外文翻譯--混合整數(shù)非線性規(guī)劃（minlp）方式的滾子和滑門結(jié)構(gòu)

1、<p><b>　　外文翻譯原文</b></p><p><b>　　ABSTRACT</b></p><p>　　Part III of this three-part series of papers describes the synthesis of roller and sliding hydraulic steel gate

2、 structures performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP </p><p>　　approach enables the determination of the optimal number of gate structural elements (girders, plates),

3、 optimal gate geometry, optimal intermediate distances between structural elements and all continuous and </p><p>　　standard crossectional sizes. For this purpose, special logical constraints for topology al

4、terations and interconnection relations between the alternative and fixed structural elements are formulated. They have been embedded into a mathematical optimization model for roller and sliding steel gate structures GA

5、TOP. GATOP has been developed according to a special MINLP model formulation for mechanical superstructures (MINLP-MS), introduced in Parts I and II. The model contains an economic objectiv</p><p>　　KEY WORD

6、S: structural synthesis; optimization; topology optimization; discrete variable optimization; Mixed-Integer Non-linear Programming; MINLP; the Modified OA/ER algorithm; MINLP strategy; hydraulic gate; sliding gate; rolle

7、r gate; Aswan </p><p>　　1. INTRODUCTION </p><p>　　This paper describes the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of roller and sliding gate structures, i.e. the

8、simplest types among vertical-lift hydraulic steel gates, see Figure 1. Roller and sliding gates are also regarded as the most frequently manufactured types of hydraulic steel gates for headwater control. They are used t

9、o regulate the water stream on hydro-electric plants, dams or spillways. </p><p>　　As hydraulic steel gates are very special structures, only a few authors have discussed their optimization, e.g. Kravanja et

10、 al.,1D. Jongeling and Kolkman. as well as Almquist et al.. Particular interest was shown in the optimization not of these (roller and sliding gates) but of similar structures. In such investigations, Vanderplaats and We

11、isshaar. as well as Gurdal et al.. optimized stiffened laminated composite panels, Butler. and Ringertz. optimized stiffened panels, Farkas and Jarmai1. opt</p><p>　　In Parts I of this three-part series of p

12、apers, a general view of the MINLP approach to the simultaneous topology and parameter optimization of structures is presented. Part II describes the extension to the simultaneous standard dimension optimization. Based o

13、n the superstructure approach defined in Parts I and II, the main objective of this paper (Part III) is the MINLP synthesis of roller and sliding hydraulic steel gate structures, obtained at minimal gate costs and subjec

14、ted to defined desi</p><p>　　1. Section 2 describes how different topology and standard dimension alternatives are postulated and how their interconnection relations are formulated by means of explicit logic

15、al constraints in order to perform topology and standard dimension alterations within the optimization procedure. </p><p>　　2. Section 3 represents a general MINLP optimization model for roller and sliding g

16、ate structures GATOP. </p><p>　　3. Finally, in Section 4, the proposed superstructure MINLP approach is applied to the synthesis of an already erected roller gate, the so-called Intake Gate in Aswan II in Eg

17、ypt. </p><p>　　2. SUPERSTRUCTURE ALTERNATIVES AND THE MODELLING OF THEIR DISCRETE DECISIONS </p><p>　　2.1. Postulation of topology and standard dimension alternatives </p><p>　　The

18、first step in the synthesis of the gate is the generation of an MINLP superstructure in which different topology/structure and standard dimension alternatives are embedded to be selected as the optimal result. The gate s

19、uperstructure also contains the representation of structural elements which may construct each possible structure alternative as well as different sets of discrete values, defined for each standard dimension alternative.

