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.... Show moreExpensive 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 (ICSA-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-SAMOCOBRA 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 twoobjective 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. Show less
Milatz, B.; Winter, R. de; Ridder, J.D.J.; Engeland, M. van; Mauro, F.; Kana, A.A. 2023
The prediction of the statutory attained subdivision index is a challenging issue for the initial design of ships due to the design freedom offered by a probabilistic damage stability assessment.... Show moreThe prediction of the statutory attained subdivision index is a challenging issue for the initial design of ships due to the design freedom offered by a probabilistic damage stability assessment. To this end, optimisation techniques integrated with a parametric model of the internal layout may generate a preliminary subdivision design, fulfilling damage stability regulations and cargo volume requirements. The present study explores using a multiobjective constrained optimisation algorithm coupled with a parametric model of a single hold cargo vessel, first investigating two design goal alternatives and secondly performing a global sensitivity analysis on the design variables for the most promising solution. The adoption, in parallel, of state-of-the-art practices shows the validity of the obtained solutions and the time benefits for designers. Nonetheless, the non-linear nature of probabilistic damage stability does not allow for clearly identifying the most impactful parameters on the attained survivability index. Show less
Stein. N. van; Winter, R. de; Bäck, T.H.W.; Kononova, A. V. 2023
Thirty years, 1993–2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30... Show moreThirty years, 1993–2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30 years. These include the covariance matrix adaptation evolution strategy and some fast-growing fields such as multimodal optimization, surrogate-assisted optimization, multiobjective optimization, and automated algorithm design. Moreover, we also discuss particle swarm optimization and differential evolution, which did not exist 30 years ago, either. One of the key arguments made in the paper is that we need fewer algorithms, not more, which, however, is the current trend through continuously claiming paradigms from nature that are suggested to be useful as new optimization algorithms. Moreover, we argue that we need proper benchmarking procedures to sort out whether a newly proposed algorithm is useful or not. We also briefly discuss automated algorithm design approaches, including configurable algorithm design frameworks, as the proposed next step toward designing optimization algorithms automatically, rather than by hand. Show less
Decisions made in the early phases of ship design have a large influence on the capital and operational expenses of a vessel. In order to support decision making in this phase, big data and machine... Show moreDecisions made in the early phases of ship design have a large influence on the capital and operational expenses of a vessel. In order to support decision making in this phase, big data and machine learning techniques can be of great use. This work shows how Explainable Artificial Intelligence (XAI) and Global Sensitivity Analysis (GSA) combined with Autonomous Identification System (AIS) and static ship data can be used to find important design characteristics of ships. A data collection framework is setup that collects AIS data over a five month time period. Static ship design data is used to predict performance related target features that are calculated from AIS data. By applying XAI and GSA methods to the regression models that predict these target features, insight can be gained on how design features influence the performance of ships. Experiments showed that for most ship types, the overall length is the most important design feature for speed related target features. Besides the overall length, the draught also has a significant impact on the rotation capabilities. Show less
Winter, R. de; Bronkhorst, P.; Stein, B. van; Bäck, T.H.W. 2022
This paper proposes the Self-Adaptive algorithm for Multi-Objective Constrained Optimization by using Radial Basis Function Approximations, SAMO-COBRA. This algorithm automatically determines the... Show moreThis paper proposes the Self-Adaptive algorithm for Multi-Objective Constrained Optimization by using Radial Basis Function Approximations, SAMO-COBRA. This algorithm automatically determines the best Radial Basis Function-fit as surrogates for the objectives as well as the constraints, to find new feasible Pareto-optimal solutions. SAMO-COBRA is compared to a wide set of other state-of-the-art algorithms (IC-SA-NSGA-II, SA-NSGA-II, NSGA-II, NSGA-III, CEGO, SMES-RBF) on 18 constrained multi-objective problems. In the first experiment, SAMO-COBRA outperforms the other algorithms in terms of achieved Hypervolume (HV) after being given a fixed small evaluation budget on the majority of test functions. In the second experiment, SAMO-COBRA outperforms the majority of competitors in terms of required function evaluations to achieve 95% of the maximum achievable Hypervolume. In addition to academic test functions, SAMO-COBRA has been applied on a real-world ship design optimization problem with three objectives, two complex constraints, and five decision variables. Show less
