run_BFOA_TransferFunction_Study.m

% Binary Fossa Optimization Algorithm (BFOA) with 8 Transfer Functions
% Evaluates BFOA on 25 binary knapsack problems using 8 different transfer functions

function run_BFOA_TransferFunction_Study()
    %% Setup
    problems = define_problems();
    transfer_funcs = define_transfer_functions();
    num_runs = 30;
    max_iter = 100;
    pop_size = 30;

    % Output table: rows = problems, columns = transfer functions
    results_std = zeros(length(problems), length(transfer_funcs));

    %% Main Loop
    for p = 1:length(problems)
        problem = problems(p);
        fprintf('Running problem: %s\n', problem.id);
        for t = 1:length(transfer_funcs)
            tf = transfer_funcs(t);
            best_vals = zeros(num_runs, 1);
            for run = 1:num_runs
                [~, best_fit, ~] = BFOA(problem.weights, problem.profits, problem.capacity, tf.func, max_iter, pop_size);
                best_vals(run) = best_fit;
            end
            results_std(p, t) = std(best_vals);
            fprintf('  Transfer Function %s - STD: %.2f\n', tf.name, results_std(p, t));
        end
    end

    %% Compute Friedman Mean Ranks
    ranks = zeros(size(results_std));
    for i = 1:size(results_std, 1)
        [~, sorted_idx] = sort(results_std(i, :));
        rank = 1:length(transfer_funcs);
        ranks(i, sorted_idx) = rank;
    end
    mean_ranks = mean(ranks, 1);
    mean_ranks_row = [{'Mean Rank'}, arrayfun(@(x) sprintf('%.2f', x), mean_ranks, 'UniformOutput', false)];

    %% Display Results Table in Exponential Format
    disp('Standard Deviation Table (BFOA, 30 runs)');

    header = ['ID', {transfer_funcs.name}];
    formatted_vals = cell(size(results_std));
    for i = 1:size(results_std,1)
        for j = 1:size(results_std,2)
            formatted_vals{i,j} = sprintf('%.2E', results_std(i,j));
        end
    end

    table_data = [cellstr({problems.id})', formatted_vals];
    table_data = [table_data; mean_ranks_row];
    results_table = cell2table(table_data, 'VariableNames', header);

    format shortE
    disp(results_table);
end


%% BFOA core with injected transfer function
function [best_pos, best_fit, convergence] = BFOA(weights, profits, capacity, transfer_func, max_iter, pop_size)
    dim = length(weights);
    positions = randi([0 1], pop_size, dim);
    fitness = zeros(pop_size, 1);
    territories = positions;
    territory_strength = ones(pop_size, 1);

    for i = 1:pop_size
        fitness(i) = knapsack_fitness(positions(i,:), weights, profits, capacity);
    end

    [best_fit, best_idx] = min(fitness);
    best_pos = positions(best_idx, :);
    convergence = zeros(max_iter, 1);

    for iter = 1:max_iter
        a = 2 - 2 * iter / max_iter;
        for i = 1:pop_size
            r = rand();
            new_pos = positions(i,:);
            influence = zeros(1, dim);

            if r < 0.3
                influence = 0.3 * a * (2*rand(1,dim) - 1);
            elseif r < 0.7
                r1 = rand(1,dim);
                r2 = rand(1,dim);
                influence = 2 * r1 .* (best_pos - positions(i,:)) + 1.5 * r2 .* (territories(i,:) - positions(i,:));
            else
                if rand < 0.5
                    influence = zeros(1,dim);
                else
                    idx = randi(pop_size);
                    while idx == i, idx = randi(pop_size); end
                    influence = 0.5 * rand(1,dim) .* (positions(idx,:) - positions(i,:));
                end
            end

            if territory_strength(i) > rand()
                influence = influence + 0.2 * rand(1,dim) .* (territories(i,:) - positions(i,:));
            end

            if rand() < 0.1
                neighbor = randi(pop_size);
                while neighbor == i, neighbor = randi(pop_size); end
                influence = influence + 0.1 * rand(1,dim) .* (positions(neighbor,:) - positions(i,:));
            end

