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poolsearch.m
function poolsearch() % Copyright 2018, Gurobi Optimization, LLC % % We find alternative epsilon-optimal solutions to a given knapsack % problem by using PoolSearchMode % define primitive data groundSetSize = 10; objCoef = [32; 32; 15; 15; 6; 6; 1; 1; 1; 1]; knapsackCoef = [16, 16, 8, 8, 4, 4, 2, 2, 1, 1]; Budget = 33; % Initialize model model.modelsense = 'max'; model.modelname = 'poolsearch'; % Set variables model.obj = objCoef; model.vtype = repmat('B', groundSetSize, 1); model.lb = zeros(groundSetSize, 1); model.ub = ones(groundSetSize, 1); for j = 1:groundSetSize model.varnames{j} = sprintf('El%d', j); end % Build constraint matrix model.A = sparse(knapsackCoef); model.rhs = Budget; model.sense = '<'; model.constrnames = {'Budget'}; % Set poolsearch parameters params.PoolSolutions = 1024; params.PoolGap = 0.10; params.PoolSearchMode = 2; % Save problem gurobi_write(model, 'poolsearch_m.lp'); % Optimize result = gurobi(model, params); % Capture solution information if ~strcmp(result.status, 'OPTIMAL') fprintf('Optimization finished with status %s, quit now\n', result.status); return; end % Print best solution fprintf('Selected elements in best solution:\n'); for j = 1:groundSetSize if result.x(j) >= 0.9 fprintf('%s ', model.varnames{j}); end end fprintf('\n'); % Print all solution objectives and best furth solution if isfield(result, 'pool') && ~isempty(result.pool) solcount = length(result.pool); fprintf('Number of solutions found: %d\n', solcount); fprintf('Objective values for all %d solutions:\n', solcount); for k = 1:solcount fprintf('%g ', result.pool(k).objval); end fprintf('\n'); if solcount >= 4 fprintf('Selected elements in fourth best solution:\n'); for k = 1:groundSetSize if result.pool(4).xn(k) >= 0.9 fprintf(' %s', model.varnames{k}); end end fprintf('\n'); end else fprintf('Number of solutions found: 1\n'); fprintf('Solution 1 has objective: %g \n', result.objval); end