def optimize( self, optName, tol, optOptions={}, storeHistory=False, setDV=None, xScale=1.0, objScale=1.0, conScale=1.0, offset=0.0, check_solution=True, ): # Optimization Object optProb = Optimization("HS071 Constraint Problem", self.objfunc) # Design Variables x0 = [1.0, 5.0, 5.0, 1.0] optProb.addVarGroup("xvars", 4, lower=1, upper=5, value=x0, scale=xScale, offset=offset) # Constraints optProb.addConGroup("con", 2, lower=[25, 40], upper=[None, 40], scale=conScale) # Objective optProb.addObj("obj", scale=objScale) # Optimizer try: opt = OPT(optName, options=optOptions) except Error: raise unittest.SkipTest("Optimizer not available:", optName) if isinstance(setDV, str): optProb.setDVsFromHistory(setDV) elif isinstance(setDV, dict): optProb.setDVs(setDV) outDV = optProb.getDVs() assert_allclose(setDV["xvars"], outDV["xvars"]) sol = opt(optProb, sens=self.sens, storeHistory=storeHistory) # Check Solution if check_solution: self.fStar = 17.0140172 self.xStar = (1.0, 4.743, 3.82115, 1.37941) self.lambdaStar = (0.55229366, -0.16146857) assert_allclose(sol.objectives["obj"].value, self.fStar, atol=tol, rtol=tol) assert_allclose(sol.xStar["xvars"], self.xStar, atol=tol, rtol=tol) if hasattr(sol, "lambdaStar"): assert_allclose(sol.lambdaStar["con"], self.lambdaStar, atol=tol, rtol=tol) return sol
class TestOptProb(unittest.TestCase): def objfunc(self, xdict): """ This is a simple quadratic test function with linear constraints. The actual problem doesn't really matter, since we are not testing optimization, but just optProb. However, we need to initialize and run an optimization in order to have optimizer-specific fields in optProb populated, such as jacIndices. This problem is probably not feasible, but that's okay. """ funcs = {} funcs["obj_0"] = 0 for x in xdict.keys(): funcs["obj_0"] += np.sum(np.power(xdict[x], 2)) for iCon, nc in enumerate(self.nCon): conName = "con_{}".format(iCon) funcs[conName] = np.zeros(nc) for x in xdict.keys(): for j in range(nc): funcs[conName][j] = (iCon + 1) * np.sum(xdict[x]) return funcs, False def setup_optProb(self, nObj=1, nDV=[4], nCon=[2], xScale=[1.0], objScale=[1.0], conScale=[1.0], offset=[0.0]): """ This function sets up a general optimization problem, with arbitrary DVs, constraints and objectives. Arbitrary scaling for the various parameters can also be specified. """ self.nObj = nObj self.nDV = nDV self.nCon = nCon self.xScale = xScale self.objScale = objScale self.conScale = conScale self.offset = offset # Optimization Object self.optProb = Optimization("Configurable Test Problem", self.objfunc) self.x0 = {} # Design Variables for iDV in range(len(nDV)): n = nDV[iDV] lower = np.random.uniform(-5, 2, n) upper = np.random.uniform(5, 20, n) x0 = np.random.uniform(lower, upper) dvName = "x{}".format(iDV) self.x0[dvName] = x0 self.optProb.addVarGroup( dvName, n, lower=lower, upper=upper, value=x0, scale=xScale[iDV], offset=offset[iDV], ) # Constraints for iCon in range(len(nCon)): nc = nCon[iCon] lower = np.random.uniform(-5, 2, nc) upper = np.random.uniform(5, 6, nc) self.optProb.addConGroup( "con_{}".format(iCon), nc, lower=lower, upper=upper, scale=conScale[iCon], ) # Objective for iObj in range(nObj): self.optProb.addObj("obj_{}".format(iObj), scale=objScale[iObj]) # Finalize self.optProb.printSparsity() # run optimization # we don't care about outputs, but this performs optimizer-specific re-ordering # of constraints so we need this to test mappings opt = OPT("slsqp", options={"IFILE": "optProb_SLSQP.out"}) opt(self.optProb, "FD") def test_setDV_getDV(self): """ We just test that setDV and getDV work, even with scaling """ self.setup_optProb( nObj=1, nDV=[4, 8], nCon=[2, 3], xScale=[4, 1], objScale=[0.3], conScale=[0.1, 8], offset=[3, 7], ) # test getDV first x0 = self.optProb.getDVs() self.assert_dict_allclose(x0, self.x0) # now set, get, and compare newDV = {"x0": np.arange(4), "x1": np.arange(8)} self.optProb.setDVs(newDV) outDV = self.optProb.getDVs() self.assert_dict_allclose(newDV, outDV) def test_setDV_VarGroup(self): """ Test that setDV works with a subset of VarGroups """ self.setup_optProb( nObj=1, nDV=[4, 8], nCon=[2, 3], xScale=[4, 1], objScale=[0.3], conScale=[0.1, 8], offset=[3, 7], ) oldDV = self.optProb.getDVs() # set values for only one VarGroup newDV = {"x0": np.arange(4)} self.optProb.setDVs(newDV) outDV = self.optProb.getDVs() # check x0 changed assert_allclose(newDV["x0"], outDV["x0"]) # check x1 is the same assert_allclose(oldDV["x1"], outDV["x1"]) def test_mappings(self): """ This test checks the various mapping and process helper functions in pyOpt_optimization. In this function we just set up an optimization problem, and the actual test is done in `map_check_value`. """ nDV = [4, 8, 1] nCon = [2, 3, 1, 1] self.setup_optProb( nObj=1, nDV=nDV, nCon=nCon, xScale=[np.random.rand(i) for i in nDV], objScale=[0.3], conScale=[np.random.rand(i) for i in nCon], offset=[np.random.rand(i) * np.arange(i) for i in nDV], ) # first test X x = self.optProb.getDVs() self.map_check_value("X", x) # next we check the objective funcs, _ = self.objfunc(x) obj_funcs = {} for key in funcs.keys(): if "obj" in key: obj_funcs[key] = funcs[key] self.map_check_value("Obj", obj_funcs) # lastly we check the constraints funcs, _ = self.objfunc(x) con_funcs = {} for key in funcs.keys(): if "con" in key: con_funcs[key] = funcs[key] self.map_check_value("Con", con_funcs) def map_check_value(self, key, val): """ This function checks all the mapping and process functions in both directions, for a given key = {'X', 'Con', 'Obj'} and val in dictionary format. """ # dictionary of function handles to test map_funcs = { "X": [self.optProb._mapXtoOpt, self.optProb._mapXtoUser], "X_Dict": [self.optProb._mapXtoOpt_Dict, self.optProb._mapXtoUser_Dict], "Con": [self.optProb._mapContoOpt, self.optProb._mapContoUser], "Con_Dict": [self.optProb._mapContoOpt_Dict, self.optProb._mapContoUser_Dict], "Obj": [self.optProb._mapObjtoOpt, self.optProb._mapObjtoUser], "Obj_Dict": [self.optProb._mapObjtoOpt_Dict, self.optProb._mapObjtoUser_Dict], } process_funcs = { "X": { "vec": self.optProb.processXtoVec, "dict": self.optProb.processXtoDict }, "Con": { "vec": self.optProb.processContoVec, "dict": self.optProb.processContoDict }, "Obj": { "vec": self.optProb.processObjtoVec, "dict": self.optProb.processObjtoDict }, } def processValue(key, val, output): """helper function since some functions have optional arguments that are needed""" if key == "Con": return process_funcs[key][output](val, scaled=False, natural=True) elif key == "Obj": return process_funcs[key][output](val, scaled=False) else: return process_funcs[key][output](val) # test dict to vec mappings vec = processValue(key, val, "vec") dictionary = processValue(key, vec, "dict") self.assert_dict_allclose(val, dictionary) # test mappings using dictionaries val_opt = map_funcs[key + "_Dict"][0](val) val_user = map_funcs[key + "_Dict"][1](val_opt) self.assert_dict_allclose(val_user, val) self.assert_dict_not_allclose(val_user, val_opt) # test mappings using vectors val = processValue(key, val, "vec") val_opt = map_funcs[key][0](val) val_user = map_funcs[key][1](val_opt) assert_allclose(val_user, val, atol=tol, rtol=tol) self.assert_not_allclose(val_user, val_opt) # check that the scaling was actually done correctly # we only check this for the array version because # it's much simpler if key == "X": scale = np.hstack(self.xScale) offset = np.hstack(self.offset) assert_allclose(val_opt, (val_user - offset) * scale) else: if key == "Obj": scale = np.hstack(self.objScale) else: scale = np.hstack(self.conScale) assert_allclose(val_opt, val_user * scale) def assert_dict_allclose(self, actual, desired, atol=tol, rtol=tol): """ Simple assert for two flat dictionaries, where the values are assumed to be numpy arrays The keys are checked first to make sure that they match """ self.assertEqual(set(actual.keys()), set(desired.keys())) for key in actual.keys(): assert_allclose(actual[key], desired[key], atol=atol, rtol=rtol) def assert_dict_not_allclose(self, actual, desired, atol=tol, rtol=tol): """ The opposite of assert_dict_allclose """ self.assertEqual(set(actual.keys()), set(desired.keys())) for key in actual.keys(): if np.allclose(actual[key], desired[key], atol=tol, rtol=tol): raise AssertionError( "Dictionaries are close! Inputs are {} and {}".format( actual, desired)) def assert_not_allclose(self, actual, desired, atol=tol, rtol=tol): """ The numpy array version """ if np.allclose(actual, desired, atol=atol, rtol=tol): raise AssertionError( "Arrays are close! Inputs are {} and {}".format( actual, desired))