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Selected Continuous Global Optimization Test Problems

The models shown are a collection of continuous global optimization test problems originally used in

A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems, Ali, Khompatraporn and Zabinsky, Journal of Global Optimization (2005) 31:635-672.

The model were made available by the authors of the article in their original C format. The models were translated into GAMS by Andre Savitsky. In order to minimize the chance of translation errors we have been sampling random points and evaluating the objective of these points. The results have been exported and were compared in a C program (testme.c) that used the original C model. Minor adjustments to the C models have been done and users of the C files are advised to compare them with versions distributed by the authors of the paper. The raw GAMS models were converted into GAMS scalar format using the CONVERT facility. The global optimum reported in the paper has been added to the scalar model.

* The GAMS model translations have an additional objective variable which models the objective function to optimize. This results in the models having variables and number of nonzeroes which are one greater than the C implementations. The model statistics listed are from the original C model representations as they are given in the reference above.

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Download SelConGlobal.zip


Total number of models:   55

Number
in Paper
GAMS/C Name Name in
Paper
Type #Eqns #Vars #NZ #NNZ Global
Minimum
GAMS
Original
GAMS
Scalar
C Source
1.    Ackleys Ackley’s Problem (ACK) NLP 1 10 10 10 0.0000 gms gms header file
2.    AluffiPentini Aluffi-Pentini’s Problem (AP) NLP 1 2 2 2 -0.3523 gms gms header file
3.    BeckerLago Becker and Lago Problem (BL) NLP 1 2 2 2 0.0000 gms gms header file
4.    Bohachevsky1 Bohachevsky 1 Problem (B1) NLP 1 2 2 2 0.0000 gms gms header file
5.    Bohachevsky2 Bohachevsky 2 Problem (B2) NLP 1 2 2 2 0.0000 gms gms header file
6.    Branin Branin Problem (BR) NLP 1 2 2 2 0.3979 gms gms header file
7.    Camel3 Camel Back-3 Three Hump Problem (CB3) NLP 1 2 2 2 0.0000 gms gms header file
8.    Camel6 Camel Back-6 Six Hump Problem (CB6) NLP 1 2 2 2 -1.0316 gms gms header file
9.    CosMix2 Cosine Mixture Problem (CM) NLP 1 2 2 2 -0.2000 gms gms header file
9.    CosMix4 Cosine Mixture Problem (CM) n=4 NLP 1 4 4 4 -0.4000 gms gms header file
10.    DekkersAarts Dekkers and Aarts Problem (DA) NLP 1 2 2 2 -24776.5183 gms gms header file
11.    Easom Easom Problem (EP) NLP 1 2 2 2 -1.0000 gms gms header file
12.    EMichalewicz Epistatic Michalewicz Problem (EM) DNLP 1 5 5 5 -4.6877 gms gms header file
13.    Expo Exponential Problem (EXP) DNLP 1 10 10 10 -1.0000 gms gms header file
14.    GoldPrice Goldstein and Price Problem (GP) NLP 1 2 2 2 3.0000 gms gms header file
15.    Griewank Griewank Problem (GW) NLP 1 10 10 10 0.0000 gms gms header file
16.    Gulf Gulf Research Problem (GRP) NLP 1 3 3 3 0.0000 gms gms header file
17.    Hartman3 Hartman 3 Problem (H3) NLP 1 3 3 3 -3.8628 gms gms header file