20、 As both the roller and sliding gates have almost the sa</p><p>　　2.1.1. Topology alternatives </p><p>　　The gate superstructure typically includes a representation of main gate elements, where

21、each gate element is composed of various structural elements, such as horizontal girders, vertical girders, stiffeners and plate elements of the skin plate, see Figure 2. The superstructure comprises </p><p>

22、;　　n main gate elements, n3N, each containing m horizontal girders, m3M, the (3#2v) number of vertical girders through the entire gate, v3., and the corresponding (m!1)](2#2v) number of skin-plate elements. </p>&

23、lt;p>　　To each mth horizontal girder of the nth main gate element an extra binary variable yn,m is assigned. The number of horizontal girders and corresponding plate elements of the skin plate, distributed over the nt

24、h main gate element, can therefore be determined simply by. Note </p><p>　　that the proposed minimal number of identical vertical girders is 3 and that they can take only odd numbers. If a binary variable y

25、v is assigned to each v, v∈V., the number of vertical girders can be obtained by (3+2 ∑vyv). In the same way an even number (2+2 .∑vyv) of equal horizontal partitions of the entire gate is proposed. In the case of vertic

26、al girders, we can see that the structural elements can also be determined by suitable linear combinations of binary variables. Among the maximal num</p><p>　　2.1.2. Standard dimension alternatives </p>

27、;<p>　　Four standard dimensions are additionally defined to represent the standard thicknesses of sheet-iron plates: the thickness of the skin-plate tsn for each nth main gate element, the .flange thickness of th

28、e horizontal girder tfn, the web thickness of the outer horizontal girder m=1or m=M ,and the web thickness of the inner horizontal girder ,1(m(M. Since the thickness tsn has a common value for the entire skin-plate of th

29、e nth main gate element and the tare the same for all horizontal girders o</p><p>　　MINLP-MS model formulation in Part II. Similarly, the web thicknesses , which take a common value for both outer horizontal

30、 girders of the nth main gate element, and , which are the same for all the inner horizontal girders, correspond to the common standard design variables of the alternative structural elements. An extra set of discrete v

31、alues of standard dimension alternatives and a special set of the same size of binary variables are introduced for each mentioned standard dimension. </p><p>　　Each standard dimension tsn shall be expressed

32、within the given i standard dimension alternatives, i∈I, standard dimension tfnby k alternatives, k∈K, standard dimension by p alternatives, p∈P, and standard dimension by r alternatives, r∈R. The vector of i binary var

33、iables yn,i and the vector of i discrete values qn,I are assigned to the variable tsn, the vectors of k elements yn,k and qn,k to the variable tfn, the vectors of p elements yn,pand qn,kto the variableand the vectors

34、 of r element</p><p>　　2.2. Modeling of discrete decisions </p><p>　　The postulated gate superstructure of topology and standard dimension alternatives can be formulated as an MINLP problem usin

35、g a special MINLP model formulation (MINLP-MS) for simultaneous topology, parameter and standard dimension optimization of mechanical superstructures, described in Part II. As can be seen from the (MINLP-MS), the objecti

36、ve function is typically subjected to structural analysis and logical constraints. While structural analysis constraints represent a mathematical model of </p><p>　　Modeling of discrete decisions to determin

37、e topology alternatives is an objective of the highest importance for the synthesis. In order to perform these decisions within the MINLP optimization, interconnection logical constraints Dy+R(d, p)≤r are proposed. While

38、 variables, their bounds and most of the constraints of the MINLP-MS model formulation are represented in Part II, interconnection logical constraints and the constraints defining topology alterations are described in th

39、is section. The la</p><p>　　Select exactly M units: . (1)</p><p>　　Select M units at the most: . (2)</p><p>　　Select at least

40、M units: . (3)</p><p>　　(b) If then conditions: </p><p>　　if unit k is selected then unit i must be selected: yk -yi≤0 (4)</p><p>　　(c) Activat

41、ion or deactivation of continuous variables, inequalities or equations: </p><p>　　1. example to relate continuous variable x to the scalar value U: </p><p>　　x=Uy

42、 (5)</p><p><b>　　if </b></p><p>　　2. an opposite relation: </p><p>　　X=U（1-y） (6)</p><p>　　3

43、. example for the bounds of continuous variable x: </p><p>　　x1,0y≤x≤xupy (7)</p><p><b>　　if </b></p><p>　　(d) Integer cuts co

44、nstraint eliminates unnecessary integer combinations yk={}∈{0,1}me.g. those found at previous MINLP iterations: </p><p><b>　　(8)</b></p><p><b>　　where , </b></p>

45、<p>　　In order to describe the modeling of discrete decisions, a general gate superstructure from Figure 2 is addressed in which the defined structural elements are typically horizontal and vertical girders. As the

