数，同时将纯度的n次方作为罚函数。

The results of numberical simutation show that the new algorithm is more effective than the other algorithms.

该算法弥补了仅用罚函数作为遗传算法的适应函数之不足，数值模拟结果表明该算法比其他算法更加有效。

This problem has been solved by SQP method, implicit programming method and penalty method etc..

针对该问题，早期的方法有SQP方法、隐式规划法、罚函数方法等。

The algorithm is based on simulated annealing algorithm and penalty function method .

提出了一种解水平轨道的列车节能控制问题的算法，该算法考虑了无限制速度和有限制速度两种情形，并基于模拟退火算法、动态罚函数法。

Heavy fighting in the same office hit, or * in the hole with the ball last entered the boundaries of a water hazard front office, and even extend the line into the penalty shot does not drop from the extension of unlimited future.

在原击球处重打，或*在球洞与该球最后进入正面水障碍的界线处，连成的延长线上抛球不罚杆，距离往后延伸无限制。

The modified particle swarm optimization is utilized to solve the proposed reactive power optimization model; and combining with non–stationary multi-stage assignment penalty function, the reactive power optimization problem is transferred into a problem to solve extreme-value without constraints, thus the calculation accuracy and global convergence ability of MPSO are effectively improved, and power grid company can achieve maximal economic benefit by means of the proposed algorithm.

应用改进粒子群优化算法求解该无功优化模型，并结合动态调整罚函数法将无功优化问题转化成无约束求极值问题，从而有效地提高了改进粒子群优化算法的全局收敛能力和计算精度，使电网公司取得了最大经济效益。

It is no need for this algorithm to linearize the nonlinear system and to decouple the strong-coupling MIMO system. It is also convenient to use the penalty function to solve the restriction.

该算法对非线性系统不需要进行线性化，对带强耦合的MIMO系统不需要解耦，使用罚函数处理约束也非常方便。

A new heuristic solution algorithm is presented using an improved genetic algorithm. In the improved genetic algorithm, nondifferentiable exact penalty functions are used to transform a constrained optimization problem into a single unconstrained optimization problem, and hybrid crossovers and intermittent are applied to increase the search capability.

设计了基于改进遗传算法的启发式求解算法，该算法借助不可微精确罚函数将约束问题转化为单个无约束问题来解决，采用混合杂交和间歇变异提高算法的搜索能力。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。