18.    Hartman6 Hartman 6 Problem (H6) NLP 1 6 6 6 -3.3224 gms gms header file
19.    Helical Helical Valley Problem (HV) DNLP 1 3 3 3 0.0000 gms gms header file
20.    Hosaki Hosaki Problem (HSK) NLP 1 2 2 2 -2.3458 gms gms header file
21.    Kowalik Kowalik Problem (KL) DNLP 1 4 4 4 0.0003 gms gms header file
22.    LM1 Levy and Montalvo 1 Problem (LM1) NLP 1 3 3 3 0.0000 gms gms header file
23.    LM2n5 Levy and Montalvo 2 Problem (LM2) NLP 1 5 5 5 0.0000 gms gms header file
23.    LM2n10 Levy and Montalvo 2 Problem (LM2) n=10 NLP 1 10 10 10 0.0000 gms gms header file
24.    McCormic McCormick problem (MC) NLP 1 2 2 2 -1.9133 gms gms header file
25.    MeyerRoth Meyer and Roth Problem (MR) NLP 1 3 3 3 0.0019 gms gms header file
26.    MieleCantrell Miele and Cantrell Problem (MCP) NLP 1 4 4 4 0.0000 gms gms header file
27.    Modlangerman Modified Langerman Problem (ML) NLP 1 10 10 10 -0.9650 gms gms header file
28.    ModRosenbrock Modified Rosenbrock Problem (MRP) NLP 1 2 2 2 0.0000 gms gms header file
29.    MultiGauss Multi-Gaussian Problem (MGP) NLP 1 2 2 2 -1.2970 gms gms header file
30.    Neumaier2 Neumaier 2 Problem (NF2) NLP 1 4 4 4 0.0000 gms gms header file
31.    Neumaier3 Neumaier 3 Problem (NF3) NLP 1 10 10 10 -210.0000 gms gms header file
32.    Oddsquare Odd Square Problem (OSP) DNLP 1 10 10 10 -1.1438 gms gms header file
33.    Paviani Paviani’s Problem (PP) NLP 1 10 10 10 -45.7784 gms gms header file
34.    Periodic Periodic Problem (PRD) NLP 1 2 2 2 0.9000 gms gms header file
35.    PowellQ Powell’s Quadratic Problem (PQ) NLP 1 4 4 4 0.0000 gms gms header file
36.    PriceTransistor Price’s Transistor Modelling Problem (PTM) DNLP 1 9 9 9 0.0000 gms gms header file
37.    Rastrigin Rastrigin Problem (RG) NLP 1 10 10 10 0.0000 gms gms header file
38.    Rosenbrock Rosenbrock Problem (RB) DNLP 1 10 10 10 0.0000 gms gms header file
39.    Salomon Salomon Problem (SAL) NLP 1 5 5 5 0.0000 gms gms header file
40.    Schaffer1 Schaffer 1 Problem (SF1) NLP 1 2 2 2 0.0000 gms gms header file
41.    Schaffer2 Schaffer 2 Problem (SF2) NLP 1 2 2 2 0.0012 gms gms header file
42.    Schubert Shubert Problem (SBT) NLP 1 2 2 2 -186.7309 gms gms header file
43.    Schwefel Schwefel Problem (SWF) DNLP 1 10 10 10 -4189.8289 gms gms header file
44.    Shekel5 Shekel 5 Problem (S5) NLP 1 4 4 4 -10.1532 gms gms header file
45.    Shekel7 Shekel 7 Problem (S7) NLP 1 4 4 4 -10.4029 gms gms header file
46.    Shekel10 Shekel 10 Problem (S10) NLP 1 4 4 4 -10.5364 gms gms header file
47.    Shekelfox5 Shekel’s Foxholes Problem (FX) NLP 1 5 5 5 -10.4056 gms gms header file
47.    Shekelfox10 Shekel’s Foxholes Problem (FX) n=10 NLP 1 10 10 10 -10.2087 gms gms header file
48.    Zeldasine10 Sinusoidal Problem (SIN) NLP 1 10 10 10 -3.5000 gms gms header file
48.    Zeldasine20 Sinusoidal Problem (SIN) - 20 NLP 1 20 20 20 -3.5000 gms gms header file
49.    STChebychev9 Storn’s Tchebychev Problem (ST) DNLP 1 9 9 9 0.0000 gms gms header file
49.    STChebychev17 Storn’s Tchebychev Problem (ST) n=17 DNLP 1 17 17 17 0.0000 gms gms header file
50.    Wood Wood’s Problem (WP) NLP 1 4 4 4 0.0000 gms gms header file