Handbook of Test Problems in Local and Global Optimization

by Floudas, Christodoulos A.; Pardalos, Panos M.; Adjiman, Claire S.; Esposito, William R.; Gumus, Zeynep H.

• ISBN13: 9780792358015
• ISBN10: 0792358015
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: Kluwer Academic Pub

Summary

This collection of challenging and well-designed test problems arising in literature studies also contains a wide spectrum of applications, including pooling/blending operations, heat exchanger network synthesis, homogeneous azeotropic separation, and dynamic optimization and optimal control problems.

Table of Contents

Introduction	1	(5)
Quadratic Programming Problems	5	(16)
Introduction	5	(1)
Test Problem 1	5	(1)
Test Problem 2	6	(1)
Test Problem 3	7	(1)
Test Problem 4	8	(2)
Test Problem 5	10	(1)
Test Problem 6	11	(1)
Test Problem 7	12	(3)
Test Problem 8	15	(1)
Test Problem 9	16	(2)
Test Problem 10	18	(3)
Quadratically Constrained Problems	21	(6)
Introduction	21	(1)
Test Problem 1	21	(2)
Test Problem 2	23	(1)
Test Problem 3	24	(1)
Test Problem 4	25	(2)
Univariate Polynomial Problems	27	(6)
Introduction	27	(1)
Test Problem 1	27	(1)
Test Problem 2	28	(1)
Test Problem 3	28	(1)
Test Problem 4	29	(1)
Test Problem 5	29	(1)
Test Problem 6	30	(1)
Test Problem 7	30	(1)
Test Problem 8	30	(1)
Test Problem 9	31	(2)
Bilinear problems	33	(26)
Introduction	33	(1)
Pooling Problems	34	(9)
Introduction	34	(1)
Haverly Pooling Problem	34	(2)
Ben-Tal et al. (1994) Problems: General Formulation	36	(2)
Ben-Tal et al. (1994) Problems: Test Problem 1	38	(2)
Ben-Tal et al. (1994) Problems: Test Problem 2	40	(3)
Distillation Column Sequencing Problems	43	(8)
Introduction	43	(1)
Nonsharp separation of propane, isobutane and n-butane	44	(2)
Nonsharp separation of propane, isobutane, n-butane and isopentane	46	(5)
Heat Exchanger Network Problems	51	(8)
Introduction	51	(1)
Test Problem 1	51	(1)
Test Problem 2	52	(2)
Test Problem 3	54	(5)
Biconvex and (D.C.) Problems	59	(26)
Introduction	59	(1)
Phase and Chemical Equilibrium Problems	59	(5)
Introduction	59	(1)
Mathematical Formulation	60	(4)
Biconvex Problems	64	(6)
NRTL Equation	64	(2)
Test Problem 1	66	(1)
Test Problem 2	67	(1)
Test Problem 3	68	(1)
Test Problem 4	69	(1)
Difference of Convex Functions (D.C.) Problems	70	(15)
UNIQUAC Equation	70	(1)
Test Problem 5	71	(1)
Test Problem 6	72	(1)
Test Problem 7	73	(1)
Test Problem 8	74	(1)
UNIFAC Equation	75	(1)
Test Problem 9	76	(1)
Test Problem 10	77	(1)
Test Problem 11	78	(1)
ASOG Equation	79	(2)
Test Problem 12	81	(1)
Test Problem 13	81	(1)
Modified Wilson Equation	82	(2)
Test Problem 14	84	(1)
Generalized Geometric Programming	85	(22)
Introduction	85	(1)
Literature Problems	86	(11)
Test Problem 1: Alkylation process design	86	(3)
Test Problem 2: CSTR Sequence Design	89	(1)
Test Problem 3: Heat exchanger design	90	(1)
Test Problem 4: Optimal Reactor Design	91	(1)
Test Problem 5: Colville's Test Problem	92	(1)
Test Problem 6	93	(1)
Test Problem 7	94	(1)
Test Problem 8	94	(1)
Test Problem 9	95	(1)
Test Problem 10	96	(1)
Robust Stability Analysis	97	(10)
Test Problem 11	98	(1)
Test Problem 12	99	(1)
Test Problem 13	100	(1)
Test Problem 14	101	(1)
Test Problem 15	102	(1)
Test Problem 16	103	(4)
Twice Continuously Differentiable NLPs	107	(98)
Introduction	107	(1)
Literature Problems	108	(6)
Test Problem 1	108	(1)
Test Problem 2: Pseudoethane	109	(1)
Test Problem 3: Goldstein and Price function	110	(1)
Test problem 4: Three-hump camelback function	110	(1)
Test Problem 5: Six-hump Camelback Function	111	(1)
Test Problem 6: Shekel Function	111	(1)
Test Problem 7	112	(1)
Test Problem 8	113	(1)
Batch Plant Design Under Uncertainty	114	(14)
Introduction	114	(1)
Single-Product Campaign Formulation	115	(3)
