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Introduction
Modern ideas for solving optimization problems, particularly evolutionary computation (EC) and its many variants, are making their way with profound success into the realm of real-world use. There is an endlessly growing list of applications which have either been tested with promising results on real-world problems, or describe applications in regular deployment, often producing results greatly improved over the previously employed solution.
The proud march of EC into industrial and commercial life is in large part a result of its underlying efficacy as an optimization tool, but also owes much to its convenience. EC imposes no requirement for a problem to be formulated in a particular constraint language, or for the function in question to be differentiable (or even continuous), and does not ask that the number of parameters be limited, or of any particular data-type. Rather, EC is universally applicable (it may not always work, but at least it can always be attempted), and asks only two key things of the practitioner: (1) that there be some (almost any) way to encode a candidate solution to the problem, and (2) that there be an algorithm in place for calculating the quality of any such encoded solution – the so-called fitness function.
However, despite freeing the practitioner from the shackles applied by many other optimization techniques, there is one essential freedom which is, as we contend, far too little exploited. Note that the fitness function, the necessity for which is one of very few burdens imposed a priori by EC on its user, need not be restricted to return only a single scalar value. Many may be forgiven for assuming that the prowess of EC is solely to be found in the optimization of a single objective, since until recently the algorithmic machinery available for handling multiple objectives well was not particularly convincing or effective. However, things are now changing markedly in this regard.
As recently well-put in Michalewicz and Fogel (2000), there are basically two ways to solve problems: one is to simplify the model so that traditional methods of optimization can be applied, and the other is to keep the model as it is – with no simplifications or transformations which pander to the needs of specific approaches – and use a ‘non-traditional’ approach, Our observation about recent decades of ‘real-world’ optimization is that the first of these has been used far more deeply than practitioners are ready to realize. That is, by far the most common way to handle multi-criteria optimization problems has been to simplify them as single-criterion problems, and this is commonly done without conscious reflection! Evidence for this view is apparent in the frequent appearance of ‘penalty-based methods’ in which a number of different components of a quality function (such as mass and aerodynamicity, or makespan and flowtime, or cost and reliability, and so on …) are simply combined into a single scalar objective via a weighted, usually linear sum.
It is currently endemic in the optimization community to treat this way of combining criteria as natural and, by implication, harmless. However, we would beg to differ, and would stress the following points. First, transforming a multi-criteria problem into a single-criterion problem is, in all but pathological cases, quite a radical simplification of the problem, so much so that the new optimization problem which results is saliently different, and very often not the problem that really needs to be solved. Second, this simplifying transformation is, arguably, no longer necessary in the light of recent progress in the field of evolutionary multi-objective optimization. We now have a sparkling collection of algorithms which can apply to multi-criteria problems without requiring their simplification, and furthermore these algorithms are becoming increasingly fast, efficient, and effective. Certainly, there is much progress still to be made, and we do not yet have a panacea for every awkward feature that a particular real-world problem will present. However, our chief point is that the proper treatment of a multi-criterion real-world problem without this simplification is now an eminently viable and recommended approach.
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