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poolsearch.py
#!/usr/bin/python # Copyright 2019, Gurobi Optimization, LLC # We find alternative epsilon-optimal solutions to a given knapsack # problem by using PoolSearchMode from __future__ import print_function from gurobipy import * try: # Sample data Groundset = range(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 # Create initial model model = Model("poolsearch") # Create dicts for tupledict.prod() function objCoefDict = dict(zip(Groundset, objCoef)) knapsackCoefDict = dict(zip(Groundset, knapsackCoef)) # Initialize decision variables for ground set: # x[e] == 1 if element e is chosen Elem = model.addVars(Groundset, vtype=GRB.BINARY, name='El') # Set objective function model.ModelSense = GRB.MAXIMIZE model.setObjective(Elem.prod(objCoefDict)) # Constraint: limit total number of elements to be picked to be at most # Budget model.addConstr(Elem.prod(knapsackCoefDict) <= Budget, name='Budget') # Limit how many solutions to collect model.setParam(GRB.Param.PoolSolutions, 1024) # Limit the search space by setting a gap for the worst possible solution that will be accepted model.setParam(GRB.Param.PoolGap, 0.10) # do a systematic search for the k-best solutions model.setParam(GRB.Param.PoolSearchMode, 2) # save problem model.write('poolsearch.lp') # Optimize model.optimize() model.setParam(GRB.Param.OutputFlag, 0) # Status checking status = model.Status if status == GRB.Status.INF_OR_UNBD or \ status == GRB.Status.INFEASIBLE or \ status == GRB.Status.UNBOUNDED: print('The model cannot be solved because it is infeasible or unbounded') sys.exit(1) if status != GRB.Status.OPTIMAL: print('Optimization was stopped with status ' + str(status)) sys.exit(1) # Print best selected set print('Selected elements in best solution:') print('\t', end='') for e in Groundset: if Elem[e].X > .9: print(' El%d' % e, end='') print('') # Print number of solutions stored nSolutions = model.SolCount print('Number of solutions found: ' + str(nSolutions)) # Print objective values of solutions for e in range(nSolutions): model.setParam(GRB.Param.SolutionNumber, e) print('%g ' % model.PoolObjVal, end='') if e % 15 == 14: print('') print('') # print fourth best set if available if (nSolutions >= 4): model.setParam(GRB.Param.SolutionNumber, 3); print('Selected elements in fourth best solution:') print('\t', end='') for e in Groundset: if Elem[e].Xn > .9: print(' El%d' % e, end='') print('') except GurobiError as e: print('Gurobi error ' + str(e.errno) + ": " + str(e.message)) except AttributeError as e: print('Encountered an attribute error: ' + str(e))