Evolutionary Algorithms, Multiobjective Optimization, and Applications

This paper gives an introduction into evolutionary computation, in particular in the light of multiobjective optimization, and demonstrates how evolutionary algorithms can be used to tackle a highly demanding application in telecommunications, namely the design of a network processor. 1 Introductory Example To illustrate the basic principles of multiobjective optimization and evolutionary algorithms, consider the following example: given is a set of items together with a profit and a weight associated with each item; the goal is to determine a subset of items such that the overall profit, i.e., the sum of the profits of the selected items, is maximum, while the overall weight, i.e., the sum of the weights of the selected items, is minimal. This problem is generally denoted as knapsack problem. Now assume that four items are available: a camera (weight = 750, profit = 5), a thermos flask (weight = 1500, profit = 8), a pocket knife (weight = 300, profit = 7), and a book (weight = 1000, profit = 3). The set of all possible selections contains 16 possible subsets (cf. Fig. 1), in general 2 where n is the number of items. In this context, two observations can be made: there is no single optimal selection of items, and some subsets are better than others. With respect to the first issue, the empty subset minimizes the overall weight, while the set containing all items maximizes the overall profit. We say the two optimization criteria are conflicting. Nevertheless, subsets for which there exists another subset that is better in at least one criterion, while not being worse in the other criterion, can be neglected. As a consequence, a set of optimal tradeoffs emerges as shown in Fig. 1 at the bottom. At the end, though, we are interested in a single solution, and therefore a decision making process is necessary: which of the optimal trade-offs represents the best compromise for our needs? In practice, the search for optimal solutions by using an appropriate optimization algorithm and the decision making process can be integrated in different ways. One possibility is to aggregate the multiple optimization criteria into a single one. That means the decision is made before the search. In our example, one could transform the second objective into a constraint and look for the selection with maximum profit that does not exceed a given weight bound. Alternatively, we can first search for all optimal trade-offs and then choose one solution out of them. In this case, decision making is done after the search, which is especially useful if little is known about the underlying problem. Although being simple regarding the problem formulation, the above knapsack problem reflects two problem difficulties that arise in many real-world applications: i) the set of possible solutions is large, and ii) multiple, competing optimization criteria are involved. Thus, efficient search strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable in this context. The term evolutionary algorithm (EA) stands for a class of randomized search Figure 1: Illustration of the search space for a simple knapsack problem instance. At the bottom, the dark-shaeded solutions connected by the dotted line represent the optimal trade-offs.