### Table 1. Negotiation with global constraints: Route sharing.

2001

"... In PAGE 5: ...The initial state before negotiation is shown in Table1 . Observe that some route types may already be common to multiple domains; e.... In PAGE 6: ...ible application of the least privilege principle); i.e., if two or more domains are capable of sharing the same route type, then the one that comprises the lowest number of routes will be used. Upon inspection of Table1 , we observe that two common states would satisfy these constraints. Domains D1, D2 and D3 could share route types {1,6}, {3} and {2,4,5} respectively (we call this Solution A).... In PAGE 8: ... In light of this second example, let us reexamine our four questions for the general case of any negotiation that can be cast in terms of objective values and resources, as in Table 2. (Note that our previous example (in Table1 ) can also be recast in this form.) a.... ..."

Cited by 9

### Table 1. Negotiation with global constraints: Route sharing.

2001

"... In PAGE 5: ...The initial state before negotiation is shown in Table1 . Observe that some route types may already be common to multiple domains; e.... In PAGE 6: ...ible application of the least privilege principle); i.e., if two or more domains are capable of sharing the same route type, then the one that comprises the lowest number of routes will be used. Upon inspection of Table1 , we observe that two common states would satisfy these constraints. Domains D1, D2 and D3 could share route types {1,6}, {3} and {2,4,5} respectively (we call this Solution A).... In PAGE 8: ... In light of this second example, let us reexamine our four questions for the general case of any negotiation that can be cast in terms of objective values and resources, as in Table 2. (Note that our previous example (in Table1 ) can also be recast in this form.) a.... ..."

Cited by 9

### Table A.1: Abbreviations used in the voting strategies for the global constraints.

### Table 3. Test Functions for Global Optimization Function Constraints

1995

"... In PAGE 8: ... 123 { 141. Berlin: Springer{Verlag 1995 For the test functions of Table3 we get the results shown in Figure 5 (Schwe- fel apos;s function F7 is normalized to make a log-plot possible) which con rm the relation (6). For these function we observe di erent regions of convergence.... In PAGE 15: ...able 5. lt;feval gt; vs. n for Function F6 (left) with f 9 10?1, I = 1:4, Rm = 0:1 , Rmin = 10?1 , pm = 1=n , bm = 2, 20 runs, and for Function F7 (right) with f fopt + 5 10?4 jfoptj , I = 1:4, Rm = 0:75 ,Rmin = 10?4 , pm = 1=n , bm = 2, 20 runs, lt;feval gt; vs. n for Function F8 (left) with f 10?3, I = 1:4, Rm = 0:1 , Rmin = 10?6 , pm = 1=n , bm = 2, 20 runs, and for Function F9 (right) with f 10?3 , I = 1:4, Rm = 0:1 ,Rmin = 10?4, pm = 1=n , bm = 2, 20 runs, BGA data from [10] Rastrigin apos;s Function F6 Schwefel apos;s Function F7 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 20 6098 20 3608 20 20 10987 500 16100 100 20 45118 20 25040 100 20 101458 1000 92000 200 20 98047 20 52948 200 20 241478 2000 248000 400 20 243068 20 112634 400 20 430084 4000 699803 1000 20 574561 20 337570 1000 20 1067221 || ||| Griewangk apos;s Function F8 Ackley apos;s Function F9 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 500 26700 500 66000 30 20 13997 20 19420 100 500 77250 500 361722 100 20 57628 20 53860 200 500 128875 500 748300 200 20 122347 20 107800 400 500 229750 500 1630000 400 20 262606 20 220820 1000 500 563350 | ||| 1000 20 686614 20 548306 The test functions given in Table3 are very popular in the literature on global optimization. The main results of this paper are summarized in Table 5 with n the number of variables, N the population size, and feval the average number of function evaluations for 20 runs.... ..."

Cited by 8

### Table 3. Results on Hamiltonian path problems 3.2 Global Constraints In this section, we describe methods to implement global constraints in E- GENET. We rst report the new performance gures for the cumulative con- straint previously presented in [12]. Then we describe the implementations of the three global constraints, namely the among, diffn and cycle constraints, in E-GENET and present their performance gures.

1998

Cited by 7

### Table 1: The data structures that are used to represent variables, constraints, methods, and global

1996

"... In PAGE 14: ...1.4 Data Structures Table1 shows the data structures that are used by both the incremental and non-incremental versions of QuickPlan to represent variables, constraints, and methods. It also shows the global variables used by the non-incremental version of QuickPlan.... ..."

Cited by 51

### Table 2 Summary of handling of constraints in various global optimization algorithms.

"... In PAGE 10: ... However, ex- tensive numerical results using these techniques have not been published. (See Table2 ; blank spaces mean the feature is absent.) Handling of simple bound constraints through the tessellation process has been... ..."

### Table 4.2: The graph structures used to produce the arcs in the con- straint network for a global constraint. Each graph structure takes either one or two vectors of vertices, and connects these using directed arcs.

2004