### Table 1. Meta-heuristic classification.

"... In PAGE 5: ... Similarly, scatter search was accompanied by adaptive memory elements as a result of being associated with early tabu search ideas, but this connection is likewise only beginning to be pursued. A few proponents of simulated annealing and genetic algorithms have recently gone farther in modifying the original conceptions than indicated in Table1 , to propose the inclusion of elements of adaptive memory as embodied in tabu search. Such proposals are often described by their originators as hybrid methods, due to their marriage of aspects from different frameworks.... ..."

### Table 1: Evidence about some of the advantages in solving SCOPs via meta- heuristics instead of using exact classical methods.

2006

"... In PAGE 2: ... In contrast, approaches based on metaheuristics are capable of finding good and sometimes optimal solutions to problem instances of realistic size, in a generally smaller computation time. Table1 lists some papers in the literature providing evidence about the advantages in solving SCOPs1 via metaheuristics instead of using exact classical methods. This survey paper is the first attempt to put under a unifying view the several applications of metaheuristics to SCOPs, and it should contribute in balancing the literature, where a number of surveys and books about solving SCOPs via classical techniques exist, but none about using metaheuristics, despite the re- search literature is already quite rich.... In PAGE 2: ... Finally, section 6 highlights the conclusions. 1Legend for the SCOPs of Table1 : VRPSD = vehicle routing problem with stochastic demands, SCP = set covering problem, TSPTW = traveling salesman problem with stochastic time windows, PTSP = probabilistic traveling salesman problem, SSP = shop scheduling problem, SDTCP = stochastic discrete time-cost problem, SOPTC = sequential ordering problem with time constraints, VRPSDC = vehicle routing problem with stochastic demands and customers.... ..."

### Table 1: p-median heuristic references (the types are: Constructive heuristics (CH), Local Search (LS), Mathematical Programming (PM) and MetaHeuristics (MH)).

"... In PAGE 16: ... An interesting idea of flnding the partition of L, and thus the number of subproblems, by using dynamic programming is developed in the DEC procedure. 7 Conclusions Table1 presents an overview on the development of heuristics for solving the p-median problem (PMP). We should ask a basic question given the nature of this survey: Has the advent of metaheuristics advanced the state-of-the-art signiflcantly? Based on a large body of empirical... ..."

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### Table 1 Internal comparisons

"... In PAGE 11: ... First, a comparison is made between the sequential methods involved in the cooperative search. Results are displayed in Table1 . The FFve meta-heuristics equally solve the problems of type C that have clustered customers.... ..."

### Table 1. Comparisons of results over ten seeds

1998

"... In PAGE 6: ... The 600,000 value was appropriate for the larger Armour and Buffa problem while the smaller Bazaraa problem converged in much fewer number of solutions searched. Objective function values from the perimeter metric are in Table1 , where the best, median, worst and standard deviation over ten random seeds are shown. The twenty department Armour and Buffa (A amp;B) problem was studied with maximum aspect ratios of 10, 7, 5, 4, 3 and 2, which represent problems ranging from lightly constrained to extremely constrained.... ..."

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### TABLE II. A COMPARISON AMONG THE META-HEURISTICS RECENTLY PUBLISHED WITH RESPECT TO THE QUALITY OF THE SOLUTION IN RPE INDEX.

### Table 1. Simulation Results on Traveling Salesman Problems

2007

"... In PAGE 4: ... To qualify how much better our proposed algorithm is making shorter routes than the traditional approaches, we have tested all of the algorithms with a large number of Traveling Salesman Problems up to 532 cities and all the simulations are run 10 times, and then compared to several known algorithms: Kohonen Networks [6] [7], a conventional genetic algorithm using a greedy crossover operator [8] [9]. The results of these simulations are summarized in Table1 . The first three columns indicate the problem ... In PAGE 5: ... And the symbol - means no convergence. From Table1 , we can see that the proposed algorithm has superior ability to search the shortest routes and cost less computation times. 5.... ..."

### Table 2. The performance of different meta-heuristic strategies Solution Quality % Deviation CPU time (s) Ranking Diversification generation method

2007

"... In PAGE 21: ... 4.2 Structural analysis of the scatter search procedure Table2 displays the effect of different meta-heuristic principles implemented in our ... ..."

### Table 10: Comparison with Lin and Kernighan apos;s heuristic on the traveling salesman problem for cities on a lattice with up to 50% perturbation.

1988

"... In PAGE 18: ... We also experimented with different numbers of cities on a lattice with up to 50% perturbation. As expected, the speedups shown in Table10 fall in between those for the uniformly distributed cities and the cities on a lattice. In contrast to Lin and Kernighan apos;s heuristic, simulated annealing is relatively insensitive to the structure and regularity of an optimization problem; the CPU time spent by simulated annealing for different city distributions stays fairly constant for a given quality of solution.... ..."

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