"Handbook of Test Problems in Local and Global
Optimization", C.A. Floudas, P.M. Pardalos et al.,
Kluwer Academic Publishers, 1999.
This is the list of inaccuracies compiled by Oleg Shcherbina
on June 29, 2002.
Below are 2 tables: 1st - with open questions and 2nd
with confirmed corrections. The corrections in the second table are
confirmed by C.Floudas. The others are still under investigation.
Problem | In the book | Our result | Comment | Correction by the authors | Comment2 |
---|---|---|---|---|---|
Test Problem 8 from Section 2.9, Chapter
2
p.15 |
Objective function: 15639 ##ERROR! ##
#X[1,1]=6, X[1,2]=2, X[2,2]=3, X[2,4]=21, X[3,1]=20, # X[4,1]=24, X[5,1]=3, X[5,3]=13, X[6,2]=12, # This solution is infeasible because # sum X[*,1]=6+20+24+3=53,but b[1]=29. |
objective 16831
# X [*,*] # 1 2 3 4 := #1 4 4 0 0 #2 0 3 0 21 #3 20 0 0 0 #4 2 22 0 0 #5 3 0 13 0 #6 0 12 0 0 |
The solution in the book is infeasible.
The bound constraints in the book may be incorrect. |
The bound constraint in the book are incorrect.
Running the GAMS model ex2.1.8.gms from site [1] gives us result with objective function value 15990. |
|
Test problem 2 from Section 6.3, Chapter
6
p.p.66-68 |
Objective function: -0.03247
x[1] = 0.00421; x[2] = 0.99579; |
Objective function for above x's is equal to 0.54729 | There are misprints in the definition of C^U(x). The
definition should be:
<Description> |
This formula for C^U(x) is on p.71, not here.
Correction is not clear. |
|
Test problem 6 from Section 6.4, Chapter
6
p.p.72-73 |
Objective function: 0.0
# x.[1] = 0.51802; # x.[2] = 0.0511; # x.[3] = 0.43088; Note.Objective function for above x's = 0.280976. |
Objective 0.2138712304
x =(0.676406,0.150677, 0.172917) |
There is a misprint in the book, in the transformation constraints should be modified. Then solution is correct. | There is no transformation on p.72-73.
It is not clear. |
|
Test Problem 10 from the Chapter 7, p.96-97 | # Objective Function: 1.1406; (ERROR: 1/7.112=0.1406)
# t[1] = 7.004; # t[2] = 7.646; # t[3] = 7.112; # t[4] = 0.0125; # t[5] = 0.8120; # t[6] = 0.9558; # t[7] = 0.3820; # t[8] = 0.3580; # t[9] = 0.3530; # t[10] = 2.0770; # t[11] = 0.4530; |
Objective 0.1;
# t[1]= 0.01 # t[2]= 0.01 # t[3]=10 # t[4]= 0.019732 # t[5]= 0.018799 # t[6]= 0.0102814 # t[7]= 0.47248 # t[8]= 0.0491182 # t[9]= 0.962626 # t[10]= 1.06924 # t[11]= 1.06263 |
Our solution
is better |
The solution in the book is correct. Note the constraint
t3*t4*(1+t9^2)/t2<=1 is not sutisfied in the suggested correction. |
Solution is incorrect. Given constraint is absent
in the book, but there is the following:
t3*t6*(1+t9^2)/t2 <=1. Replacement of this constraint with t3*t4*(1+t9^2)/t2<=1 in the GAMS model gives us the following result: objective 0.1 t[1] = 0.010084 t[2]=0.017138 t[3]=10 ... |
Test problem 1 from Section 13.5, Chapter 13, p.310-311 | An optimal permutation
(9 1 8 3 6 7 2 5 4 10). objective is 2227. # Note. For above x's function=2364. |
We found permutation (1,2,3,4,5,6,7,8,9,10)
and
# objective function =0 - minimal. If diagonal solution is not feasible, then adding costraint x[i,i]=0, we get solution # (8,4,1,9,7,10,5,3,2,6) with objective function=1445 |
The following constraint is missing from the formulation:
x[i,i]=0 for all i=1,...,n. With this constraint the solution to the problem is correct. The objective function value for the suggested correction is 2710 not 2364 |
But permutation
(9 1 8 3 6 7 2 5 4 10) is not feasible, because x[10,10]=1 for it. |
Problem | Correction by the authors | Comment |
---|---|---|
Test Problem 2 from Section 2.3, Chapter
2
p.6 |
Misprint:
in the book Q=100I, it should read Q=I |
OK |
Test Problem 3 from Section 2.4, Chapter
2
p.7
|
The problem and solution in the book are correct.
y9 must be eliminated from the solution. |
Ok. Objective function value in the book is missing and
has the value
-194. |
Test Problem 4 from Section 2.5, Chapter
2
p.8
|
Misprint: the constraint 0<=x<=1 in the book
should read
0<=z |
OK |
Test Problem 9 from Section 2.10, Chapter
2
p.16 |
There is a misprint in the book, "min" should read "max" | OK |
Test Problem 1 from Section 4.2, Chapter
4
p.27 |
There is a misprint in the book, the objective function
should be:
1/6*x^6-... |
OK |
Test Problem 5 from the Chapter 7
# Colville's Test Problem. p.p.92-93 |
The optimal objective function is given as f=1.1436. In the paper of Rijckaert and Martens (1978) it is given as 10127.13 for the same values of t. The correction suggested has an objective value of 10122.49. | Solution is correct but
correct objective function value is 10122.49 |
Test problem 3 from Section 9.2, Chapter 9, p.211-212 | Misprint in the book;
the outer objective function should read -29.2. |
OK |
Test problem 2 from Section 12.1, Chapter 12, p.265 | Misprint in the book; sign on the right hand side of a constraint, the correct constraint is: x2 + 1.1*y <=-1 | OK |
Test problem 5 from Section 12.2, Chapter 12, p.267-268 | Misprints in the book; signs on the right hand sides
of the constraints, the misprinted constraints should read:
-y1 - 2*y2 <= -5, y1^1.2*y2^1.7 - 7*y1-9*y2 <= -24 |
OK |