46、modeling of vertical girders is simplified and needs no special interconnection logical constraints, the modeling of discrete decisions regarding horizontal girders proved to be more sophisticated. </p><p>　

47、　2.2.1. Modeling of topology alterations </p><p>　　Let us consider the vertical cross-section of the gate element superstructure with fixed and alternative horizontal girders, see Figure 3(a). The number of

48、fixed and alternative girders and their locations in the superstructure can be described by the following logical constraints: </p><p>　　(9) (10)</p><p><

49、b>　　(11)</b></p><p>　　Logical constraint (9) defines the minimal (Mmin) and maximal (Mmax) number of structural elements (girders). While number Mmin represents the number of fixed structural elemen

50、ts, the difference between the maximal and minimal number of elements (Mmax-Mmin) gives thenumber of alternative structural elements. Constraint (10) defines the direction of the removal of alternative elements: from the

51、 top down the superstructure. From Figure 3 is evident that the most upper element is the fixed one, whi</p><p>　　2.2.2. Modeling of interconnection relations</p><p>　　Interconnection relations

52、between alternative and fixed structural elements within the superstructure require special attention paid to the structural synthesis performed by the MINLP approach. Interconnection relations either restore the connect

53、ions between currently selected (existing) structural elements or cancel the relations between currently rejected (disappearing) structural elements. Since MINLP methods optimize the topology and parameters simultaneousl

54、y, it is necessary to define these</p><p>　　The modeling of interconnection logical constraints, however, requires additional effort, since most element constraints include functions not only of their own va

55、riables but also of the variables belonging to their adjoining structural elements. Such an example is, e.g. the constraint of the moment of inertia In,mof the mth horizontal girder of the nth main gate element (see equa

56、tion (23) in the following section), which includes the substituted expression (S6) of the skin-plate effective width</p><p>　　m=2,3…,M-1 (12)</p><p>　　The problem

57、arises if hm+1is not defined when the adjoining upper alternative girder to the mth horizontal girder does not exist. For example, let us consider the third girder in Figure 3(a) which is the uppermost existing intermedi

58、ate element. In order to define h4so as to fulfil the constraints of girder 3, h4should temporarily become equal to the height of the uppermost fixed girder h6 =hM (Figure 3(b)). The main idea is to set all heights of no

59、n-existing intermediate girders </p><p>　　(girders 4 and 5 in Figure 3(a)) to the value of h6by means of the logical constraints </p><p>　　, m=2,3,…,M-1 (13)</

60、p><p>　　, m=2,3,…,M-1 (14)</p><p>　　Note, that constraints (13) and (14) restore the upper and lower bounds of the distancewhen the corresponding girder exists (ym=1)

61、 and set it to zero, otherwise. When the distance is zero, it follows from constraint (12) that hm becomes equal to h. In this way all distances and heights are defined for any girder that becomes the uppermost selected

62、intermediate one and re-establishes its connection to the uppermost fixed girder. As the uppermost selected intermediate girder is connected to the u</p><p>　　should be defined and substituted for hM-1. The

63、vertical distance dhs of the uppermost selected intermediate girder is then defined by the constraint: </p><p><b>　　(15)</b></p><p>　　The selection of the height hs among all hm can

64、be performed by the following logical constraints: </p><p>　　, m=2,3,…,M-2 (16)</p><p>　　, m=2,3,…,M-2 (17)</p><p><b>　　(18)</b>&

65、lt;/p><p><b>　　(19)</b></p><p>　　Constraints (16) and (17) set hS to the height hm of that mth existing horizontal girder (ym=1), which has the existing adjoining lower girder (ym-1=1)

66、and the disappearing adjoining upper girder (ym+1=0). However, for m"M!1 the next upper girder always exists, since it is fixed, i.e. (yM =1). In this case we need additional constraints, i.e. (18) and (19), which s

67、et hS to the height hM-1. </p><p>　　3. THE MINLP OPTIMIZATION MODEL FOR ROLLER AND SLIDING HYDRAULIC STEEL GATE STRUCTURESDGATOP </p><p>　　An MINLP mathematical optimization model for roller and

