### Table 1 Coefficients of Weighted Sum

### Table 2. Selected Results for Weighted Sums

2006

"... In PAGE 4: ... Bold entries show results superior to either heuristic alone. 4 Heuristic Combinations Based on Weighted Sums Table2 gives results, in terms of nodes searched, for six individual heuristics and for combinations of these heuristics using the technique of weighted sums described in Section 2. For these tests, heuristics were given equal weights.... In PAGE 6: ...00,6,0.054,0.2a108 ). For these problems min do- main/forward degree gave a mean of 3886 search nodes, while the combination of five heuristics given in Table2... In PAGE 11: ... This rule is also consistent with the two cases of synergy among the products and quotients (cf. Table2 ). However, for quotients there appears to be a further (reason- able) condition: that both the numerator and denominator favor selections consistent with those favored by the original heuristic.... In PAGE 13: ... This anal- ysis involved max forward degree, min domain and the weighted sum of the two (with equal weights; cf. Table2 ). These data indicate that this heuristic combination shows better adherence to both the fail-first and promise policies than the component heuristics acting alone.... ..."

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### Table 1. Objective functions for weighted sum methods

2006

"... In PAGE 9: ... The genetic algorithm was run ten times with each weighted sum objective func- tion shown in Table1 , as well as ten times with both NSGA-II and SPEA2 multi- objective methods. Each of these runs were assessed by each of the objective func- tions in Table 1 as well as the Max Spread [9] and Morrison and De Jong [16] diversity measures.... In PAGE 9: ... The genetic algorithm was run ten times with each weighted sum objective func- tion shown in Table 1, as well as ten times with both NSGA-II and SPEA2 multi- objective methods. Each of these runs were assessed by each of the objective func- tions in Table1 as well as the Max Spread [9] and Morrison and De Jong [16] diversity measures. Averages over the ten runs of each have been taken and plotted as a percentage of the best average found.... ..."

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### Table 1. Weighted sum experimental results

in WASTE COLLECTION VEHICLE ROUTING PROBLEM WITH TIME WINDOWS USING MULTI-OBJECTIVE GENETIC ALGORITHMS

2007

"... In PAGE 7: ... The instance data name in Tables 1-3 is the number of stops in the problem. As depicted by the E2, E3 columns in Table1 , we concluded that both the route-based scheme (as proposed in Section 3.5) and the vehicle-based routing inspired by [1] performed fairly the same, hence either is suitable for our purposes.... In PAGE 7: ... This was further confirmed by Pareto results depicted in columns pE2 and pE3 in Table 2. Since the experiments with exhaustive insertion outperformed those with tournament insertion in terms of solution quality (as shown in Table1 ), we only consider the exhaustive ap- proach in Table 2. Table 2 shows a comparison between the weighted sum and Pareto rank based fitness evaluations.... ..."

### Table 7. Weighted sums for each solution (performance

1990

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### Table 6. Results for Weighted Sums with Geometric Problems

2006

"... In PAGE 6: ... 10, and tightness = 0.18. These were fairly easy for most, but not all, heuristics, with greater relative differences than those found with the homogeneous random problems. Nonethess, synergies could be readily obtained ( Table6 ). Thus, the effects generalise to at least some structured problems.... ..."

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