            for d = 1:dim
                if rand < transfer_func(influence(d))
                    new_pos(d) = 1 - positions(i,d);
                end
            end

            new_fit = knapsack_fitness(new_pos, weights, profits, capacity);

            if new_fit < fitness(i)
                positions(i,:) = new_pos;
                fitness(i) = new_fit;
                territories(i,:) = new_pos;
                territory_strength(i) = min(territory_strength(i) + 0.1, 2);
            else
                territory_strength(i) = max(territory_strength(i) - 0.05, 0.1);
            end

            if fitness(i) < best_fit
                best_fit = fitness(i);
                best_pos = positions(i,:);
            end
        end

        for i = 1:pop_size
            r = randi(pop_size);
            while r == i, r = randi(pop_size); end
            if fitness(i) < fitness(r) && rand() < 0.3
                territories(i,:) = round(0.7 * territories(i,:) + 0.3 * territories(r,:));
            end
        end

        convergence(iter) = best_fit;
    end
end

%% Fitness function for binary knapsack
function f = knapsack_fitness(x, weights, profits, capacity)
    total_w = sum(weights .* x);
    total_p = sum(profits .* x);
    if total_w > capacity
        f = 1e6 + total_w;
    else
        f = -total_p;
    end
end

%% Transfer Functions
function tf = define_transfer_functions()
    tf(1).name = 'Ts1'; tf(1).func = @(x) 1 ./ (1 + exp(-x));
    tf(2).name = 'Ts2'; tf(2).func = @(x) 1 ./ (1 + exp(-2*x));
    tf(3).name = 'Ts3'; tf(3).func = @(x) 1 ./ (1 + exp(-x/2));
    tf(4).name = 'Ts4'; tf(4).func = @(x) 1 ./ (1 + exp(-x/3));
    tf(5).name = 'Tv1'; tf(5).func = @(x) abs(tanh(x));
    tf(6).name = 'Tv2'; tf(6).func = @(x) abs(x ./ sqrt(1 + x.^2));
    tf(7).name = 'Tv3'; tf(7).func = @(x) abs(2/pi * atan(pi/2 * x));
    tf(8).name = 'Tv4'; tf(8).func = @(x) abs(erf(sqrt(pi)/2 * x));
end



%% Knapsack problem definitions (ks8a to ks24e)
function problems = define_problems()
    % Define the knapsack problems (paste all ks8a to ks24e here from your dataset)
    % Due to length, paste manually from your dataset
    % Example for ks8a:
    problems(1).id = 'ks8a';
    problems(1).weights = [12630 284975 583838 575342 780934 164152 912739 412657];
    problems(1).profits  = [25424 604597 1272766 1174735 1707707 313906 1689410 860062];
    problems(1).capacity = 1863633;
    problems(2).id = 'ks8b';
problems(2).weights = [666885 346111 97003 337746 507338 836649 564424 289280];
problems(2).profits  = [1452321 747077 209067 674618 1076193 1619423 1212262 538078];
problems(2).capacity = 1822718;

problems(3).id = 'ks8c';
problems(3).weights = [580593 34916 848308 528023 497440 490277 97943 141338];
problems(3).profits  = [1155261 73653 1631996 1130519 1045697 1061672 193508 296438];
problems(3).capacity = 1609419;

problems(4).id = 'ks8d';
problems(4).weights = [800588 496540 364175 699421 179078 778021 206205 700556];
problems(4).profits  = [1521886 919285 794937 1296002 354090 1582223 409313 1401234];
problems(4).capacity = 2112292;

problems(5).id = 'ks8e';
problems(5).weights = [862754 318418 651921 844733 438185 591527 810761 468202];
problems(5).profits  = [1582289 640086 1270769 1839736 795116 1099087 1524697 951036];
problems(5).capacity = 2493250;

problems(6).id = 'ks12a';
problems(6).weights = [672437 664905 66143 670473 649045 513812 638975 262871 79332 334123 620541 437769];
problems(6).profits  = [1370413 1281034 124356 1296241 1410881 993625 1209949 573180 147263 617431 1193525 861742];
problems(6).capacity = 2805213;

