Abstract The preference incorporated space (IOPIS) paradigm in interactive multiobjective optimization introduces a transformation or mapping of the objective space to a space where the coordinates are the values of scalarization functions. The scalarization functions include preference information provided by a decision maker. Therefore, IOPIS provides new possibilities for solving multiobjective optimization problems. In this paper, we investigate the effects of the transformation on the landscapes of multiobjective optimization problems by altering the landscape and the distribution of locally Pareto optimal solutions. The analysis includes both theoretical proofs and illustrations showcasing the landscapes of multiobjective optimization problems. Theoretical results establish that the transformation using achievement scalarizing functions does not introduce any new locally Pareto optimal solutions, i.e., if a solution is not locally Pareto optimal for the original problem, it cannot become locally Pareto optimal after the transformation. Moreover, we derive conditions under which local Pareto optima in the original problem are preserved and derive a geometrical description of the region where local optima can be found. Visualizations illustrate the theoretical findings for a number of examples. Besides its advantages in interactive multiobjective optimization, the IOPIS transformation may also help “smooth out” local optima in conventional a posteriori methods while retaining global optima.
Saini et al. (Sat,) studied this question.