G. Sorkin. Efficient simulated annealing on fractal energy landscapes. Algorithmica,  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Moreover, it is shown that the choice of g 1 and g 2 is related to properties of the objective function in a neighborhood of the global optimum. 5. WHEN IS SIMULATED ANNEALING EFFECTIVE Some papers have tried to explain the success of SA algorithms for some classes of problems. In [64] and [68] it is suggested that SA algorithms are successful when the so called energy landscape, i.e. the graph of the objective function, is of some special form. Here we briefly summarize the ideas of the detailed analysis presented in [64] Although the analysis is related to combinatorial optimization ....

Sorkin G.B., Efficient Simulated Annealing on Fractal Energy Landscapes, Algorithmica, 6, 367-418 (1991)

....specify an initial temperature, a cooling scheme to decrease the temperature, a criterion for determining the number of state transitions per temperature, the final temperature and the stopping criterion of the procedure. There are different cooling schedule proposed in the specialiced literature [15]. As regards the initial temperature value, we will use the next formula: T o = Gamma ln(OE) Cost(S o ) with T o being the initial temperature, S o being the initial solution and OE being the probability of acceptance for a solution that can be per 1 worse than Cost(S o ) These two last ....

Sorkin, G. Efficient simulated annealing on fractal energy landscapes, Algorithmica 6, 1991, pp.367418.

....also referred to the work of Strenski and Kirkpatrick [34] and Althofer and Koschnick [2] which we discuss later in this section. Second, current SA and TA implementations are blind to the specific features of the cost surface in any given optimization instance. Previous work [22] 20] 21] [33] has shown that large, real world cost surfaces exhibit strong fits to models of self similar random structure (e.g. VLSI placement problems have hierarchical scaling properties which resemble high dimensional fractional Brownian motions [33] The parameters of such fitted models vary with the ....

....optimization instance. Previous work [22] 20] 21] 33] has shown that large, real world cost surfaces exhibit strong fits to models of self similar random structure (e.g. VLSI placement problems have hierarchical scaling properties which resemble high dimensional fractional Brownian motions [33]) The parameters of such fitted models vary with the individual problem instances, and again, evidence suggests that optimal hill climbing schedules should be tuned to these parameters [21] These two observations prompt a variety of questions and simple thought experiments. Consider the BSFE ....

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G. Sorkin, Efficient simulated annealing on fractal energy landscapes, Algorithmica, 6 (1991), pp. 367--418.

....to Ref. 96] these metaphors have also been recently addressed by Hinton and Nowlan [65] and R. Belew and co workers [10] while an earlier reference is the work of W.A. Kornfeld [84] 85] The whole field can be viewed as cases of adaptation in rugged landscapes [82] 123] 81] 96] 92] 91] [124] [125] 99] These results on the TSP show that there is computational evidence which is consistent with the hypothesis that a group of competing and cooperating individual processes, which undergo periods of individual optimization can overcome the gap from local to global optimization. In ....

G.B. Sorkin, Efficient Simulated Annealing on Fractal Energy Landscapes, Algorithmica 6 (1991) 367-418.

....are accustomed. It is possible to vary p m and, in fact, declining mutation rates are used in this paper s simulations. Optimal neighborhood sizes are problem specific and their discussion is beyond the scope of this paper. Cooling schedules are thoroughly discussed in the existing SA literature [2, 6, 26, 28, 35, 39, 42]; many of the SA results should extend to PRSA. In the runs that follow, temperature is decremented via multiplication with a positive constant, CC 1 :0 . PRSA appears sufficiently resilient to operate under most reasonable cooling schedules and parameter settings. As demonstrated in a later ....

....polynomial time by exploiting regularities in the energy or fitness landscape. While such desirable behavior should not be expected for arbitrary problems, it can be demonstrated for restricted classes of problems. For instance, SA globally converges in polynomial time for certain fractal problems [39]. Additionally, some SA techniques take advantage of problem specific regularities to periodically, dynamically alter the annealing schedule [28, 35] though global convergence is currently unproven) Similarly, GAs consistently solve problems of bounded deception (deception is defined in Section ....

G. B. Sorkin, Efficient simulated annealing on fractal energy landscapes, Algorithmica 6 (1991) 367--418.

....globally optimal solution given infinitely large M and a temperature schedule that converges to 0 sufficiently slowly [17] i.e. P r(s M 2 R) 1 as M 1 (1) where R ae S denotes the set of all globally optimal solutions. In other words, SA is optimal in the limit of infinite time [13] Sorkin [22] showed that certain classes of geometric cooling schedules are efficient on one dimensional, deterministically fractal, error surfaces; this result is interesting because our recent work [10] 11] has shown that neural network error surfaces indeed resemble a class of high dimensional statistical ....