Test Problem 1	118	(3)
Test Problem 2	121	(2)
Test Problem 3	123	(1)
Unlimited Intermediate Storage Formulation	124	(2)
Test Problem 4	126	(1)
Test Problem 5	127	(1)
Chemical Reactor Network Problems	128	(38)
Introduction	128	(1)
General Formulation	129	(3)
Specific Information	132	(1)
Problem Characteristics	133	(1)
Test Problems	134	(1)
Test Problem 1: Nonisothermal Van de Vusse Reaction Case I	134	(5)
Test Problem 2: Isothermal Van de Vusse Reaction Case I	139	(2)
Test Problem 3: Isothermal Van de Vusse Reaction Case II	141	(2)
Test Problem 4: Isothermal Van de Vusse Reaction Case III	143	(2)
Test Problem 5: Isothermal Van de Vusse Reaction Case IV	145	(2)
Test Problem 6: Isothermal Trambouze Reaction	147	(2)
Test Problem 7: Isothermal Denbigh Reaction Case I	149	(2)
Test Problem 8: Isothermal Denbigh ReactionCase II	151	(2)
Test Problem 9: Isothermal Levenspiel Reaction	153	(2)
Test Problem 10: α-Pinene Reaction	155	(2)
Test Problem 11: Nonisothermal Van de Vusse Reaction Case II	157	(2)
Test Problem 12: Nonisothermal Naphthalene Reaction	159	(3)
Test Problem 13: Nonisothermal Parallel Reactions	162	(2)
Test Problem 14: Sulfur Dioxide Oxidation	164	(2)
Parameter Estimation problems	166	(12)
Introduction	166	(1)
General formulation	167	(1)
Test Problem 1: Linear Model	167	(2)
Test Problem 2: Polynomial Model	169	(1)
Test Problem 3: Non-linear Model	169	(2)
Test Problem 4: Respiratory Mechanical Model	171	(1)
Test Problem 5: Kowalik Problem	172	(1)
Test Problem 6: Pharmacokinetic Model	173	(1)
Test Problem 7: Steady-State CSTR	174	(2)
Test Problem 8: Vapor-Liquid Equilibrium Model	176	(2)
Phase and Chemical Equilibrium Problems	178	(8)
Introduction	178	(1)
General formulation - Tangent Plane Distance Minimization	179	(1)
Van der Waals Equation	180	(1)
Test Problem 1	180	(1)
Test Problem 2	181	(1)
SRK Equation	182	(1)
Test Problem 3	182	(1)
Test Problem 4	183	(1)
Peng-Robinson Equation	184	(1)
Test Problem 5	185	(1)
Test Problem 6	186	(1)
Clusters of Atoms and Molecules	186	(19)
Introduction	186	(1)
General Formulation	187	(1)
Lennard-Jones Potential	188	(5)
Morse Potential	193	(4)
Tersoff Potential	197	(2)
Brenner Potential	199	(3)
Bolding-Andersen Potential	202	(3)
Bilevel Programming Problems	205	(28)
Introduction	205	(2)
Terminology and Properties	206	(1)
Solution Techniques	206	(1)
Bilevel Linear Programming Problems	207	(13)
Karush-Kuhn-Tucker Approach	208	(1)
Test Problem 1	208	(2)
Test Problem 2	210	(1)
Test Problem 3	211	(1)
Test Problem 4	212	(1)
Test Problem 5	213	(1)
Test Problem 6	214	(1)
Test Problem 7	215	(1)
Test Problem 8	216	(2)
Test Problem 9	218	(1)
Test Problem 10	219	(1)
Bilevel Quadratic Programming Problems	220	(13)
Introduction	220	(1)
Test Problem 1	221	(1)
Test Problem 2	222	(1)
Test Problem 3	223	(2)
Test Problem 4	225	(1)
Test Problem 5	226	(1)
Test Problem 6	227	(1)
Test Problem 7	228	(1)
Test Problem 8	229	(1)
Test Problem 9	230	(3)
Complementarity Problems	233	(18)
Introduction	233	(1)
Linear Complementarity Problems	234	(8)
Test Problem 1	234	(1)
Test Problem 2	235	(1)
Test Problem 3	236	(1)
Bimatrix Games	236	(1)
Test Problem 4	237	(1)
Equilibrium Transportation Model	238	(1)
Test Problem 5	239	(1)
Traffic Equilibrium Problem	240	(1)
Test Problem 6	241	(1)
Nonlinear Complementarity Problems	242	(9)
Test Problem 1	243	(1)
Test Problem 2	243	(1)
Test Problem 3	244	(1)
Nash Equilibrium	245	(1)
Test Problem 4	246	(1)
Test Problem 5	246	(1)
Invariant Capital Stock Problem	247	(1)
Test Problem 6	248	(3)
Semidefinite Programming Problems	251	(12)
Introduction	251	(3)
Problem formulation	251	(1)
Semidefinite Programming Applications	252	(2)
Educational Testing Problem	254	(4)
General formulation	255	(3)
Maximum Cut Problem	258	(5)
