As metaheuristics continue to play an increasingly important role in the field of Analytics, the connection between metaheuristics and Analytics invites closer examination. This leads, improbably but interestingly, to the topic of metaheuristic metaphors and – as I’ll describe in a moment – to the topic of sex.
To set the stage, it is useful to observe where the link between metaheuristics and Analytics comes from. As noted in other installments of this blog, the Analytics field depends greatly on the domain of optimization for some of its most successful approaches. And within optimization, the realm of metaheuristics is responsible for some of the most impressive recent advances in solving hard optimization problems, particularly those encountered in real world applications.[i]
Scores of “nature metaphors” for metaheuristics have emerged in recent years, ranging widely from thermodynamics to genetics to zoology to quantum mechanics. Even if such metaphors often appear to be more strongly based on a quest to achieve brand name recognition than to establish useful insights, there has been no inhibition in trying to squeeze metaphorical content out of anything that remotely offers an opportunity. Reflecting on this situation when the proliferation of these metaphors was in its infancy, Manuel Laguna and I couldn’t resist writing.[ii]
Models of nature that are relied upon for inspiration [in creating new metaheuristics] are ubiquitous, and it is easy to conjure up examples whose metaphorical possibilities have not yet been tapped. To take an excursion in the lighter side of such possibilities (though not too far from the lanes currently traveled), we may observe that a beehive offers a notable example of a system that possesses problem solving abilities. Bees produce hives of exceptional quality and complexity, coordinate diverse tasks among different types of individuals, perform spatial navigation, and communicate via multiple media. (It is perhaps surprising in retrospect that the behavior of bees has not been selected as a basis for one of the “new” problem solving methods.)
Those who follow the fashions in metaheuristic metaphors know that a number of years after these words were written, metaheuristics have indeed begun to appear that claim to be based on the behavior of bees.
All this spirited activity to come up with catchy new metaphors to promote various metaheuristic proposals, if viewed from the standpoint of overall efficacy, discloses a clear shortcoming. The metaphors currently in vogue, to put it charitably, are decidedly stodgy. More to the point, they lack the power to stir primordial responses within the psyche of their intended audience.
This leads to the main thesis of this current writing. The world of advertising has long taught us that nothing sells like sex, and I would maintain that we should not hesitate to take advantage of this fundamental truth. Admittedly, on a plane that may be appreciated by a circle of academics, there is already a natural candidate for the title of “the sexiest metaheuristic.” Given that all sex is based on genetics, the class of genetic algorithms should unquestionably take top billing. Yet the topic of cavorting chromosomes isn’t the sort of thing that would play well in a commercial slot on prime-time TV. After all, given that the developers and users of metaheuristics are humans, it’s human sex rather than chromosomal sex that is more apt to attract our attention.
In addition, if the goal is to have a metaphor that can be a model for complex problem solving, I suspect a focus on the primitive biological processes such as gene transmission harbors a more telling deficiency. It would be hard to say how smart a chromosome might be when confronted with a task like building a space satellite or a biotech lab, but I’d be willing to bet that humans are better suited to handling these kinds of challenges. If so, why not develop a metaheuristic based on a metaphor of human sex?
More particularly, it would seem worthwhile to focus on the aspect of human sex that most fully draws upon our inherent ingenuity. I refer, of course, to courtship. Throughout the millennia we have generated a rich array of strategies to handle the intricacies of courtship as a means to navigate the tumultuous seas of human relationships as affected by varying social and cultural norms (which we seem to have perversely created to make the process of courtship more difficult).
In short, Courtship Algorithms provide a natural foundation for developing new metaheuristic processes. To inform such processes, it is possible to formulate a collection of Key Strategic Principles, as embodied in time-honored expressions that people have applied to courtship. Below I undertake to show how these expressions translate directly into principles for metaheuristic methods, listing first the classical version of these principles, followed by their associated metaheuristic counterparts in parentheses.
| Key Strategic Principles
|Have we met before? (Use memory to exploit recurrences.)|
|Your place or mine? (Consider the benefits of regional exploration.)|
|Variety is spice. (Employ diversification at all levels.)|
|Would you like to see my etchings? (Decide what is worth exploring.)|
|Try it, you'll like it. (Experiment and probe beyond the surface.)|
|Opposites attract. (Join diversification (via opposites) and intensification (via attraction).)|
|Familiarity breeds … (Watch for important affinities.)|
|When in Rome … (Adapt to the terrain.)|
|Once is not enough. (Iterate over good options.)|
|Play the field. (Don’t be restricted to a single move or strategy.)|
|Are there any more at home like you? (Employ comparative analysis.)|
|Two’s company, three’s a crowd. (Sometimes paired combinations work well.)|
|Ménage à trois (And sometimes it can be worthwhile to go beyond pairs.)|
|The more the merrier. (And then sometimes …)|
|Am I getting warmer? (Test the setting to determine the next move.)|
|Don’t stop now! (Take advantage of momentum.)|
|Be gentle. (But do so prudently.)|
|What will you think of me in the morning? (Consider downstream consequences.)|
|Be prepared. (Initial strategies can set the stage for later ones.)|
|Let’s compare our … (Discover advantageous similarities and differences.)|
|Be selective. (Sift through options.)|
|Don’t leave things to chance. (Random behavior can sometimes be counterproductive.)|
|When you’re hot you’re hot. (Launch intensification at propitious moments.)|
|No need to be timid. (Well-timed aggressive moves can pay off.)|
|Go with the moment. (Include short term strategies for congenial terrain.)|
|Find the sweet spot(s). (Allow guidance by multiple criteria of attractiveness.)|
|Trust your instincts. (Intuitive exploration can supplement strict analysis.)|
|Go for the prize. (Don’t get bogged down with trivia.)|
|We’ve got to stop meeting like this! (Introduce variation to avoid cycling traps.)|
|The bar is closing. Let’s find someplace more interesting to go! (Establish limits and follow through with exploration of new terrain.)|
Undoubtedly I’ve barely scratched the surface of the potential that resides in the realm of human courtship as a source of new metaheuristic processes. It is tempting to speculate that courtship algorithms may not only offer a useful foundation for future study, but may possibly offer a chance to elevate the area of metaheuristics to new heights. The field of analytics – which benefits from advances in metaheuristics – might then in turn experience significant gains.
Note: The reader is invited to contribute additional Strategic Principles of Courtship Algorithms in their comments. These will be assembled and posted on a subsequent blog where viewers will be able to vote on their favorites and a (sexy) prize will be awarded to the winner.
The original version of this material appears as an article in ORMS Today, October 11, 2011, pages 20-21. (See http://www.orms-today.org/.)
[i] A comprehensive survey appears in Sorensen, K., and Glover, F. (in press). “Metaheuristics,” in Encyclopedia of Operations Research and Management Science(3e), S. I. Gass and M. C. Fu, eds., Springer, New York.
[ii] From Chapter 1 of Tabu Search by F. Glover and M. Laguna, Kluwer Academic Publishers, 1997.