1. Title: "Parallel multi-objective optimization for expensive and inexpensive objectives and constraints" 2. Author information: Roy de Winter Einsteinweg 55, 2333 CC Leiden, The Netherlands r.de.winter@liacs.leidenuniv.nl +31621441180 Bas Milatz Regulusplein 1, 2132 JN Hoofddorp, The Netherlands basmilatz@hotmail.com +31646285305 Julian Blank 428 S. Shaw Lane, 2120 EB East Lansing, MI 48824, USA blankjul@msu.edu +15179273547 Niki van Stein Einsteinweg 55, 2333 CC Leiden, The Netherlands n.van.stein@liacs.leidenuniv.nl +31653204164 Thomas Bäck Einsteinweg 55, 2333 CC Leiden, The Netherlands t.h.w.baeck@liacs.leidenuniv.nl +491773295153 Kalyanmoy Deb 428 S. Shaw Lane, 2120 EB East Lansing, MI 48824, USA kdeb@egr.msu.edu +15179300846 3. Corresponding Author: Roy de Winter r.de.winter@liacs.leidenuniv.nl 4. Abstract: "Expensive objectives and constraints are key characteristics of real-world multi-objective optimization problems. In practice, they often occur jointly with inexpensive objectives and constraints. This paper presents the Inexpensive Objectives and Constraints Self-Adapting Multi-Objective Constraint Optimization algorithm that uses Radial Basis function Approximations (IOC-SAMO-COBRA) for such problems. This is motivated by the recently proposed Inexpensive Constraint Surrogate-Assisted Non-dominated Sorting Genetic Algorithm II (IC-SA-NSGA-II). These algorithms and their counterparts that do not explicitly differentiate between expensive and inexpensive objectives and constraints are compared on 22 widely used test functions. The IOC-SAMO-COBRA algorithm finds significantly better (identical/worse) Pareto fronts in at least 78% (6%/16%) of all test problems compared to IC-SA-NSGA-II measured with both the hypervolume and Inverted Generational Distance+ performance metric. The empirical cumulative distribution functions confirm this advantage for both algorithm variants that exploit the inexpensive constraints. In addition, the proposed method is compared against state-of-the-art practices on a real-world cargo vessel design problem. On this 17-dimensional two-objective practical problem, the proposed IOC-SAMO-COBRA outperforms SA-NSGA-II as well. From an algorithmic perspective, the comparison identifies specific strengths of both approaches and indicates how they should be hybridized to combine their best components." 5. Work satisfies criteria: [B, D, E, F, G] 6. Statement why the results satisfies criterion [B, D, E, F, and G]: The results satisfy criterion B: "The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal." This is because the problem has been published before in the International Journal of Naval Architecture and Ocean Engineering (see [1]). A previous optimization algorithm has been published in the Memetic Computing Journal (see [2]). In [1], the SAMO-COBRA algorithm [2] was used to find a Pareto frontier of a computationally expensive probabilistic damage stability problem, often encountered in ship design problems. In the paper of this submission, we propose a new method (IOC-SAMO-COBRA) that combines computationally inexpensive evaluations with computationally expensive evaluations and parallelism in constraint multi-objective problems. This has drastically improved the number of solutions found on the Pareto frontier. Whereas the original work found 13 solutions on the Pareto frontier, in the paper at hand we have found 69 Pareto-efficient solutions in significantly less time. More detailed results are described in Section 7 of the paper. In conclusion, there are significant improvements over earlier published results. The results satisfy criterion D: "The result is publishable in its own right as a new scientific result independent of the fact that the result was mechanically created." This is because real-world ship designs are the output of the optimization process. These ship designs proposed by the algorithm all comply with the International Convention for the Safety of Life at Sea (see [3] for all rules). The algorithm found a configuration for the ship design damage stability problem that makes it less likely for the design to sink in case of a collision while still being able to carry a lot of cargo. This makes the ship designs very valuable from a commercial point of view and from a safety point of view. More details regarding this can be found in Section 7 and in [1]. In conclusion, the result is publishable due to real-world applicability and compliance with international standards. The results satisfy criterion E: "The result is equal to or better than the most recent human-created solution to a long-standing problem for which there has been a succession of increasingly better human-created solutions." This is because the problem at hand is based on an