Recent research activity has shown an interest in multi-objective optimization of dynamic processes, both for design and for real-time control; see Liu et al. (2018), Valderrama & Ruiz (2018), and de Sousa Santos et al. (2018) for some recent examples. Many of the methods proposed for these problems are based on converting the multi-objective problem into a single objective through the use of weights. Some works, for instance, Liu et al. (2018), however, consider the multi-objective problem directly but even in these cases, the problem is treated as a single objective problem with other objectives incorporated as constraints. All of these methods may not necessarily generate a satisfactory trade-off or Pareto optimal curve when this trade-off curve is non-convex. In this paper, we illustrate the use of a plant propagation nature inspired algorithm for the solution of design and control problems for dynamic processes. Being population based, it is able to identify an approximation to the Pareto optimal frontier simultaneously. A simple example from the literature is used to demonstrate how this problem can be formulated. The open source, freely available, Fresa application (http://www.ucl.ac.uk/~ucecesf/fresa.html),written in Julia, is used and the discussion concentrates on the problem formulation.
The result shows how a multi-objective approach may lead to better insight into the design or control issues. The illustrated problem was originally formulated as a single objective problem. In doing so, information about alternative designs and how these could affect the performance of the system may be hidden. A multi-objective formulation allows the engineer to make better informed design decisions.