68、 sliding hydraulic steel gate structures GATOP (GATe OPtimization) has been developed. The model has proven efficient for the synthesis of roller and sliding gates. As an interface for mathematical modeling and data inpu

69、ts/outputs GAMS (General Algebraic Modeling System) by Brooke et al.14 ,a high-level language has been used. The first version of GATOP was developed to perform NLP optimization problems of fixed gate structures, while t

70、he de</p><p>　　GATOP model is formulated as an MINLP problem performing gate synthesis. </p><p>　　In the process of the development of the GATOP model, the following assumptions and simplificati

71、ons have been considered: </p><p>　　1. A simplified static system for roller and sliding gates is to be used. It includes independent simply supported horizontal girders that are combined with independent cl

72、amped skin-plate elements. Such a static system is convenient for gates in which the horizontal girders are much longer than their intermediate vertical distances. Vertical girders have the same height as horizontal ones

73、. </p><p>　　2. In the above case, the horizontal girders transmit almost all the water load, so that the participation of vertical girders can be neglected. Although the vertical girders are not analysed, th

74、ey are nevertheless considered as a geometrical and economic fact in the objective function. </p><p>　　3. Only the water load, i.e. the hydrostatic pressure on the skin plate, is taken into consideration, wh

75、ile the dead weight, friction and buoyancy are neglected. </p><p><b>　　外文翻譯譯文</b></p><p><b>　　摘要</b></p><p>　　執(zhí)行的水力鋼門結(jié)構(gòu)綜合非線性規(guī)劃方法使能門結(jié)構(gòu)元素(大梁，板材)，優(yōu)選的門幾何、結(jié)構(gòu)元素和所有

76、連續(xù)和標(biāo)準(zhǔn)剖面圖大小之間的結(jié)構(gòu)元素和所有連續(xù)和標(biāo)準(zhǔn)尺寸的最佳優(yōu)選中間距離。為此，拓?fù)浣Y(jié)構(gòu)改變和互聯(lián)聯(lián)系的特別邏輯限制在選擇和被修理的結(jié)構(gòu)元素之間被公式化。他們被埋置了入路輾和滑的鋼門結(jié)構(gòu)GATOP一個(gè)數(shù)理優(yōu)化模型。GATOP根據(jù)已經(jīng)制定了一個(gè)特殊的MINLP機(jī)械上層上層建筑（MINLP - MS）的第一和第二部分介紹了模型的制定。該模型包含一個(gè)自我制造和運(yùn)輸費(fèi)用的經(jīng)濟(jì)大門的目標(biāo)函數(shù)。由于GATOP模型非凸，高度非線性的，它是由鏈接解決兩

77、相的MINLP戰(zhàn)略，無論是在頂級(jí)計(jì)算機(jī)代碼中實(shí)現(xiàn)辦公自動(dòng)化陪同的改性推理算法的手段。一個(gè)綜合的例子是作為一個(gè)比較設(shè)計(jì)已經(jīng)豎立滾子門，所謂的二進(jìn)水口閘門埃及阿斯旺的研究工作。最優(yōu)結(jié)果產(chǎn)生凈儲(chǔ)蓄占百分之二十九點(diǎn)四的時(shí)候相比，在門口豎立的實(shí)際成本。</p><p>　　關(guān)鍵詞：結(jié)構(gòu)合成，優(yōu)化，拓?fù)鋬?yōu)化，離散變量?jī)?yōu)化，混合整數(shù)非線性規(guī)劃;的MINLP;修正辦公/推理算法;MINLP（非線性規(guī)劃）的戰(zhàn)略液壓?jiǎn)㈤]閘門，推拉門

78、;輥閘門;阿斯旺</p><p><b>　　1。簡(jiǎn)介</b></p><p>　　本文介紹了混合整數(shù)非線性規(guī)劃（MINLP）的方式來滾子和滑門結(jié)構(gòu)，即在垂直升降水工鋼閘門合成最簡(jiǎn)單的類型，見圖1。滾子和閘也被視為最頻繁對(duì)水源的控制水工鋼閘門制造類型。它們用來規(guī)管水力發(fā)電廠，大壩或溢洪道的水流。</p><p>　　由于水工鋼閘門是非常特殊的結(jié)

