The mathematical model of optimal placement of active members in truss adaptive structures is essentially a nonlinear multi-objective optimization problem with mixed variables.It is usually much difficult and costly to be solved.In this paper,the optimal location of active members is treated in terms of (0,1) discrete variables.Structural member sizes,control gains,and (0,1) placement variables are treated simultaneously as design variables.Then,a succinct and reasonable compromise scalar model,which is transformed from original multi-objective optimization,is established,in which the (0,1) discrete variables are converted into an equality constraint.Secondly,by penalty function approach,the subsequent scalar mixed variable compromise model can be formulated equivalently as a sequence of continuous variable problems.Thirdly,for each continuous problem in the sequence,by choosing intermediate design variables and temporary critical constraints,the approximation concept is carried out to generate a sequence of explicit approximate problems which enhance the quality of the approximate design problems.Considering the proposed method,a FORTRAN program OPAMTAS2.0 for optimal placement of active members in truss adaptive structures is developed,which is used by the constrained variable metric method with the watchdog technique (CVMW method).Finally,a typical 18 bar truss adaptive structure as test numerical examples is presented to illustrate that the design methodology set forth is simple,feasible,efficient and stable.The established scalar mixed variable compromise model that can avoid the ill-conditioned possibility caused by the different orders of magnitude of various objective functions in optimization process,therefore,it enables the optimization algorithm to have a good stability.On the other hand,the proposed novel optimization technique can make both discrete and continuous variables be optimized simultaneously.
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