Bayesian optimization is often used to optimize expensive black box optimization problems with long simulation times. Typically Bayesian optimization algorithms propose one solution per iteration.... Show moreBayesian optimization is often used to optimize expensive black box optimization problems with long simulation times. Typically Bayesian optimization algorithms propose one solution per iteration. The downside of this strategy is the sub-optimal use of available computing power. To efficiently use the available computing power (or a number of licenses etc.) we introduce a multi-point acquisition function for parallel efficient multi-objective optimization algorithms. The multi-point acquisition function is based on the hypervolume contribution of multiple solutions simultaneously, leading to well spread solutions along the Pareto frontier. By combining this acquisition function with a constraint handling technique, multiple feasible solutions can be proposed and evaluated in parallel every iteration. The hypervolume and feasibility of the solutions can easily be estimated by using multiple cheap radial basis functions as surrogates with different configurations. The acquisition function can be used with different population sizes and even for one shot optimization. The strength and generalizability of the new acquisition function is demonstrated by optimizing a set of black box constraint multi-objective problem instances. The experiments show a huge time saving factor by using our novel multi-point acquisition function, while only marginally worsening the hypervolume after the same number of function evaluations. Show less
Bronkhorst, P.; Winter, R. de; Velner, T.; Kana, A.A. 2022
Decades of progress in simulation-based surrogate-assisted optimization and unprecedented growth in computational power have enabled researchers and practitioners to optimize previously intractable... Show moreDecades of progress in simulation-based surrogate-assisted optimization and unprecedented growth in computational power have enabled researchers and practitioners to optimize previously intractable complex engineering problems. This paper investigates the possible benefit of a concurrent utilization of multiple simulation-based surrogate models to solve complex discrete optimization problems. To fulfill this, the so-called Self-Adaptive Multi-surrogate Assisted Efficient Global Optimization algorithm (SAMA-DiEGO), which features a two-stage online model management strategy, is proposed and further benchmarked on fifteen binary-encoded combinatorial and fifteen ordinal problems against several state-of-the-art non-surrogate or single surrogate assisted optimization algorithms. Our findings indicate that SAMA-DiEGO can rapidly converge to better solutions on a majority of the test problems which shows the feasibility and advantage of using multiple surrogate models in optimizing discrete problems Show less
This paper proposes a novel Self-Adaptive algorithm for Multi-Objective Constrained Optimization by using Radial Basis Function Approximations, SAMO-COBRA. The algorithm automatically determines... Show moreThis paper proposes a novel Self-Adaptive algorithm for Multi-Objective Constrained Optimization by using Radial Basis Function Approximations, SAMO-COBRA. The algorithm automatically determines the best Radial Basis Function-fit as surrogates for the objectives as well as the constraints, to find new feasible Pareto-optimal solutions. The algorithm also uses hyper-parameter tuning on the fly to improve its local search strategy. In every iteration one solution is added and evaluated, resulting in a strategy requiring only a small number of function evaluations for finding a set of feasible solutions on the Pareto frontier. The proposed algorithm is compared to a wide set of other state-of-the-art algorithms (NSGA-II, NSGA-III, CEGO, SMES-RBF) on 18 constrained multi-objective problems. In the experiments we show that our algorithm outperforms the other algorithms in terms of achieved Hypervolume after given a fixed small evaluation budget. These results suggest that SAMO-COBRA is a good choice for optimizing constrained multi-objective optimization problems with expensive function evaluations. Show less
This contribution shows how, in the preliminary design stage, naval architects can make more informed decisions by using machine learning. In this ship design phase, little information is available... Show moreThis contribution shows how, in the preliminary design stage, naval architects can make more informed decisions by using machine learning. In this ship design phase, little information is available, and decisions need to be made in a limited amount of time. However, it is in the preliminary design phase where the most influential decisions are made regarding the global dimensions, the machinery, and therefore the performance and costs. In this paper it is shown that a machine learning algorithm trained with data from reference vessels are more accurate when estimating key performance indicators compared to existing empirical design formulas. Finally, the combination of the trained models with optimization algorithms shows to be a powerful tool for finding Pareto-optimal designs from which the naval architect can learn. Show less