79、構(gòu)，只有一個(gè)已經(jīng)討論了一些作者的優(yōu)化，例如卡爾文尼伽、蔣格林和柯克曼以及阿爾姆基斯特等人。特別有趣的是表現(xiàn)在沒有這些（輥閘），但類似的結(jié)構(gòu)優(yōu)化。在這種調(diào)查，萬德普拉斯和維斯哈爾以及戈達(dá)爾等。加筋復(fù)合材料層合板優(yōu)化，巴特勒和瑞格提斯加筋板的優(yōu)化，法卡斯和加麻依優(yōu)化焊接矩形蜂窩板，菲克肯等。斯特林格氣瓶和治療皮膚茛蒂等。加勁板。幾乎所有使用的非林程式學(xué)（NLP）技術(shù)作家。 茛蒂等。提出了遺傳算法，而科若文等.-推出的MINLP算法和拓?fù)浣Y(jié)構(gòu)

80、的同時(shí)和參數(shù)的閘門優(yōu)化策略。</p><p>　　圖1。垂直升降水工鋼閘門結(jié)構(gòu)</p><p>　　在我對(duì)這個(gè)文件三個(gè)部分組成的系列部分，一個(gè)是的MINLP方法和參數(shù)的同步拓?fù)浣Y(jié)構(gòu)優(yōu)化的一般看法是主辦。第二部分描述了標(biāo)準(zhǔn)尺寸的同時(shí)優(yōu)化擴(kuò)展。根據(jù)在第一和第二部分所定義的上層建筑的方法，本文件（第三部分）是合成和滑動(dòng)滾輪的MINLP水工鋼閘門結(jié)構(gòu)，取得了以最小的成本，受到明確的設(shè)計(jì)，材料，應(yīng)力

81、的主要目標(biāo)，偏轉(zhuǎn)和穩(wěn)定性約束。隨著的MINLP方法能夠同時(shí)拓?fù)浣Y(jié)構(gòu)，參數(shù)和標(biāo)準(zhǔn)尺寸的優(yōu)化，一門結(jié)構(gòu)構(gòu)件（梁，板），門全球性的幾何形狀，結(jié)構(gòu)之間的所有連續(xù)元素和中間的距離和數(shù)量的標(biāo)準(zhǔn)尺寸可同時(shí)得到。這種對(duì)論文三部分組成的系列的最后一部分，分為三個(gè)主要部分：</p><p>　　1。第2節(jié)介紹了如何不同拓?fù)浣Y(jié)構(gòu)和標(biāo)準(zhǔn)尺寸的替代品是假設(shè)以及如何聯(lián)網(wǎng)關(guān)系是由明確的邏輯約束手段，制定以執(zhí)行在優(yōu)化過程的拓?fù)浣Y(jié)構(gòu)和標(biāo)準(zhǔn)尺寸的改

82、變。</p><p>　　2。第3代表滾子，滑動(dòng)閘門結(jié)構(gòu)GATOP一般的MINLP優(yōu)化模型。</p><p>　　3。最后，在第4節(jié)，建議上層建筑的MINLP方法應(yīng)用到一個(gè)已經(jīng)豎立滾筒門，所謂的二進(jìn)水口閘門埃及阿斯旺合成。</p><p>　　2。上部結(jié)構(gòu)及其替代品和離散決策建模</p><p>　　2.1。推導(dǎo)的拓?fù)浣Y(jié)構(gòu)和標(biāo)準(zhǔn)尺寸的替代品&

83、lt;/p><p>　　在合成大門的第一步是一個(gè)混合整數(shù)非線性規(guī)劃上層建筑中不同拓?fù)?結(jié)構(gòu)和標(biāo)準(zhǔn)尺寸的嵌入式替代品被選定為最佳結(jié)果的產(chǎn)生。選定為最佳效果。門上層建筑也包含了結(jié)構(gòu)元素可建造每一個(gè)可能的結(jié)構(gòu)替代以及不同套離散值，每個(gè)標(biāo)準(zhǔn)尺寸替代不同代表性。但由于該輪和滑動(dòng)閘門幾乎相同的結(jié)構(gòu)，它是合理的建議上層建筑，這很可能是為他們兩個(gè)非常有用。</p><p>　　2.1.1。拓?fù)浣Y(jié)構(gòu)的替代品&l

