### Table 2: Multiobjective optimization problems. problem objectives ranges

1997

"... In PAGE 5: ... 8 RESULTS We tested the performance of our approach on three problems of increasing di culty, and compared it to the nPGA. The objective functions that de ne each one of these problems are listed in Table2 . Table 1 summarizes the value of parameters for the nPGA and our non-generational GA in all experiments performed.... ..."

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### Table 3. Distributed Q-learning for multiobjective optimization problems.

### Table 3. The average time for obtaining a solution for the multi-objective optimization problems by using TGP. The results are averaged over 30 independent runs.

"... In PAGE 13: ...igure 5. Diversity metric computed at every 10 generations. The results are averaged over 30 independent runs. Numerical values of the convergence and diversity metrics for the last generation are also given in section 9. 8 Running time Table3 is meant to show the efiectiveness and simplicity of the TGP algorithm by giving the time needed for solving these problems using a PIII Celeron computer at 850 MHz. Table 3 shows that TGP without archive is very fast.... In PAGE 13: ... 8 Running time Table 3 is meant to show the efiectiveness and simplicity of the TGP algorithm by giving the time needed for solving these problems using a PIII Celeron computer at 850 MHz. Table3 shows that TGP without archive is very fast. An average of 0.... ..."

### Table 3. Comparison of 4 methods for multiobjective optimization. Average and standard deviation values of six performance measures over a set of 27 problems. Methods N. of points k-distance

2005

"... In PAGE 17: ... In this case, however, we have added a Time column to show the average and standard deviation of the CPU seconds associated with each procedure. Table3 summarizes the results of our second experiment. Table 3.... In PAGE 17: ...8.860 0.031 0.347 0.303 0.168 446.714 The results in Table3 indicate that SSPMO is capable of finding efficient frontiers with a large number of points and high density, as indicated by the small k-distance values. The number of points is not an input parameter of SSPMO.... ..."

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### Table 2: Percentages of job areas that involve work in different problem types.

2007

"... In PAGE 6: ...rations (33.1%), invention (27.8%), testing (15.9%) and other (14.6%). Of the 31 responses for other, 10 were for optimization. Next we looked into how application areas varied by industry to see which combinations stand out ( Table2 ). Some specific combinations that we found are that those working in the automotive and robotics industries are interested in multi-objective and numerical optimization problems, while people working in the energy and entertainment industries are interested in multi-objective and classification problems.... ..."

### TABLE VII. OVERALL RESULTS FOR THE MULTIOBJECTIVE OPTIMIZATION - AVERAGED BY

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 1. Possible design objectives of #0Clter banks. Refer to #281#29 for explanation.

"... In PAGE 3: ... This design problem is a multi-objective nonlinear optimization problem, whose objectives consist of performance metrics of both the overall #0Clter bank and the single prototype low-pass #0Clter. Table1 summarizes the various design objectives. The design objectives of #0Clter banks have the following features: #0F They are not unique and may be con#0Dicting, leading to designs with di#0Berent tradeo#0Bs.... ..."