Abstract. This chapter presents a number of illustrative case studies of a wide range of applications of multiobjective optimization methods, in areas ranging from engineering design to medical treatments. The methods used include both conventional mathematical programming and evolutionary optimization, and in one case an integration of the two approaches. Although not a comprehensive review, the case studies provide evidence of the extent of the potential for using classical and modern multiobjective optimization in practice, and opens many opportunities for further research. IntroductionThe intention with this chapter is to provide illustrations of real applications of multiobjective optimization, covering both conventional mathematical programming approaches and evolutionary multiobjective optimization. These illustrations do cover a broad range of application, but do not attempt to provide a comprehensive review of applications.

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In practical situations, complex systems are often composed of subsystems or subproblems with single or multiple objectives. These subsystems focus on different aspects of the overall system, but they often have strong interactions with each other and they are usually not sequentially ordered or obviously decomposable. Thus, the individual solutions of subproblems do not generally induce a solution for the overall system. Here, we strive to identify "re-composition architectures" of such "interwoven" systems. Our intention is to connect the subsystems adequately, analyze the resulting performance, model/solve the overall system, and improve the overall solution instead of just solving each subsystem separately. We review recent developments in this field and discuss modeling and solution paradigms in a general and unified framework using the example of an interwoven system consisting of two interacting subsystems. KEYWORDSinterwoven systems, multiobjective optimization, systems of systems 1 As discussed in the next section, models and methods for dealing with multiobjective complex systems have been proposed in the literature, especially in the area of engineering optimization. However, they lack rigorous mathematical analyses and optimality proofs.

Abstract. This chapter provides a description of multiobjective optimization software with a general overview of selected few available tools developed in the last decade. This chapter can be considered a revision of previous valid papers and chapters on nonlinear multiobjective optimization software such as the ones written by Weistroffer et al. (2005) and Miettinen (1999) that lists existing software packages up to the year 1999. More precisely, this chapter is focused on the tools and features that advisable multiobjective optimization software should contain.