84、t;/p><p>　　門上層建筑通常包括一門主要元素，其中每個(gè)元素是門各種結(jié)構(gòu)元素，如梁橫向，縱向梁，加勁和面板塊內(nèi)容，代表組成，見圖2。上層建筑包括N邁門元素，n∈N，每個(gè)包含米的水平梁，m∈M，縱向大梁（3+2V）通過整個(gè)大門，v∈V, v3的數(shù)量，以及相應(yīng)的（m-1）×（2+2V）的數(shù)目皮板元素。</p><p>　　圖2。門的上層建筑，由三個(gè)主要元素門，建造水平和每個(gè)包含六縱

85、九梁</p><p>　　對(duì)每一個(gè)m個(gè)第n個(gè)元素的水平梁大門額外二進(jìn)制變量yn,m是勁分配。橫向梁和相應(yīng)的面板單元板，在第n個(gè)元素的分布大門，因此被確定數(shù)量可以簡(jiǎn)單地用∑mYn,m 表示。附注k勁，該垂直梁相同數(shù)量最少為3，他們可以只需要奇數(shù)。如果一個(gè)二進(jìn)制變量yv是分配給每個(gè)v，v∈V的，縱向大梁可以用（3+2∑v yv ）表示。以同樣的方式一個(gè)偶數(shù)（2+2∑v yv）的同等水平將得到整個(gè)分區(qū)的建議。在縱向大

86、梁的情況下，我們可以看到，結(jié)構(gòu)構(gòu)件，也可確定合適的二元變量的線性組合。</p><p>　　其中最大數(shù)量Mmax的水平梁，每門各主要元素，上下梁連同中間水平梁和毗鄰的面板元素的最小數(shù)Mmin是當(dāng)作固定結(jié)構(gòu)的部分，它們總是在優(yōu)化本。所有其他（Mmax -Mmin）的中間與鄰接面橫板單元對(duì)應(yīng)的數(shù)字，然后把梁結(jié)構(gòu)元素作為替代，這可能不是消失或者被選中。由于唯一的選擇結(jié)構(gòu)元素的離散優(yōu)化參與，離散決定大小顯著減少。選定的

87、替代結(jié)構(gòu)之間的每個(gè)元素和固定結(jié)構(gòu)元素可能組合形式一門額外的拓?fù)?結(jié)構(gòu)的選擇。</p><p>　　2.1.2。標(biāo)準(zhǔn)尺寸的替代品</p><p>　　四個(gè)標(biāo)準(zhǔn)尺寸此外定義代表鐵皮板的標(biāo)準(zhǔn)厚度：面板噸tsn每n個(gè)元素的正門厚度，水平梁的法蘭厚度tfn，外層的水平梁腹板厚度噸，m=1或m=M，和內(nèi)部橫向梁腹板厚度噸，1<m<M自厚度tsn有一個(gè)對(duì)整個(gè)面的第n個(gè)元素的大門板共同的價(jià)值和

88、分別為第n個(gè)元素的所有大門梁的水平相同，即它們對(duì)應(yīng)到上層建筑或部分從特殊噸的MINLP - MS在第二部分制定模型的通用標(biāo)準(zhǔn)設(shè)計(jì)變量。同樣，門頁(yè)厚度噸，它為第n個(gè)元素外正門水平梁的共同價(jià)值，這是所有內(nèi)部橫向梁相同，對(duì)應(yīng)的共同的可替代的標(biāo)準(zhǔn)設(shè)計(jì)變量結(jié)構(gòu)元件。一種額外的標(biāo)準(zhǔn)離散值設(shè)置一個(gè)替代品和一維二元變量的大小相同，介紹了一套特別的標(biāo)準(zhǔn)尺寸為每個(gè)提及。</p><p>　　每個(gè)標(biāo)準(zhǔn)尺寸tsn應(yīng)表示在給定的標(biāo)準(zhǔn)尺寸i

