9,(x)+c,=0j∈I(x") (8) where the I(x)is called the active constraint set of the discrete optimum,it is determined according to following conditions Suppose the ci=-g;(x) if the c;=c,,Then jel(x) here c,is constrained violated evaluation of g,(x),it can be calculated by the following formulas: ,=8(-）△x,(A) (9) g={1sg(-8,）ax,(合）>0，vi} (10) As above illustration the discrete optimum of problems (1)may be defined as follows:Supposing the xEDCR,for all xEUN(x),if there exists f(x) f(x),then x is a constrained discrete local optimum,and that for all x NC(x),if there exists f(x)<f(x),then x is a false constrained discrete local optimum.In a lot of papers at present,authors only discussed the solving methods for the false local optimum,as a consequence,those can not be consi- dered as complete algorithms. If the x is a discrete local optsmum,consider a convergence condition of discrete search,then a set of T T=W∩S=Φ (11) must be an empty one.Where the set of Wand S are W={△x|Axt Vf(x)≤0} (12) S={△xl△x'Vg,(x)≤C,j∈I(x·)} (13) here,Ax,=141,0,47}(i=1,n),v f(x)and vg;(x)are the quasi-gradi- ents of the objective and constrained functions at x. On the basis of above illustrated concepts,any of the complete algorithm for discrete optimization must consist of two strategies,that is the step by step searching in discrete space and the finding out better point in the unit neighbor- hood.And that a multi-function composited algorithm is superiorer to a single one in either the ability or the reliabibity of the obtained optimum in engine- ering design.Based on this,we have developped the five general constrained nonlinear discrete optimization algorithms,namely,the direct search method MDOD,combined complex method MDCP,the random search method MDRP, 342劣 ’ ， “ 了任 ， 、 、 劣 ， ， 〔 〕 叫 一 劣 五 二 任 劣 ’ ， 、 ’ ， 石 ， 二 系 · 一 姜 。 二 ‘ 会 · 一 釜 △一 瓮 ” ， ‘ 二 〔 二 ， 〔 ， ， 义 。 ， 。 二 任 ， ， 二 ， ， ， ， ， ， ， 牙 自 必 。 平 户、 ‘ 牙 占 了 △二 △二 二 ‘ 廷 ， 毛 ， 任 ‘ ，，白 ， △ ‘ 落 ， ， 」丁 ， ， 二 ’ ， · 一 劣 。 ， ， 。 一 且 。 ， 、 ， ， ， ， ，