The code is supplementary to the corresponding paper: An effective topological representation and dimensional reduction approach for multi-material topology optimization, Jianwen Bao, Zhaoyou Sun, Pai Liu, Yangjun Luo.

1. The present code uses the MMA Matlab routines (which is widely used in the structural optimization community) as the optimizer. The present code calls the subroutine mmasub.m (“Version September 2007”) from the MMA Matlab routines, which in turn calls another MMA subroutine subsolv.m (“Version Dec 2006”). As the authors of the MMA matlab routines require, the MMA Matlab routines can be obtained by contacting Prof. Svanberg (krille@math.kth.se).

2. Once the MMA matlab routines are obtained, some modifications of the optimization parameters need to be done as follows to run the design problem in the present paper: (i) set the parameter asyinit = 0.1, (ii) change the move limits of the design variables by replacing the original lines:

    if iter < 2.5 
      low = xval - asyinit*(xmax-xmin); 
      upp = xval + asyinit*(xmax-xmin); 
    else 
      zzz = (xval-xold1).*(xold1-xold2); 
      factor = eeen; 
      factor(find(zzz > 0)) = asyincr; 
      factor(find(zzz < 0)) = asydecr; 
      low = xval - factor.*(xold1 - low); 
      upp = xval + factor.*(upp - xold1); 
      lowmin = xval - 10*(xmax-xmin); 
      lowmax = xval - 0.01*(xmax-xmin); 
      uppmin = xval + 0.01*(xmax-xmin); 
      uppmax = xval + 10*(xmax-xmin); 
      low = max(low,lowmin); 
      low = min(low,lowmax); 
      upp = min(upp,uppmax); 
      upp = max(upp,uppmin); 
    end
   

   with

    if iter < 2.5 
      low = xval - asyinit*1; 
      upp = xval + asyinit*1; 
    else 
      zzz = (xval-xold1).*(xold1-xold2); 
      factor = eeen; 
      factor(find(zzz > 0)) = asyincr; 
      factor(find(zzz < 0)) = asydecr; 
      low = xval - min(1,factor.*(xold1 - low)); 
      upp = xval + min(1,factor.*(upp - xold1)); 
    end