89、中選擇替代尺寸，i∈I，被K的替代，k∈K，標(biāo)準(zhǔn)尺寸噸標(biāo)準(zhǔn)尺寸由P選擇，p∈P的，由R所替代， r∈R。 i的二進(jìn)制變量載體yn,r和離散值qn,r分配給變量載體tfn時(shí)，p元素yn,p 和qn,p的變量載體和R元素的載體yn,r和qn,k 分配給變量。因此，分配到門上層建筑整體向量變量是y=｛yn,m ,y1,v ,yn,I yn,k ,yn,p ,yn,r｝</p><p>　　2.2。離散決策建模&l

90、t;/p><p>　　該拓?fù)浣Y(jié)構(gòu)和標(biāo)準(zhǔn)尺寸的替代假設(shè)門上層建筑可歸結(jié)為一個(gè)混合整數(shù)非線性規(guī)劃MINLP模型采用一種特殊配方（的MINLP - MS）的拓?fù)浣Y(jié)構(gòu)的同時(shí)，參數(shù)和機(jī)械超標(biāo)準(zhǔn)尺寸的優(yōu)化結(jié)構(gòu)第二部分所述的問題。由于可以從（的MINLP - MS）的出現(xiàn)，其目標(biāo)函數(shù)通常受到結(jié)構(gòu)分析和邏輯約束。雖然結(jié)構(gòu)分析制約代表了一個(gè)綜合結(jié)構(gòu)的數(shù)學(xué)模型，邏輯約束是用于顯式建模的邏輯判斷</p><p>　

91、　決定確定的離散拓?fù)浣Ｊ且环N替代品為合成最為重要的目標(biāo)。為了執(zhí)行內(nèi)部的MINLP優(yōu)化這些決定，互連邏輯約束Dy+R（d,p）≤r是建議。而變量，其范圍和對(duì)的MINLP - MS模型制定的限制大多數(shù)是在第二部分，互連邏輯約束和約束丹寧拓?fù)浣Y(jié)構(gòu)的改變代表介紹本節(jié)。后者的是來源于以下基本的整數(shù)或混合整數(shù)邏輯約束：</p><p>　?。ㄒ唬┰谖以O(shè)置的單位選擇多個(gè)選擇的限制：</p><p>　

92、　精確地選擇測(cè)繪單位：</p><p><b>　　選擇M單位至多：</b></p><p><b>　　選擇至少M(fèi)單位：</b></p><p>　?。ǘ┤绻?dāng)時(shí)條件：</p><p>　　如果單位k為單位選定，然后我必須選擇：</p><p>　?。ㄈ┘せ罨蜻B續(xù)變量，

93、不等式或方程組的失活：</p><p>　　1。連續(xù)的例子，涉及到的標(biāo)量變量x的值：</p><p><b>　　如果,如果</b></p><p><b>　　2。相反的關(guān)系x：</b></p><p><b>　　如果如果</b></p><p>　

94、?。ㄋ模┱麛?shù)削減約束消除不必要的整數(shù)組合，如在以前的MINLP迭代中發(fā)現(xiàn)的：</p><p><b>　　其中</b></p><p>　　為了描述的離散決策模型，從圖2是針對(duì)一般的門上層建筑中定義的結(jié)構(gòu)元素通常水平和垂直</p><p>　　圖3。垂直截面通過門：（a）有固定門上層建筑（=）和替代（ - - - ）的結(jié)構(gòu)的內(nèi)容;（b），只有固

95、定結(jié)構(gòu)元素的最小結(jié)構(gòu)</p><p>　　梁。至于梁的垂直造型，不需要特殊的簡(jiǎn)單互連邏輯的制約，對(duì)于離散決策水平梁建模證明更加復(fù)雜。</p><p>　　2.2.1。模型的拓?fù)渥兓?lt;/p><p>　　讓我們考慮垂直交叉與固定和替代水平梁門元素上層建筑部分，見圖3（a）。 固定和替代的主梁和上層建筑的數(shù)量及其位置可以描述如下邏輯約束：</p><

