### Table 1: User Defined Constants for the Evolutionary Algorithm.

"... In PAGE 13: ... In the present formulation, all values of gt; are 1.0 as indicated in Table1 . More specifically, the component penalty for the sixth individual in the population is, The rank based fitness for an individual ten segment cantilever column can then be written as follows; In the present study, the scaling multipliers are assigned constant values which reflect the importance of each component.... In PAGE 18: ... It is recognized that the most correct procedure is to report averages of many runs [29]. Furthermore, Table1 should be referenced for information regarding the evolutionary algorithm parameters used for all runs. The design loads were chosen to illustrate one of the complexities of multiple constraint optimization.... ..."

### TABLE 1.1 Examples of Commonly Used Structure-Based Drug Design Packages

### Table 1: Parameters of truss structure

"... In PAGE 5: ... Designing a truss structure is chosen as a numerical example in this paper. A model of truss structure is shown in Figure 3 and the parameters of the truss structure are shown in Table1 . This is 128 stage truss and a cross section is circle.... ..."

### Table 11: Pareto Selection Techniques: Ranking and Niching Approach Description Application Objectives (#) Chromosome

"... In PAGE 27: ...ajor MOEA sharing techniques are used; Section 8.2.3 discusses them in detail. Table11 lists the known Pareto ranking- and niching-based MOEA techniques. Table 11: Pareto Selection Techniques: Ranking and Niching Approach Description Application Objectives (#) Chromosome... In PAGE 28: ...A POSTERIORI TECHNIQUES 5.4 Pareto Sampling Techniques Table11 : (continued) Approach Description Application Objectives (#) Chromosome GA [96] (1997) Parallelized; Inte- grated with CFD and CEM codes; Uses NSGA [133] with tournament selection Two-dimensional airfoil design (2) Drag coe - cient; Transverse magnetic radar cross section Real values Multiobjective GA [113] (1997) Uses Fonseca apos;s MOGA [48]; Elitism in- corporated; Integrated with Navier-Stokes code Cascade airfoil de- sign (3) Pressure rise; Flow turning angle; Pressure loss Real values Multi-Objective EP (MOEP) [107] (1998) ( + ) elitist strategy; Pcurrent solutions se- lected with high prob- ability Voltage reference circuit parameter optimization (2) Room tempera- ture reference volt- age; Temperature variation Implies real values MOGA [111] (1998) Uses Fonseca apos;s [48] MOGA; Integrated with Navier-Stokes and Squire-Young codes Transonic wing de- sign (2) Lift; Drag Real values Multi-Objective Genetic Program- ming (MOGP) [68] (1998) Uses Fonseca apos;s [48] MOGA; Results compared to single- objective GP on same problems Model derivation for distillation col- umn and cooking extruder (4) RMS error; Residual vari- ance; Residual and output correlation; Model string length Program Strength Pareto Evolutionary Algo- rithm (SPEA) [166] (1998) Actively uses secondary population in tness as- signment and selection; Uses clustering to re- duce secondary popula- tion size; Pareto-based niching parameter None (2,3,4) Combina- torial optimization example (0/1 knapsack problem) Binary string; Genes are items present in ith knapsack 5.4.... ..."

### Table 4 Member areas for the optimized truss structure.

"... In PAGE 7: ... population size 280 has a weight of 544.852 lbs. Out of seven groups of member areas used in the ground structure, the optimized truss has only five groups (Groups 0 and 3, to- talling five members have been deleted). Member areas cor- responding to this solution are listed in Table4 . This truss is also optimal or near-optimal, because the deflection of top two nodes (1 and 2) is equal to the maximum allowable de- flection (0.... ..."

### Table 1. Summary of Truss Structural Tests

in Structural Analysis and Testing of an Erectable Truss for Precision Segmented Reflector Application

"... In PAGE 3: ... Some additional details related to the analysis models and test methods are included in this paper. Table1 lists the tests that are discussed in the present paper and indicates those tests that were first pre- sented in reference 1. This report begins with a brief description of the truss, including its geometry and component parts, after which finite-element models that are used to analyze the truss are described.... ..."

### Table 1. Summary of Truss Structural Tests

in Structural Analysis and Testing of an Erectable Truss for Precision Segmented Reflector Application

1995

"... In PAGE 3: ... Some additional details related to the analysis models and test methods are included in this paper. Table1 lists the tests that are discussed in the present paper and indicates those tests that were first pre- sented in reference 1. This report begins with a brief description of the truss, including its geometry and component parts, after which finite-element models that are used to analyze the truss are described.... ..."

### Table 5.13: Problems solved in different evolutionary algorithms Method Unimodal Basic Multimodal Expanded Hybrid Composition

2006

### Table 3: Member areas of the optimized truss for 2-D, 11-member, six-node ground structure.

2001

"... In PAGE 9: ... The member areas obtained using the proposed GA is compared with the best-known solution available (Ringertz, 1985), which used a multi-level linear and nonlinear programming method, where the same topology with 6 members and 5 nodes was obtained. Table3 shows that the proposed GA is able to obtain a truss with slightly smaller weight than that reported in Ringertz (1985). It is also interesting to note that although both weights are very similar, the combination of member areas in both trusses is a little different.... In PAGE 10: ...70 lbs (Hajela, Lee, and Lin, 1993), which is about 30 lbs more than that obtained by our algorithm. The corresponding member areas are presented in Table3 . Since the proposed GA has found a truss which requires 1 inBE less area in both members 4 and 5 (which are the largest members in the truss) compared to that in Hajela, Lee, and Lin (1993), the overall weight is smaller.... ..."

Cited by 12

### Table 1 Member areas of the optimized truss for 2-D, 11-member, six-node ground structure.

"... In PAGE 4: ... The member areas obtained using the proposed GA is compared with the best-known solution available (Ringertz, 1985), which used a multi-level linear and nonlinear program- ming method, where the same topology with 6 members and 5 nodes was obtained. Table1 shows that our GA is able to ob- tain a truss with slightly smaller weight than that reported in Ringertz (1985). It is also interesting to note that although both weights are very similar, the combination of member areas in both trusses is a little different.... In PAGE 4: ...70 lbs (Hajela, Lee, and Lin, 1993), which is about 30 lbs more than that obtained by our algorithm. The corresponding member areas are presented in Table1 . Since our GAs have found a truss which requires 1 in2 less area in both members 4 and 5 (which are the largest members in the truss) compared to that in Hajela, Lee, and Lin (1993), the overall weight is smaller.... ..."