draw_prim_curves.m

% IP
T = 800; % Since CPLEX exhibits unstable behavior as it approaches the time limit, we exclude the final portion from our plots (e.g., when the time limit is 1000s, we only plot results up to 800s)
nam = '(a) IP';
% nexttile;
default_file = ".\IP-r\exp-cplex-method-['fixTop']-perc-0.0-Mt3600\primals.mat";
ori_fix_file = ".\IP-r\exp-cplex-method-['fixTop']-perc-0.1-Mt1000\primals.mat";
ori_ps_file = ".\IP-r\exp-cplex-method-['PS']-perc-0.1-Mt1000\primals.mat";
opt_fix_file = ".\IP-rs\exp-cplex-method-['fixTop']-perc-0.1-Mt1000\primals.mat";
opt_ps_file = ".\IP-rs\exp-cplex-method-['PS']-perc-0.1-Mt1000\primals.mat";

draw_primal_curves(default_file,ori_fix_file,ori_ps_file,opt_fix_file,opt_ps_file,nam,T);
ylim([0.5,1]);
xlim([10,T]);

% SMSP
figure;
nam = '(b) SMSP';
default_file = ".\SMSP-r\exp-cplex-method-['fixTop']-perc-0.0-Mt3600\primals.mat";
ori_fix_file = ".\SMSP-r\exp-cplex-method-['fixTop']-perc-0.5-Mt1000\primals.mat";
ori_ps_file = ".\SMSP-r\exp-cplex-method-['PS']-perc-0.5-Mt1000\primals.mat";
opt_fix_file = ".\SMSP-rs\exp-cplex-method-['fixTop']-perc-0.5-Mt1000\primals.mat";
opt_ps_file = ".\SMSP-rs\exp-cplex-method-['PS']-perc-0.5-Mt1000\primals.mat";

draw_primal_curves(default_file,ori_fix_file,ori_ps_file,opt_fix_file,opt_ps_file,nam,T);
ylim([0.4,1.3]);
xlim([10,T]);




function draw_primal_curves(default_path,ori_fix_path,ori_ps_path,opt_fix_path,opt_ps_path,nam,T)
    

    default_primals = load(default_path).primals;
    ori_fix = load(ori_fix_path).primals;
    ori_ps = load(ori_ps_path).primals;
    opt_fix = load(opt_fix_path).primals;
    opt_ps = load(opt_ps_path).primals;

    


    default_BKV = default_primals(:,size(default_primals,2));
    ori_fix_BKV = ori_fix(:,size(ori_fix,2));
    ori_ps_BKV = ori_ps(:,size(ori_ps,2));
    opt_fix_BKV = opt_fix(:,size(opt_fix,2));
    opt_ps_BKV = opt_ps(:,size(opt_ps,2));

    BKV= [default_BKV,ori_fix_BKV,ori_ps_BKV,opt_fix_BKV,opt_ps_BKV];
    BKV = min(BKV,[],2);
    
    pag_default = mean(abs(default_primals-BKV)./abs(BKV),1);
    pag_ori_fix = mean(abs(ori_fix-BKV)./abs(BKV),1);
    pag_ori_ps = mean(abs(ori_ps-BKV)./abs(BKV),1);
    pag_opt_fix = mean(abs(opt_fix-BKV)./abs(BKV),1);
    pag_opt_ps = mean(abs(opt_ps-BKV)./abs(BKV),1);

    
    % align
    % Since the optimal value of each SMSP instance are greater than 1772
    % resulting in extremely small-valued primal gaps, thus re-scaled values (between 0 and 1) of
    % primal gaps are ploted. 
    if strcmp(nam ,'(b) SMSP') 
        scale = 100; 
        pag_default = pag_default*scale;
        pag_ori_fix = pag_ori_fix*scale;
        pag_ori_ps = pag_ori_ps*scale;
        pag_opt_fix = pag_opt_fix*scale;
        pag_opt_ps = pag_opt_ps*scale;
    end

    % limited length
    pag_default = pag_default(1:T);
    pag_ori_fix = pag_ori_fix(1:T);
    pag_ori_ps = pag_ori_ps(1:T);
    pag_opt_fix = pag_opt_fix(1:T);
    pag_opt_ps = pag_opt_ps(1:T);