96、p>　　邏輯約束（9）德納的（梁）結(jié)構(gòu)元素的最小（MMIN）和最大值（MMAX）的數(shù)量。雖然數(shù)MMIN代表固定結(jié)構(gòu)的元素個(gè)數(shù)，元素之間的最大和最小數(shù)量（Mmax -Mmin ）給出了替代結(jié)構(gòu)元素的個(gè)數(shù)。約束（10）德納的另類元素去除方向：從下拉上層建筑頂部。從圖3可見，最上面的元素是固定之一，這是由約束（11）。然后再?gòu)娜缦录s束（10），所有的閑置固定元素在上層建筑的底部。因此，限制（9） - （11）代表梁的水平顯式模型的拓?fù)浣Y(jié)

97、構(gòu)的改變。</p><p>　　2.2.2?；ミB關(guān)系建模</p><p>　　之間的替代性和互連結(jié)構(gòu)元件固定在上層建筑的關(guān)系需要特別注意的結(jié)構(gòu)合成的混合整數(shù)非線性規(guī)劃方法進(jìn)行?；謴?fù)之間的互連關(guān)系之一，目前選定的（現(xiàn)有）結(jié)構(gòu)構(gòu)件之間的連接或取消目前拒絕（消失）的結(jié)構(gòu)元素的關(guān)系。由于混合整數(shù)非線性規(guī)劃方法優(yōu)化的拓?fù)浣Y(jié)構(gòu)和參數(shù)的同時(shí)，有必要在簡(jiǎn)明的方程式中形成這些互連關(guān)系，使他們可以使在優(yōu)化過程

98、中的元素之間的互連和斷開。特別互連之間的替代性和固定結(jié)構(gòu)元件的互連關(guān)系的邏輯約束已提出。他們將被嵌入到門結(jié)構(gòu)的MINLP優(yōu)化模型，從而使后者成為自自動(dòng)拓?fù)浼皡?shù)優(yōu)化足夠了 </p><p>　　聯(lián)網(wǎng)的邏輯約束建模，但是，需要額外的補(bǔ)充，因?yàn)榇蠖鄶?shù)元素的制約因素包括功能不只是他們自己的變量，而是屬于他們的毗鄰結(jié)構(gòu)元素變數(shù)也。這樣的例子是，例如，轉(zhuǎn)動(dòng)慣量約束In,m的第m個(gè)元素的第n個(gè)正門水平梁（見以下部分方程（23

99、）），其中包括取代表達(dá)的面板的與高度有效寬度bsn,m與（梁與窗臺(tái)之間）hm-1和hm+1兩個(gè)毗鄰梁的高度有效寬度bsn,m。第m個(gè)中間水平梁的約束是典型的三種高度的功能：hm-1 ,hm ,hm+1 兩個(gè)水平之間的垂直距離梁dhm-1 和dhm。距離dhm是被約束簡(jiǎn)單地定義</p><p>　　這個(gè)問題出現(xiàn)時(shí)，如果hm+1不是定義毗鄰的上梁替代的m個(gè)水平梁不存在。例如，讓我們考慮圖3(一)中的第三次梁，這是

100、最主要的現(xiàn)有中間元素。為了定義h4，以充分的約束梁3，?4應(yīng)暫時(shí)成為平等的最頂部的固定梁的高度h6 =hM（圖3（b））。其主要思想是將所有的高度非現(xiàn)有中梁（圖3（一）梁4和梁5項(xiàng)）在h6由邏輯約束價(jià)值方式</p><p>　　請(qǐng)注意，約束（13）和（14）恢復(fù)上和的距離下邊界dhm時(shí)相應(yīng)的梁存在（ym =1）并將其設(shè)置為0，否則,，當(dāng)距離是零，它遵循從約束（12）的hm變成等于hM小時(shí)。在這所有的距離和高度是任

101、何梁即成為最主要的中間選擇一個(gè)，并重新建立其連接到最上面的固定梁定義方式。</p><p>　　作為最主要的是選擇一些中間梁連接到最上面的固定梁（如在圖3（一）梁3到梁 6項(xiàng)），后者也應(yīng)在類似的方式，連接到前一個(gè)（在圖3（一）梁3到梁6項(xiàng)）。為至上固定梁約束是當(dāng)時(shí)的兩個(gè)高峰只是功能：hm和hm-1和一個(gè)距離dhm-1。如果出現(xiàn)一些問題是不存在的中間梁，梁如在圖3（一）中4和5 。在這種情況下，hm-1不應(yīng)予以考慮