existing vessel that nearly sank [4] after it encountered a storm and water ballast leaked into the cargo hold. This is very problematic because if you lose the cargo hold due to flooding, a single-hold cargo ship is likely to sink. This original design was created by humans and, although it complied with the International Convention for the Safety of Life at Sea [3], it could have been safer. In this study, we show how to properly optimize a damage stability problem with optimization algorithms. Along with this, alternative designs that are safer are proposed so that in case the owner of the vessel ever decides to build a new ship or reposition bulkheads, they can make it safer. In conclusion, our results surpass traditional human-created solutions, providing safer and more optimized designs. The results satisfy criterion F: "The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered." This is because two consecutive papers are published in journals. In [1], the original problem was described for a maritime audience in the Journal of Naval Architecture. In [2], the SAMO-COBRA algorithm is introduced. Later, we show how this problem can be solved even more effectively by proposing a new optimization algorithm that generates an even better Pareto frontier. In conclusion, there are definite advances compared to previous significant achievements. The results satisfy criterion G: "The result solves a problem of indisputable difficulty in its field." This is because for naval architects and structural engineers alone, it is impossible to oversee the consequences of moving a single bulkhead or opening. Would that make the ship safer, is it still strong enough, and does it influence the cargo volume we can bring? Imagine now getting the freedom to move 17 bulkheads and openings simultaneously. To oversee this is very difficult, if not impossible, for humans. Therefore, a state-of-the-art new constraint multi-objective optimization algorithm is created that can actually optimize this problem efficiently. In conclusion, our solution solves a complex, real-world problem. [1] Milatz, B., de Winter, R., van de Ridder, J. D., van Engeland, M., Mauro, F., & Kana, A. A. (2023). Parameter space exploration for the probabilistic damage stability method for dry cargo ships. International Journal of Naval Architecture and Ocean Engineering, 15, 100549. https://doi.org/10.1016/j.ijnaoe.2023.100549 [2] de Winter, R., Bronkhorst, P., van Stein, B., & Bäck, T. (2022). Constrained multi-objective optimization with a limited budget of function evaluations. Memetic Computing, 14(2), 151-164. https://doi.org/10.1007/s12293-022-00363-y [3] IMO, Chapter II-1 - construction - structure, subdivision and stability, machinery and electrical installations, part b - subdivision and stability (2020). https://www.imorules.com/GUID-6F1047E8-4CF7-4093-8D44-B468315E3DAD.html [4] Dutch Safety Board, Shifting cargo causes emergency. (2022). Lessons learned from the occurence involving the Eemslift Hendrika. Shipping Investigations, https://onderzoeksraad.nl/en/onderzoek/shifting-cargo-causes-emergency-lessons-learned-from-the-occurence/ 7. Full Citation: Roy de Winter, Bas Milatz, Julian Blank, Niki van Stein, Thomas Bäck, Kalyanmoy Deb Parallel multi-objective optimization for expensive and inexpensive objectives and constraints Swarm and Evolutionary Computation, Volume 86, April 2024, 101508, Elsevier ISSN 2210-6502 https://doi.org/10.1016/j.swevo.2024.101508 8. Prize money Breakdown: Roy de Winter 100% Bas Milatz 0% Julian Blank 0% Niki van Stein 0% Thomas Bäck 0% Kalyanmoy Deb 0% 9. A statement indicating why this entry could be the "best" Our submission features a technical advancement in the form of the IOC-SAMO-COBRA algorithm. The IOC-SAMO-COBRA algorithm outperforms competitor algorithms on a wide variety of test functions. It has also been applied to a practical real-world ship design optimization problem, efficiently finding feasible Pareto-optimal solutions faster than ever before by using parallelism and combining expensive and inexpensive function evaluations. When applied to the real-world ship design problem, the optimization algorithm proposes designs that are significantly safer compared to the original human-designed models. This improvement is due to the problem's complexity, which is difficult (if not impossible) for experienced naval architects and structural engineers to fully manage. Since the code for the optimization algorithm has been made publicly available, we foresee its application extending to other domains such as the aviation industry, automotive industry, and algorithm configuration. 10. Evolutionary computation type: Surrogate Assisted Optimization 11. Date of publication: Available online 16 February 2024