problems(7).id = 'ks12b';
problems(7).weights = [419614 463634 305284 918709 743181 652957 256487 790046 310107 985008 43471 629575];
problems(7).profits  = [800734 843137 551965 1921987 1429742 1272555 552649 1468914 645615 1859603 89001 1190478];
problems(7).capacity = 3259036;

problems(8).id = 'ks12c';
problems(8).weights = [399907 241106 271976 105019 65202 864369 458263 27528 667143 681262 982460 215395];
problems(8).profits  = [744436 446887 550596 191341 142738 1571133 868558 54288 1425628 1318834 2127868 422621];
problems(8).capacity = 2489815;

problems(9).id = 'ks12d';
problems(9).weights = [992884 417147 996822 591627 482278 651305 491683 727443 135904 152947 590330 677035];
problems(9).profits  = [2157066 853212 1845571 1068849 962615 1278897 1026191 1377079 264669 299959 1080762 1263347];
problems(9).capacity = 3453702;

problems(10).id = 'ks12e';
problems(10).weights = [187536 919812 281447 290967 293933 146982 335995 76949 296586 732368 912094 566115];
problems(10).profits  = [390564 1896554 518776 534038 539357 281514 679085 164965 603431 1601666 1826086 1235821];
problems(10).capacity = 2520392;

problems(11).id = 'ks16a';
problems(11).weights = [123074 517025 655582 371336 51246 296092 431720 933989 561395 376612 722734 995095 568523 168710 520215 267362];
problems(11).profits  = [248913 1051063 1211866 716645 103462 544575 860033 2039565 1174920 704133 1495071 1907792 1093059 345186 1097141 487799];
problems(11).capacity = 3780355;

problems(12).id = 'ks16b';
problems(12).weights = [31957 117108 250834 775747 994544 315281 937184 258099 877986 327103 632921 518873 708189 537974 732066 838024];
problems(12).profits  = [66111 215853 452976 1435157 1901253 649654 2034198 496995 1725886 678356 1329367 1088047 1507322 1041781 1607816 1634282];
problems(12).capacity = 4426945;

problems(13).id = 'ks16c';
problems(13).weights = [406270 182392 468242 749900 581384 334532 483985 342610 260722 970898 887883 657188 369265 252140 727195 971955];
problems(13).profits  = [837989 370555 843247 1625049 1127636 664244 900936 747010 517890 2092844 1749694 1376143 756658 483621 1583667 1826529];
problems(13).capacity = 4323280;

problems(14).id = 'ks16d';
problems(14).weights = [169122 435204 480076 638597 906325 613953 713858 817993 18612 819650 867495 992711 509674 103140 481247 334219];
problems(14).profits  = [319363 924519 1016542 1387079 1840227 1346660 1515021 1572948 37076 1702673 1623789 1968433 1004311 221324 956448 692230];
problems(14).capacity = 4450938;

problems(15).id = 'ks16e';
problems(15).weights = [615938 74618 109110 821054 458488 821360 609945 361196 633910 133731 619385 11437 232580 987645 354237 676225];
problems(15).profits  = [1188681 160632 225764 1762724 840566 1501156 1265916 672380 1336652 289808 1252296 20947 472835 1828177 759603 1253380];
problems(15).capacity = 3760429;

problems(16).id = 'ks20a';
problems(16).weights = [807304 365268 71972 635962 628375 105248 912959 102532 258867 778387 351744 775629 997576 264796 438778 549088 522456 920079 775693 76582];
problems(16).profits  = [1490790 691574 150435 1164050 1227890 219877 1934511 199053 514991 1522492 769943 1680173 1839759 523879 800279 1097473 1091605 1921590 1495883 139897];
problems(16).capacity = 5169647;

problems(17).id = 'ks20b';
problems(17).weights = [426375 91504 915455 60292 337974 336679 566396 425705 836379 27713 779627 207304 174254 703660 421993 450456 828590 121896 719160 931334];
problems(17).profits  = [928904 170787 1689092 117966 632580 731869 1185747 923646 1617156 52263 1501384 428275 368772 1513686 918075 903139 1588130 220241 1451995 1863885];
problems(17).capacity = 4681373;