General formulation	259	(4)
Mixed-Integer Nonlinear Problems	263	(40)
Introduction	263	(1)
Literature Problems	264	(5)
Test Problem 1	264	(1)
Test Problem 2	265	(1)
Test Problem 3	266	(1)
Test Problem 4	267	(1)
Test Problem 5	267	(1)
Test Problem 6	268	(1)
Heat Exchanger Network Synthesis	269	(9)
Introduction	269	(1)
General Formulation	270	(3)
Test Problem 1	273	(5)
Heat Exchanger Networks: Arithmetic Mean	278	(7)
Introduction	278	(1)
General Formulation	278	(2)
Test Problem 1	280	(2)
Test Problem 2	282	(3)
Pump network synthesis	285	(4)
Introduction	285	(1)
Test Problem 1	286	(3)
Trim Loss Minimization	289	(14)
Introduction	289	(1)
General Formulation	290	(1)
Test Problem 1	291	(3)
Test Problem 2	294	(2)
Test Problem 3	296	(3)
Test Problem 4	299	(4)
Combinatorial Optimization Problems	303	(22)
Modeling with Integer Programming	303	(1)
Test problems in the Internet	304	(1)
Quadratic Integer Programming	304	(2)
Quadratic 0-1 Test problems	304	(2)
Satisfiability Problems	306	(2)
SAT Test Problems	307	(1)
The Traveling Salesman Problem	308	(1)
TSP test Problems	309	(1)
Assignment Problems	309	(4)
QAP Test Problems	310	(3)
Graph Coloring	313	(1)
Test Problems	314	(1)
Maximum Clique Problem	314	(4)
Maximum Clique: Coding Theory Test Problems	317	(1)
Maximum Clique: Keller Graphs	317	(1)
Steiner Problems in Networks (SPN)	318	(7)
Test Problems	319	(6)
Nonlinear Systems of Equations	325	(26)
Literature problems	326	(8)
Test Problem 1: Himmelblau function	326	(1)
Test Problem 2: Equilibrium Combustion	327	(1)
Test Problem 3	328	(1)
Test Problem 4	328	(1)
Test Problem 5	329	(1)
Test Problem 6	329	(2)
Test Problem 7	331	(1)
Test Problem 8	332	(1)
Test Problem 9	333	(1)
Enclosing All Homogeneous Azeotropes	334	(17)
Introduction	334	(1)
General Formulation - Activity Coefficient Equations	335	(2)
Wilson Equation	337	(1)
Test Problem 1	337	(1)
Test Problem 2	338	(1)
Test Problem 3	339	(1)
NRTL Equation	340	(1)
Test Problem 4	341	(1)
Test Problem 5	341	(1)
UNIQUAC Equation	342	(1)
Test Problem 6	343	(1)
Test Problem 7	344	(1)
UNIFAC Equation	345	(1)
Test Problem 8	346	(1)
Test Problem 9	347	(4)
Dynamic Optimization Problems	351
Introduction	351
General Formulation	351
Solution Techniques (Local)	352
Control Parameterization	352
Solution of NLP/DAE	354
Chemical Reactor Network Problems	354
Introduction	354
General Formulation	355
Specific Information	363
Problem Characteristics	364
Test Problems	364
Test Problem 1: Nonisothermal Van de Vusse Reaction Case I	364
Test Problem 2: Isothermal Van de Vusse Reaction Case I	369
Test Problem 3: Isothermal Van de Vusse Reaction Case II	371
Test Problem 4: Isothermal Van de Vusse Reaction Case III	372
Test Problem 5: Isothermal Van de Vusse Reaction Case IV	374
Test Problem 6: Isothermal Trambouze Reaction	376
Test Problem 7: Isothermal Denbigh Reaction Case I	377
Test Problem 8: Isothermal Denbigh Reaction Case II	379
Test Problem 9: Isothermal Levenspiel Reaction	381
Test Problem 10: α-Pinene Reaction	383
Test Problem 11: Nonisothermal Van de Vusse Reaction Case II	385
Test Problem 12: Nonisothermal Naphthalene Reaction	387
Test Problem 13: Nonisothermal Parallel Reactions	389
Test Problem 14: Sulfur Dioxide Oxidation	391
Parameter Estimation Problems	393
Introduction	393
General Formulation	394
Test Problem 1	394
Test Problem 2	396
Test Problem 3: Catalytic Cracking of Gas Oil	398
Test Problem 4: Bellman's Problem	399
Test Problem 5: Methanol-to-Hydrocarbons Process	401
Test Problem 6: Lotka-Volterra Problem	403
Optimal Control Problems	404
Introduction	404
Test Problem 1	405
Test Problem 2: Singular Control Problem	406
Test Problem 3: CSTR Problem	407
Test Problem 4: Oil Shale Pyrolysis	408
Test Problem 5: Bifunctional Catalyst Blend Problem	410