G. Sorkin, "Efficient Simulated Annealing on Fractal Energy Landscapes", Algorithmica 6 (1991), pp. 367-418.

....end, our experiments point to periodic iterated descent methods [1] 8] 12] and adaptive construction of nonmonotone (warming) schedules as being especially promising. We also believe that tuning BSF optimal annealing strategies to the statistical parameters of optimization cost surfaces [17] will provide an important research direction. 6 Acknowledgements The authors wish to thank C. W. Albert Tsao for his implementation of much of the code used in these experiments. ....

G. B. Sorkin, Efficient simulated annealing on fractal energy landscapes, Algorithmica 6 (1991), 367-418.

....here point to periodic iterated descent methods [4] 11] 17] and adaptive construction of nonmonotone (warming) schedules as especially promising directions. We also believe that the tuning of BSFoptimal annealing strategies to the statistical parameters of optimization cost surfaces [24] will provide an important research direction. ....

G. B. Sorkin, "Efficient simulated annealing on fractal energy landscapes", Algorithmica 6 (1991), 367-418.

....it is, although some progress has been made along this direction [2] An issue which has been pursued by many researchers is to understand what characteristics of a function make it easy or difficult to solve by EAs. The proposed theories include epistasis analysis [30] fractal landscape analysis [31] and neighbourhood analysis [2] Although progress has been made, none of these theories can fully explain the behaviour of EAs. As indicated earlier, EAs are good at global search but not local fine tuned search. A natural step is to combine EA s global search ability with a local search ....

G. B. Sorkin, "Efficient simulated annealing on fractal energy landscapes," Algorithmica, vol. 6, pp. 367--418, 1991.

....hard to analyze rigorously. Many early results such as [8] apply only to the situation where the running time is allowed to grow exponentially in the problem size. A notable exception is an analysis of the case when the function to be minimized has a special kind of fractal like structure, where [10] proved that simulated annealing runs in polynomial time. There are now several results (see for example [6] that analyze the Metropolis algorithm, which is the special case of running simulated annealing at a fixed temperature. These results use sophisticated methods to bound mixing rates of ....

G. Sorkin. Efficient simulated annealing on fractal energy landscapes. Algorithmica, 6:367--418, 1991.

....are run for long enough (measured by number of potential solutions considered) However, long enough may be impractically long, perhaps longer than the the time required to search the entire search space. It is possible to gain some insight by considering what is known about SA. Sorkin has shown [79] that SA can be expected to work well roughly when the height of the barrier between any two adjacent basins is proportional to the difference in fitness between the basins optima. This ensures that the temperature scale is always appropriate. For example, two local optima whose fitnesses are ....

G. B. Sorkin. Efficient simulated annealing on fractal energy landscapes. Algorithmica, 6(3):367--418, 1991.

....is also referred to the work of Strenski and Kirkpatrick [33] and Althofer and Koschnick [2] which we discuss later in this section. Second, current SA and TA implementations are blind to the specific features of the cost surface in any given optimization instance. Previous work [21] 19] 20] [32] has shown that large, real world cost surfaces exhibit strong fits to models of self similar random structure (e.g. VLSI placement problems have hierarchical scaling properties which resemble high dimensional fractional Brownian motions [32] The parameters of such fitted models vary with the ....

....optimization instance. Previous work [21] 19] 20] 32] has shown that large, real world cost surfaces exhibit strong fits to models of self similar random structure (e.g. VLSI placement problems have hierarchical scaling properties which resemble high dimensional fractional Brownian motions [32]) The parameters of such fitted models vary with the individual problem instances, and again, evidence suggests that optimal hill climbing schedules should be tuned to these parameters [20] These two observations prompt a variety of questions and simple experiments. Consider the BSF performance ....

[Article contains additional citation context not shown here]

G. Sorkin, 1991. Efficient Simulated Annealing on Fractal Energy Landscapes, Algorithmica 6(3), 367-418.

.... Although recently there has been a considerable effort in analyzing these algorithms and the type of problems they are best suited for (for example a deep relationship between simulated annealing and solution space with fractal topology have been verified both experimentally and theoretically [35]) algorithm selection for the task at hand is still mainly an experimental and intuitive art. In order to satisfy all major considerations for the power minimization problem, we decided to use a combination of heuristic and probabilistic algorithms so that we can leverage on the advantages of ....

G.B. Sorkin, "Efficient Simulated Annealing on Fractal Energy Landscapes", Algoritmica, Vol. 6, No. 3, pp. 367418, 1991.

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G. Sorkin. Efficient simulated annealing on fractal energy landscapes. Algorithmica,

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G. B. Sorkin, "Efficient Simulated Annealing on Fractal Energy Landscapes", Algorithmica 6, 367-418 (1991).

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