problems(18).id = 'ks20c';
problems(18).weights = [440356 79368 945895 666364 594595 358461 666020 801970 716869 431640 576028 308237 541552 879694 18964 741144 410306 24327 868689 57104];
problems(18).profits  = [925328 164044 1966178 1440910 1288193 741301 1241063 1447446 1388189 916476 1240551 639466 1124003 1867028 40187 1361579 770874 44934 1671823 119080];
problems(18).capacity = 5063791;

problems(19).id = 'ks20d';
problems(19).weights = [637662 193120 776715 262749 23227 384111 768320 168361 650172 453970 873944 389217 579192 490419 485659 478971 79818 507772 134957 234926];
problems(19).profits  = [1252158 350292 1479672 521323 50313 715956 1462192 314251 1319970 978978 1743412 748759 1274136 1031710 890331 1029238 174683 1062778 250178 431650];
problems(19).capacity = 4286641;

problems(20).id = 'ks20e';
problems(20).weights = [63416 838949 231705 278430 579076 542663 544786 226831 362836 192630 543297 194244 668225 858827 306890 914752 243468 983177 262040 115758];
problems(20).profits  = [128319 1601667 475634 531575 1251993 1108634 1039759 468728 698158 372342 1161048 403961 1362470 1773653 580301 1947699 495773 2007127 472069 245042];
problems(20).capacity = 4476000;

problems(21).id = 'ks24a';
problems(21).weights = [382745 799601 909247 729069 467902 44328 34610 698150 823460 903959 853665 551830 610856 670702 488960 951111 323046 446298 931161 31385 496951 264724 224916 169684];
problems(21).profits  = [825594 1677009 1676628 1523970 943972 97426 69666 1296457 1678693 1902996 1844992 1049289 1252836 1319836 953277 2067538 675367 853655 1826027 65731 901489 577243 466257 369261];
problems(21).capacity = 6404180;

problems(22).id = 'ks24b';
problems(22).weights = [763783 914370 831207 100284 487486 182921 369532 727094 272162 227474 170387 697344 266796 41169 937876 883615 923090 385246 839734 423575 33377 975193 69579 418849];
problems(22).profits  = [1559844 1724668 1548321 186455 1012952 337633 806295 1329837 546869 446874 316848 1399126 578882 79486 1816706 1665934 1917601 770200 1732704 806240 65751 1870594 140713 859568];
problems(22).capacity = 5971071;

problems(23).id = 'ks24c';
problems(23).weights = [425855 348636 526169 332447 441002 924697 383512 696754 345706 295567 606800 502532 67352 991656 779035 244102 623815 460346 44551 774214 215619 914117 568645 227812];
problems(23).profits  = [911193 699561 1049934 675119 942922 1911983 766504 1428013 665388 601640 1126415 1004011 135369 2158735 1516949 505363 1160279 1003942 81812 1654345 455207 1774312 1245431 422075];
problems(23).capacity = 5870470;

problems(24).id = 'ks24d';
problems(24).weights = [844709 36928 649129 925892 475939 108733 488034 395701 550693 509694 440355 49925 100736 79142 152798 88114 941561 820124 827804 918561 261353 573421 497161 788062];
problems(24).profits  = [1844400 75605 1344522 1725990 1029572 223878 935619 725710 1003949 953278 900820 97657 215673 143729 293251 187454 1696715 1495747 1589311 1821594 495147 1250695 970416 1459955];
problems(24).capacity = 5762284;

problems(25).id = 'ks24e';
problems(25).weights = [695093 430667 233583 832832 422539 614321 898576 371233 324029 958551 381955 519075 94236 835863 352292 983000 286126 924119 679730 229377 152007 794048 566176 729710];
problems(25).profits  = [1319972 804470 487111 1636416 915637 1334476 1703095 727928 588848 1974348 818432 1012735 181004 1826340 736446 2070580 597255 1765740 1374118 467036 310529 1614819 1157316 1370965];
problems(25).capacity = 6654569;

end