Chapter 6: Multi-Objective Optimization

Majority of engineering design problems are of multi-objective nature, i.e., there are several performance figures that have to be controlled at the same time. In antenna design, typical figures include reflection response, gain, radiation pattern, axial ratio (for circular polarization antennas), as well as the structure size (for compact antennas) (Azaro, 2008; Gautam et al., 2013; Ding et al., 2008; Kuwahara, 2005; Bekasiewicz et al., 2016b; Bai et al., 2016; Smolders and Johannsen, 2011; Viani et al., 2008). In most cases, either because the designer’s priorities are known beforehand or just to simplify the design task, the problem can be reformulated into a single-objective one, which can be achieved by selecting the primary goals and handling the remaining objectives by means of constraints (Koziel and Bekasiewicz, 2015e). Another popular technique is aggregation of the objectives into a scalar cost function using a weighted sum approach (Kuwahara, 2005; Lizzi et al., 2009) or penalty functions (Bekasiewicz and Koziel, 2016b). Nevertheless, in some situations, it might be important to acquire more comprehensive information about the antenna at hand, in particular, to identify the best possible trade-offs between the conflicting criteria. If this is the case, defaulting to proper multi-objective optimization becomes necessary. Multi-objective optimization leads to a set of alternative designs representing a so-called Pareto front (Fonseca, 1995). Subsequently, a decision making process allows for selecting one of these designs as a final solution…