11Multi-objective BBO

Most real-world optimization problems are multi-objective, and therefore multi-objective optimization has been applied in many fields of science, engineering, economics and logistics. Multi-objective optimization typically includes multiple objectives which usually conflict. For example, minimizing vehicle cost while maximizing comfort, or maximizing vehicle performance while minimizing fuel consumption and pollutant emissions, involves two and three conflicting objectives, respectively.

Multi-objective optimization is also called multi-criteria optimization, multiperformance optimization and vector optimization. In this chapter, we assume that a candidate solution is n-dimensional, and that our multi-objective optimization problem (MOP) is a minimization problem for each objective. An MOP can then be written as follows:

[11.1] image

That is, we want to minimize a vector f(x) of functions. Of course, we cannot minimize a vector in the typical sense of the word minimize. Nevertheless, our goal in an MOP is to simultaneously minimize all k functions f(x). MOPs were first solved by evolutionary algorithms in [ROS 67], and we call those implementations multi-objective evolutionary algorithms (MOEAs). MOEAs have been widely studied by the operations research community for many years [SCH 85, EHR 05, SIM 13a, SIM 13b, ZIT 04].

Overview of the chapter

In this chapter, ...

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