【正文】 實驗結果如下： 表 6 實驗 2 GA、 PSO方法 結 果 對 比搜索成功率 平均行 駛 成本 平均成功搜索 時間GA 24% PSO 46% Evolving Neural Networksv Evolve neural work capable of being universal approximator, such as backpropagation or radial basis function work.v In backpropagation, most mon PE transfer function is sigmoidal function: output = 1/(1 + e input )v PSO can also be used to indirectly evolve the structure of a work. An added benefit is that the preprocessing of input data is made unnecessary.Evolving Neural Networksv Evolve both the work weights and the slopes of sigmoidal transfer functions of hidden and output PEs.v If transfer function now is: output = 1/(1 + e k*input ) then we are evolving k in addition to evolving the weights.v The method is general, and can be applied to other topologies and other transfer functions.v Flexibility is gained by allowing slopes to be positive or negative. A change in sign for the slope is equivalent to a change in signs of all input weights.Evolving Neural Networksv If evolved slope is sufficiently small, sigmoidal output can be clamped to , and hidden PE can be removed. Weights from bias PE to each PE in next layer are increased by onehalf the value of the weight from the PE being removed to the nextlayer PE. PEs are thus pruned, reducing work plexity.v If evolved slope is sufficiently high, sigmoid transfer function can be replaced by step transfer function. This works with large negative or positive slopes. Network putational plexity is thus reduced.Evolving Neural NetworksvSince slopes can evolve to large values, input normalization is generally not needed. This simplifies applications process and shortens development time.vThe PSO process is continuous, so neural work evolution is also continuous. No sudden discontinuities exist such as those that plague other approaches.Other applicationsv Scheduling (Integrated automated container terminal)v Manufacturing (Product content bination optimization)v Figure of merit for electric vehicle battery packv Optimizing reactive power and voltage controlv Medical analysis/diagnosis (Parkinson’s disease and essential tremor)v Human performance prediction (cognitive and physical)Questions and Answers Thank you!。兩種方法各運行 50次，結果如下表 2所示。 (最 優(yōu) 路徑距離 為 ) GA參數(shù)：群體規(guī)模 n=40；交叉概率 Pc=；變異概率 Pm=；輪盤賭法選擇子代，最大代數(shù) 200。將 Xr按執(zhí)行順序進行重新整數(shù)序規(guī)范。對于子群內(nèi)有多個體同為最優(yōu)值的情況，則隨機取其中一個為子群內(nèi)當前最優(yōu)解。 對每一個粒子，按式 (1)計算 Ｖ v、 Ｖ r；按照式 (2)計算 Xv、 Xr，其中 Xv向上取整；當 Ｖ、 X超過其范圍時按邊界取值； 用評價函數(shù) Eval評價所有粒子； 若某個粒子的當前評價值優(yōu)于其歷史最優(yōu)評價值，則記當前評價值為該歷史最優(yōu)評價值，同時將當前位置向量記為該粒子歷史最優(yōu)位置 Pi。 粒子群劃分成若干個兩兩相互重疊的相鄰子群； 每個粒子位置向量 Xv的每一維隨機取 1～ K（車輛數(shù)）之間的整數(shù)， Xr的每一維隨機取 1～ L(發(fā)貨點任務數(shù) )之間的實數(shù)； 每個速度向量 Vv的每一維隨機取 (K1)～ (K1)（車輛數(shù)）之間的整數(shù)， Vr的每一維隨機取 (L1)～ (L1)之間的實數(shù)； 用評價函數(shù) Eval評價所有粒子； 將初始評價值作為個體歷史最優(yōu)解 Pi，并尋找各子群內(nèi)的最優(yōu)解 Pl和總群體內(nèi)最優(yōu)解 Pg。 VRP問題為整數(shù)規(guī)劃問題，因此在算法實現(xiàn)過程中要作相應修改。 該表示方法的最大優(yōu)點是使每個發(fā)貨點都得到車輛的配送服務，并限制每個發(fā)貨點的需求僅能由某一車輛來完成，使解的可行化過程計算大大減少。為表達和計算方便，將每個粒子對應的 2L維向量 X分成兩個 L維向量： Xv (表示各任務對應的車輛 )和 Xr(表示各任務在對應的車輛路徑中的執(zhí)行次序 )。 帶時間窗車輛路徑問題（續(xù)） 如何找到一個合適的表達方法，使粒子與解對應，是實現(xiàn)算法的關鍵問題之一。 時間 窗 車輛 路徑 問題 的數(shù)學描述：帶時間窗車輛路徑問題（續(xù)） 這個模型通用性很強，經(jīng)過參數(shù)的不同設定，可以將其轉(zhuǎn)換為其他組合優(yōu)化問題的數(shù)學模型。如果車輛到達發(fā)貨點 i的時間早于 ETi，則車輛需在 i處等待；如果車輛到達時間晚于 LTi，任務 i將被延遲進行。帶時間窗車輛路徑問題（續(xù)） 時間窗車輛路徑問題一般描述為：有一個中心倉庫，擁有車 K輛，容量分別為 qk (k=1,..,K)；現(xiàn)有 L個發(fā)貨點運輸任務需要完成，以 1,…, L表示。由于在現(xiàn)實生活中許多問題都可以歸結為 VRPTW問題來處理 (如郵政投遞、火車及公共汽車的調(diào)度等 )，其處理的好壞將直接影響到企業(yè)的服務質(zhì)量 ,所以對它的研究越來越受到人們的重視。mm], and the other data of the tobelaid objects and the result of the layout is shown in TABLE 1.(a) Layout Pattern by HCIGA (b) Layout Pattern by PSOTABLE 2 COMPARISON OF LAYOUT SCHEMES FOR TEST SUIT 1Algorithm GARef [11] HCIGA PSORadius of the out warp circle (mm) Static equilibrium error () Interference (mm) 0 0 0Computation time (s) 1735 1002 1874Ps: The putation time is converted into the time of the puter with 166M main frequency, by using PSO, when the calculated radius of the out wrap circle is , the putation time is 760 seconds.Repeat the test suit by PSO for 40 times, and the results are shown as TABLE 3, that is, every time the result all satisfies the restrict conditions, and the mean radius of the out wrap circle is .TABLE 3 RESULTS OF 40 TIMES COMPUTATION FOR TEST SUIT 1Radius of the outwarp circle (mm) ≤ ( , ] (, ] (,]Times 10 16 5 2Radius of the outwarp circle (mm) (, ] (,] Times 2 2 3Test Suit 3 In order to prove the availability of PSO further, the known most optimal solution in the test suit of [8] is quoted. In the big round container, of which the radius is R=125mm, five tobelaid objects are laid out. The data of the tobelaid objects and the result of the layout are shown in TABLE 6. (In [8], the population size of GA, M, is 60, while in this paper, the number of the PSO particles, M, is 60, and the population size of neighborhood is 2, and c1=c2=, and w=, and the maximum number of iteration is 200.) Table 6 RESULTS OF LAYOUT SCHEME FOR TEST SUIT 3No r(mm)m(kg) Optimization(Known quantity) SAGA PSOx(mm) y(mm) x(mm) y(mm) x(mm) y(mm)1 2 3 4 5 (a) Optimization (b) Layout Pattern (c) Layout PatternLayout Pattern by SAGA by PSOTable 7 COMPARISON OF LAYOUT SCHEMES FOR TEST SUIT 3Algorithm SAGA GA PSORadius of the out warp circle (mm) Static equili