Targeting Evaluation, Computation and Interaction Costs in Expensive Black-Box Multi-Objective Optimization

An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Most environmental selection strategies in multiobjective evolutionary algorithms (MOEAs) select solutions based on their objective function values. However, the objective evaluations of many real-world problems are very time-consuming. The use of a large number of objective evaluations will inevitably reduce the efficiency of MOEAs. This paper proposes a fuzzy classification-assisted environmental selection (FAES) scheme to reduce the number of objective evaluations of MOEAs. The proposed method uses a fuzzy classifier to choose promising solutions in environmental selection. In the proposed method, first, solutions in the previous generations are classified into two classes using the Pareto dominance relation. The non-dominated solutions are positive class, and the dominated solutions are negative class. Next, the classified solutions are used to build a fuzzy classifier. Then, the built classifier is used to predict the membership degree of each of the current and offspring solutions. Only the offspring solutions, whose membership degrees to the positive class are larger than their parents’, are evaluated. The offspring solutions with smaller membership degrees are discarded with no objective evaluations. Therefore, the number of objective evaluations can be reduced. Finally, the evaluated offspring solutions are used in the environmental selection together with the current solutions. The proposed FAES strategy is integrated into an MOEA in computational experiments. Experimental results show the efficiency of the proposed FAES on reducing the number of objective evaluations.

Computationally expensive multiobjective optimization problems are difficult to solve using solely evolutionary algorithms (EAs) and require surrogate models, such as the Kriging model. To solve such problems efficiently, we propose infill criteria for appropriately selecting multiple additional sample points for updating the Kriging model. These criteria correspond to the expected improvement of the penalty-based boundary intersection (PBI) and the inverted PBI. These PBI-based measures are increasingly applied to EAs due to their ability to explore better nondominated solutions than those that are obtained by the Tchebycheff function. In order to add sample points uniformly in the multiobjective space, we assign territories and niche counts to uniformly distributed weight vectors for evaluating the proposed criteria. We investigate these criteria in various test problems and compare them with established infill criteria for multiobjective surrogate-based optimization. Both proposed criteria yield better diversity and convergence than those obtained with other criteria for most of the test problems.

Aiming at the problems such as low computational efficiency and long process in dynamic topology optimization, combined with bi-directional evolutional structure optimization, the dynamic optimization problem is transformed into the static optimization problem in multiple load cases. Newmark method is used to analyze the structure dynamics load. The topology optimization model based on equivalent static load is established. On the basis of the equivalent static load, multi-objective dynamics evolutionary structure optimization is studied. And the mathematical model of the dynamic stiffness and natural frequency about the multi-objective optimization is established. The mathematical formula of the sensitivity is deduced. Then a complete optimization iterative process is given. The numerical example illustrates that it is feasible to solve the multi-objective dynamic topology optimization with equivalent static loads. Modal tracking technique is introduced to the multi-objective dynamic topology optimization. The numerical example shows that modal tracking technology can track the required modal in the optimization process.

Robust multi-objective optimization has emerged as an active research. A recent study proposed two different definitions of robust solutions in the context of multi-objective optimization. In this paper, we extend the concepts for finding robust solutions in the presence of active constraints. The meaning of robust solutions for constrained problems is demonstrated by suggesting three test problems and simulating an evolutionary multi-objective optimization method using the two definitions of robustness. The inclusion of constraint handling strategies makes the multi-objective robust optimization procedure more pragmatic and the procedure is now ready to be applied to real-world problems

This study presents a new method for aerodynamic optimization of a civil aircraft fuselage. Typically, the fuselage is designed for minimum drag force at cruise conditions, which is essential for determining the flight cost. Evolutionary optimization methods, as a powerful tool, require the accurate computations of flows around several hundreds of candidate geometries, which in turn are too costly and time-consuming. One strategy is to use two-dimensional simulations that reduce the computational cost by at least one order of magnitude. This approach was applied in the current work, and the results were obtained with the aim of minimizing the drag coefficient and maximizing the lift coefficient. A genetic algorithm (GA) was used for shape optimization, and the objective function evaluation was carried out using computational fluid dynamics (CFD). A fuselage shape parameterization method is presented that accounts for important flow features. The 150-seat aircraft model designed in Amirkabir University of Technology was considered as a reference body. In the first step, the optimization is carried out for the single objective of minimizing the drag coefficient. Then, the multiobjective optimization is performed with the simultaneous drag coefficient minimization and lift coefficient maximization. Finally, the two-dimensional (2D) side view of the optimum fuselages is used for generation of the corresponding three-dimensional (3D) geometry. The results show that such 3D optimum fuselage reduced the drag coefficient by about 11% while increasing the lift coefficient by 29% in comparison with the original geometry.

Decision making for probabilistic fatigue inspection planning based on multi-objective optimization

The present work focuses on obtaining optimal operational policies of an industrial scale penicillin fed-batch fermentation process using dynamic optimization (DO). The three process objectives considered in this work include, maximization of total penicillin formed (J 1), minimization of total biomass formed (J 2), and minimization of fed-batch operation time (J 3). The control variables for the optimization study include, the feed flowrates of sugar, soyabean oil, and phenylacetic. We perform a single-objective optimization study with J 1 as the objective function and showcased the importance of DO. Consequently, we solve three multi-objective optimization (MOO) problems corresponding to all the pairwise combinations of the aforementioned three objectives. Outcomes of MOO problems are presented in terms of several non-dominated Pareto-optimal solutions. Furthermore, descriptive analysis of three representative Pareto points for all the MOO problems is presented, which highlights the importance of MOO study of the penicillin bio-reactor.

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

An improved marine predator algorithm based on epsilon dominance and Pareto archive for multi-objective optimization

For multi-objective optimization problems, particle swarm optimization (PSO) algorithm generally needs a large number of fitness evaluations to obtain the Pareto optimal solutions. However, it will become substantially time-consuming when handling computationally expensive fitness functions. In order to save the computational cost, a surrogate-assisted PSO with Pareto active learning is proposed. In real physical space (the objective functions are computationally expensive), PSO is used as an optimizer, and its optimization results are used to construct the surrogate models. In virtual space, objective functions are replaced by the cheaper surrogate models, PSO is viewed as a sampler to produce the candidate solutions. To enhance the quality of candidate solutions, a hybrid mutation sampling method based on the simulated evolution is proposed, which combines the advantage of fast convergence of PSO and implements mutation to increase diversity. Furthermore, ε-Pareto active learning (ε-PAL) method is employed to pre-select candidate solutions to guide PSO in the real physical space. However, little work has considered the method of determining parameter ε. Therefore, a greedy search method is presented to determine the value of ε where the number of active sampling is employed as the evaluation criteria of classification cost. Experimental studies involving application on a number of benchmark test problems and parameter determination for multi-input multi-output least squares support vector machines (MLSSVM) are given, in which the results demonstrate promising performance of the proposed algorithm compared with other representative multi-objective particle swarm optimization (MOPSO) algorithms.

Dynamic ensemble wind speed prediction model based on hybrid deep reinforcement learning