In orderto force the search along the boundaries of the design space we introduce athreshold value that limits the d-component of the particle’s speed orthogonal tothe face where the particle has been initially placed:|vdk |≤ |xdmax − xdmin|gd,gd< 1.0. (17)This threshold value is initially set as a fraction of the box’s dimension in thed-th direction. This limit is progressively relaxed during the iterations. By apply-ing this normal speed limiter it is possible to explore the corners of the designspace and find the correct global minimum, as reported in the example shown inFig. 1. The dashed (inner) region of the feasible space is obtained by connectingthe initial positions of the particles. Without the normal speed limiter (a), parti-cles are strongly attracted each other and tend to be confined inside the dashedregion, hence failing to locate the global optimum. The use of the normal speedlimiter (b) allows the particles to explore the design space near the boundary tooand to find the global optimum.(iii) Suppression of random coefficients: In the new version PSO is modified accord-ing to a deterministic flavor. Indeed, we decide to fix in (14) the parameters r1 and r2 equal to 1, thus we eliminate the random factor introduced by thesetwo coefficients. In this way, we transform a pure stochastic method into a de-terministic one (Pinto et al. 2004). The motivation stems from the use of PSOin combination with CPU time expensive numerical simulations used to obtainobjective function and constraints information: a stochastic approach would re-quire repeated runs which might require simply too much computing time forreal industrial applications.(iv) Particles with violated constraints:
The original PSO algorithm is defined onlyfor unconstrained optimization problems. For this reason, when we are dealingwith constrained problems we set equal to 0 the inertia weight term of particleswith violated constraints (Venter and Sobieszczanski-Sobieski 2003; Pinto et al.2004). As a consequence, (14) is substituted byvik = χ[c1(pi−xik−1)+c2(pbk−1 − xik−1)]. (18)In most cases the new velocity vector will point back to the feasible region.This feature of the DDFPSO algorithm is particularly useful in optimizationproblems with a non-convex feasible design space, as for example the ship de-sign problem that will be discussed in the following sections (Pinto et al. 2004).(v) Convergence criterion for the global search phase: In the original algorithmthere was no stopping criterion. For real applications, however, a maximumnumber of iterations is always fixed.We here introduce an heuristic convergencecriterion for the PSO phase, used in the algorithm to switch from the global tothe local search phase. For the convergence of the global phase we focus ontothe identification of all the particles which fall into the same basin of attrac-tion. In order to recognize a basin of attraction, the stored information about theprevious steps of the algorithm, i.e., the visited locations and the correspondingobjective function values, are necessary. We monitor two quantities:

摘要 本文的目的在于：在目标函数值需要高昂的仿真代码且一阶不可导的情况下，为工业应用软件解决优化设计问题。为了达到这个目标，我们从目前的两个处理方法中受到启发，提出了两个新的算法：一个是基于算法求和的填充函数，另一个是粒子群优化算法。为了检测所提出的这两个算法的效果，我们根据一些现代工业优化设计要求的标准优化算法做了一个数据分析。还要注意的是一个实际存在的问题，也就是当船舶在迎浪行进时，其垂荡的幅度会减小（一个与安全性及舒适度相关的问题）。通过一些新的代码和其他全新的局部优化，所有的数据结果都显示出了这两种新算法的效果。

毕业论文关键词 非线性规划 全局优化 仿真设计

1 介绍

    拥有极其复杂系统的仿真设计(SBD)是一个用来降低工业设计耗时的新兴工具，这些工业设计成功地将用于数值优化的计算网格和算法复杂地仿真代码结合在一起。 船舶设计问题上的新全局优化英文文献和中文翻译(5):http://www.751com.cn/fanyi/lunwen_64778.html