Solving real-world optimization problems can be very challenging. Many problems contain multiple conflicting objectives to be optimized simultaneously and are heavily constrained. Moreover, the evaluation of solutions is often performed via simulation, meaning that it is both time-consuming and black-box (i.e., the problem cannot be expressed with a formula). Such problems therefore cannot be solved by mathematical optimization methods, but rather by heuristic computational intelligence methods, such as evolutionary algorithms.
Although a lot of research effort in the last few decades has been devoted to multiobjective evolutionary algorithms, most was directed to solving optimization problems without constraints, while the constrained multiobjective optimization problems (CMOPs) have been neglected. Hence, there are many open research questions in this area and the decision which to tackle within the PhD research will be done in agreement with the candidate.
Analysis of CMOPs:
- How does the addition of constraints affect the problem landscape?
- How to characterize the CMOP landscape with numerical features?
- How to intuitively visualize the CMOP landscape and its features?
Development of efficient algorithms for solving CMOPs:
- How to best handle (hard and soft) constraints when solving CMOPs?
- How to adjust algorithm components/parameters to the problem landscape to boost its efficiency?
Benchmarking optimization algorithms:
- How to create new test CMOPs with desired properties?
- How to efficiently measure algorithm performance taking into account both objectives and constraints?