    % statistic
    pag_default_std = std(default_primals./BKV,1);
    pag_ori_fix_std = std(ori_fix./BKV,1);
    pag_ori_ps_std = std(ori_ps./BKV,1);
    pag_opt_fix_std = std(opt_fix./BKV,1);
    pag_opt_ps_std = std(opt_ps./BKV,1);

    pag_default_mean = pag_default(T);
    pag_ori_fix_mean = pag_ori_fix(T);
    pag_ori_ps_mean = pag_ori_ps(T);
    pag_opt_fix_mean = pag_opt_fix(T);
    pag_opt_ps_mean = pag_opt_ps(T);

    pag_default_std = pag_default_std(T);
    pag_ori_fix_std = pag_ori_fix_std(T);
    pag_ori_ps_std = pag_ori_ps_std(T);
    pag_opt_fix_std = pag_opt_fix_std(T);
    pag_opt_ps_std = pag_opt_ps_std(T);


    fprintf('Relative primal gap of %s\n', nam);
    fprintf('CPLEX: %f\n', pag_default_mean);
    fprintf('ND: %f\n', pag_ori_fix_mean);
    fprintf('ND+SymILO: %f\n', pag_opt_fix_mean);
    fprintf('PS: %f\n', pag_ori_ps_mean);
    fprintf('PS+SymILO: %f\n', pag_opt_ps_mean);

    w = 10;
    pag_default = smooth_v(pag_default,w);
    pag_ori_fix = smooth_v(pag_ori_fix,w);
    pag_ori_ps = smooth_v(pag_ori_ps,w);
    pag_opt_fix = smooth_v(pag_opt_fix,w);
    pag_opt_ps = smooth_v(pag_opt_ps,w);
    
    red = [0.850980392156863 0.325490196078431 0.0980392156862745];
    green = [0.466666666666667 0.674509803921569 0.188235294117647];
    purple = [0.494117647058824 0.184313725490196 0.556862745098039];
    
    linwidth = 2;
    
    plot(1:size(pag_ori_fix,2),pag_ori_fix,'LineWidth',linwidth,'Marker','o','MarkerIndices',[1,200,400,600,800],'MarkerSize',8,'LineStyle','-','Color',red);hold on;
    plot(1:size(pag_ori_ps,2),pag_ori_ps,'LineWidth',linwidth,'Marker','o','MarkerIndices',[1,200,400,600,800],'MarkerSize',8,'LineStyle','-','Color',green);hold on;
    plot(1:size(pag_default,2),pag_default,'LineWidth',linwidth,'Marker','none','MarkerIndices',[1,200,400,600,800],'MarkerSize',8,'LineStyle','--','Color','b');hold on;
    plot(1:size(pag_opt_fix,2),pag_opt_fix,'LineWidth',linwidth,'Marker','diamond','MarkerIndices',[1,200,400,600,800],'MarkerSize',8,'LineStyle','-','Color',red);hold on;
    plot(1:size(pag_opt_ps,2),pag_opt_ps,'LineWidth',linwidth,'Marker','diamond','MarkerIndices',[1,200,400,600,800],'MarkerSize',8,'LineStyle','-','Color',green);hold on;

    
    set(gca,'FontSize',12,'XTick',[ 10 200  400  600 800]); 

    
    grid on;
    xlabel({'Solving time (s)',nam},'Interpreter','tex','FontSize',20);
    ylabel('Primal gap','Interpreter','tex','FontSize',20);
    
    legend('ND','PS','Tuned CPLEX','SymILO+Fix\&optimize','SymILO+Local Branching','Color',[0.99,0.995,1],'Interpreter','latex');
    
%     st = subtitle(nam,'Interpreter','tex','FontSize',20);

end

function sv = smooth_v(v,w)
    v_len = size(v);
    v_len = v_len(2);
    sv = 1:v_len;
    tv = 1:v_len+w-1;
    for i=1:v_len
        sv(i) = v(i);
        tv(i) = v(i);
    end
    for i=1:w-1
        tv(v_len+i) = v(v_len);
    end

    for i=1:v_len
        ss = 0;
        for j=1:w
            ss = ss + tv(i+j-1);
        end
        ss = ss/w;
        sv(i) = ss;
        
    end
end