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search of very large design spaces, especially when the computation of the goal function and the constraints is comparatively inexpensive.
The motivation behind the work described here is that evolutionary computing technology has now reached the level where, we believe, it is computationally feasible to consider the automated optimal design of complete reducers. The experiments referenced above have been instrumental in highlighting the importance of using modern global optimization techniques in transmission design (as opposed to conventional, trial and error type design algorithms)
even when considering certain subproblems—here we propose to extend the technology to the broader design space of a two stage reducer, whose every element (bearings, seals, shafts, etc.) is subject to change throughout the optimization process.
The industrial relevance of the exercise is ensured by the consideration of all design constraints typically encountered in practice—we bound the design space by a total of 77 constraints categorized into 24 groups. In Sections 3 and 4 we discuss this formulation in detail, with Section 5 containing an account of the results of its deployment. First, however, we need to introduce a key element of our evolutionary computingmethodology, necessitated by the need to handle such a large number of constraints in an efficient manner.
2 An evolutionary paradigm
The inevitable paucity of the fossil record makes it rather difficult to estimate the rate of evolutionary change along any given lineage. Nevertheless, it is almost certain that evolution proceeds with varying speed. The extrema of these speed variations are, however, subject to some debate in the evolutionary biology community. It is clear from neo- Darwinian synthesis that large changes (macromutations) are almost always deleterious and this is an evolutionary upper speed limiting factor. According to the school
of thought usually associated with the seminal paper of Eldredge and Gould (1972), the lower limit is practically zero. That is, they suggest that populations evolve in bursts, which punctuate long periods of equilibrium (stasis), when no variations occur.
From the perspective of evolutionary algorithm design it is almost entirely irrelevant whether the theory of punctuated equilibria is correct or not. After all, GAs incorporating spells of Lamarckian learning are not made less successful by the fact that the Lamarckian theory of evolution is now known to be incorrect! Similarly, macromutations are often beneficial in evolutionary optimization, reminding practitioners that evolutionary computation is not an exact
simulation of nature (nor was it meant to be). Consequently, it is not surprising that the idea of punctuated equilibria has seen steady exposure over the years in the evolutionary algorithms community, in spite of the debate surrounding it in biology. This exposure is associated with two main lines of intellectual inquiry.
Firstly, many practitioners of evolutionary optimization have noted periods of stasis on multi-modal fitness landscapes. The familiar pattern sees the population converging on a local optimum, where a number of generations of stagnation (metastability) precede a beneficial mutation, which propels the population into the next, better basin
of attraction (see, for example, Oh and Yoon 1998 for a detailed account of the dynamics of this phenomenon on a one-dimensional bistable fitness landscape).
Secondly, and this is the angle we are interested in here, some success has been reported over the years in attempts to actually engineer metastable states in GAs, which would then be followed by bursts of rapid convergence. There is no unique, well-defined template for designing such heuristics; the literature contains a fairly broad range of models that are loosely based on the concept of punctuated equilibria.
Much of the work along these lines is based on multipopulation