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Emerging Trends and Concluding Remarks

And so, now, evolutionary multi-objective optimization is ready and able to take on real-world problems in their ‘real’ form – that is, as multi-objective problems rather than as potentially misleadingly simplified single-criterion formulations. But the field is very much beginning. As the efficacy of the various new algorithms has attracted more and more researchers and practitioners to the area, various issues and directions needing further research have become identified. Among these are considerations of the number of objectives in the problem, handling constraints, theoretical support for algorithm design and tailoring, each of which we briefly consider below, but this is just a small collection of topics from a field bubbling with unanswered questions. Most algorithms are developed and tested with small numbers of objectives (usually 2 or 3) in mind, but it turns out that real-world problems can often have several more; a 10-objective problem is not unusual, for example. There are many issues surrounding this, ranging from the efficacy of our existing algorithms in such circumstances, the need to better understand the landscapes of multi-objective problems, the enterprise of designing algorithms which specialize in many-objective problems, and also the careful transformation of such problems into fewer-objective ones. Progress is more apparent so far in the latter line of work, with researchers relying on identified preference relationships between the objectives, either to help the algorithm strategically consider the more important objectives when it needs to, or to exploit the problem solver herself in an interactive system (Shaw & Fleming, 1997; Kita et al, 1999; Barbosa & Barreto, 2001; Duenas & Mortt, 2001; Cvetkovic & Parmee, 2002a; 2002b). Another issue which is receiving increased attention is that of handling constraints over the decision variables (Binh & Korn, 1997; Surry & Radcliffe, 1997; Fonseca & Fleming, 1998). Dealing with constraints per se is difficult, and we can generally approach this in multi-objective optimization the same sort of way we would do so in single-objective optimization. However, the multi-objective framework provides the opportunity for new treatments, in which constraint violation is treated in any of several interesting ways currently under investigation (for example, as another objective to be minimized) (Coello Coello, 2000; Osyczka & Krenich, 2000; Hughes, 2001; Kumar & Ranjithan, 2002). Theoretical questions are also being asked, and some are being answered, concerning, for example, under what conditions algorithms will converge (Rudolph, 1998; Rudolph & Agapie, 2000), which schemes will ensure convergence at the same time as encouraging diversity (Knowles & Corne, 2003), and which schemes will, at least, converge to the nondominated subset of the candidate solutions encountered during an optimization run (Laumanns et al, 2001). The consequences and side issues of the No Free Lunch theorem (Wolpert & Macready, 1997) for multi-objective optimization are also beginning to be addressed (Corne & Knowles, 2002/3). Next, towards tailoring and tuning multi-objective optimizers, and following similar work only just starting to bear fruit in the single-objective optimization community (Merz, 2000; Merz & Freisleben, 2000), some researchers are investigating whether we can understand the structure of multi-objective landscapes well enough to tune the features of hybrid evolutionary and local search approaches (Knowles & Corne, 2002; Ishibuchi & Yoshida, 2002), since such approaches are among the most spectacularly well-performing in the field on certain problems (Ishibuchi & Murata, 1996; Czyzak & Jaszkiewicz, 1997; Jaszkiewicz, 2002). Finally, many researchers are bringing the more recent ideas fledged in single-objective optimization into the multi-objective realm, with notable promise shown by, for example, particle-swarm optimization based multi-objective search (Coello Coello & Lechuga, 2002; Hu & Eberhart, 2002; Parsopoulos & Vrahatis, 2002), and similar for ant colony optimization (Mariano & Morales, 1999; Gravel et al, 2001) and differential evolution (Abbass et al, 2001). To find out more about various aspects of this fast maturing research area, readers can turn to a multitude of resources available on the WWW, via which can be found bibliographies, online articles, public domain code for many of the top-drawer algorithms, and information on relevant conferences and other events. We have already mentioned the site: http://www.lania.mx/~ccoello/EMOO/, which provides pointers to all such resources. In conclusion, we aim in this article to bring attention to the rising success of the ‘truly’ multi-objective approach to solving real-world problems. That is, an approach where the algorithm is engineered towards finding an approximation to the Pareto front of a problem, rather than specialized towards optimizing single objectives. Such methods arising from the evolutionary computation community have been our focus, and the field of evolutionary multi-objective optimization is now rampant with capable algorithms, successful applications, and hot research questions. Perhaps the main message is that it is no longer necessary to automatically simplify a real-world problem by transforming it into one objective. We contend this is often unwise, and unlikely to be necessary. The various techniques we have discussed are now readily available for treating a problem in its realistic multi-objective form. We have the technology, and solicit its deployment, since we will understand it better the more it gets used.