# Floor planning with an optimal trade-off curve.

    % Boyd, Kim, Vandenberghe, and Hassibi, "A Tutorial on Geometric Programming"
    % Written for CVX by Almir Mutapcic 02/08/06
    % (a figure is generated)
    %
    % Solves the problem of configuring and placing rectangles such
    % that they do not overlap and that they minimize the area of the
    % bounding box. This code solves the specific instances given
    % in the GP tutorial. We have four rectangles with variable
    % width w_i and height h_i. They need to satisfy area and aspect
    % ration constraints. The GP is formulated as:
    %
    %   minimize   max(wa + wb, wc + wd)*(max(ha,hb) + max(hc,hd))
    %       s.t.   wa*ha == area_a, wb*hb == area_b, ...
    %              1/alpha_max <= ha/wa <= alpha_max, ...
    %
    % where variables are rectangle widths w's and heights h's.

    % set the quiet flag (no solver reporting)
    cvxq = cvx_quiet(true);

    % constants
    a = 0.2;
    b = 0.5;
    c = 1.5;
    d = 0.5;

    % alpha is the changing parameter
    N = 20;
    alpha = linspace(1.01,4,N);

    fprintf(1,'Solving for the optimal tradeoff curve...\n');
    min_area = [];
    for n = 1:N
      % GP variables
      cvx_begin gp
        variables wa wb wc wd ha hb hc hd

        % objective function is the area of the bounding box
        minimize( max(wa + wb, wc + wd)*(max(ha,hb) + max(hc,hd)) )
        subject to
          % constraints (now impose the non-changing constraints)
          ha*wa == a; hb*wb == b; hc*wc == c; hd*wd == d;
          1/alpha(n) <= ha/wa; ha/wa <= alpha(n);
          1/alpha(n) <= hb/wb; hb/wb <= alpha(n);
          1/alpha(n) <= hc/wc; hc/wc <= alpha(n);
          1/alpha(n) <= hd/wd; hd/wd <= alpha(n);
      cvx_end

      min_area(n,1) = cvx_optval;
    end

    % restore initial solver reporting state
    cvx_quiet(cvxq);

    figure, clf
    plot(alpha,min_area);
    xlabel('alpha'); ylabel('min area');
    axis([1 4 2.5 4]);
    disp('Optimal tradeoff curve is plotted.')

    Solving for the optimal tradeoff curve...
    Optimal tradeoff curve is plotted.