This course is aimed for the target audience of undergraduate students. Several questions in design engineering, automation, and science demand the consideration and optimization of multiple metrics. A very straightforward and relatable example is the requirement to design a car with dual metrics of fuel economy and acceleration ability. In contrast to single objective optimization problems, these problems do not lead to one solution, but a family of solutions. This family of solutions is referred to as the Pareto frontier.
In simpler terms, this means that improving in one metric comes at the compromise/tradeoff in atleast one of the other metrics. While some non-Pareto solutions have also been discussed in literature, we do not focus on such settings in this course. Our focus will be on understanding the current space of MOO (multiobjective optimization) literature along four different fronts as follows.
• Algorithms - The crux of all the methods predominantly studied so far has been to equivalently solve a series of SOO (single objective optimization) problems in place of our MOO. Here, we note that all standard mathematical programming based methods used for SOO are applicable in this context (post the reformulations). Some standard methods are the use of weights, ϵ constraints, and lexicographic methods.
• Metrics - Optimality measures can be multifold in the case of MOO. Some standard metrics include the hypervolume and spread. Here, the attempt is to quantify optimality of points by taking into consideration all the objectives.
• Applications – MOO is very important in several automotive design, energy markets, aircraft design, chemical engineering, portfolio management, and imaging based applications, to name a few. We will cover many such applications.
• Solvers – Some of the MOO type problems are additionally complicated due to the absence of derivatives (due to propriety reasons). Solvers from the standpoint of MOO also mostly attempt to address this issue. Some examples of MOO solvers are ALGLIB, MultiMADS, and USEMO. We will examine some of these solvers also as a part of this course.
- Kursverantwortliche/r: Aswin Kannan