Most of the current expensive multiobjective optimization (MOO) algorithms focus on identifying Pareto optimal solutions. However, in some applications such as multiobjective modular design, decision-makers often prefer a set of optimal solutions that share common components in the decision space, which may conflict with Pareto optimality. Existing expensive MOO algorithms are not specifically designed to address this preference. To bridge this gap, we propose modeling the component-sharing preference in MOO as a special bi-level multiobjective optimization problem. Specifically, the upper-level is a single-objective optimization problem that seeks the optimal shared variables, while the lower-level is a multiobjective optimization problem aimed at identifying trade-off solutions for given shared variable values. Moreover, the lower-level objective is expensive-to-evaluate and can only be evaluated for a limited number of times. To efficiently solve this problem, we introduce a data-efficient algorithm called Bayesian Bi-level Search (BBS). The effectiveness of BBS is validated through six new benchmark problems and a real-world application involving the planform shape design of Blended-Wing-Body underwater glider. The results show that our method effectively identifies solutions with shared components within limited computational budgets.

Leveraging on fruitful intertask knowledge transfer, multitasking evolutionary algorithms (MTEAs) exhibit superior efficiency in handling multiple optimization tasks simultaneously. In practice, it is common that the fitness evaluation of tasks is computationally expensive, leading to a very limited number of fitness evaluations for MTEAs. With this in mind, we propose a radial basis functions-assisted MTEA (RAMTEA) in this paper to better solve expensive multitasking optimization problems. In the proposed method, radial basis functions are constructed to approximate each task's real function to guide the selection of new samples. Furthermore, an adaptive sampling strategy considering intertask similarities is applied to facilitate the convergence of multiple tasks and curb negative transfer. The efficacy of our proposal is demonstrated by experimental studies including ablation experiments and comparison with advanced MTEAs on widely used benchmark problems.

Expensive many-objective optimization problems (EMaOPs) are common in the real world, whose objective values need to be calculated by time-consuming computational simulations or expensive experiments. For EMaOPs, guiding the optimization process by surrogate models is a popular method. In this paper, an FNN-assisted evolutionary algorithm is proposed for better solving EMaOPs. Concretely, a feedforward neural network (FNN) is constructed by learning the strengthened dominance relation (SDR) between two solutions. Then promising samples are generated by evolutionary search based on the constructed FNN. The proposed method is compared with four state-of-the-art peer algorithms on a set of benchmark problems. Experimental results demonstrate its superiority.

The blended-wing-body underwater glider (BWBUG) is a new type of underwater vehicle that has been applied in natural resource exploration with great success. Compared with conventional torpedo shapes, BWBUG's shape has a higher lift-to-drag ratio (LDR), so its shape design has become a research focus of ocean engineering in recent years. It is noteworthy that the traditional design process assumes no prior knowledge and starts from scratch. However, since problems rarely exist in isolation, solving the shape problem of a traditional glider may provide useful information, but the disparity in design space impedes information transmission. This paper presents a heterogeneous transfer optimization method for glider shape, which consists of four parts: simulation, image processing, manifold learning, and the evolution algorithm. The simulation's goal is to create pressure and velocity clouds. Manifold learning will use the information from cloud maps to create a low-dimensional feature space. The information mapped in low-dimensional space will be used to assist evolutionary algorithms in searching for optimal solutions. The proposed method was tested for the shape optimization problem of a BWBUG, and the results show that knowledge learned from different but related problem domains is potentially beneficial to the new design.

Maintaining a balance between convergence and diversity is particularly crucial in evolutionary multiobjective optimization. Recently, a novel dominance relation called "strengthened dominance relation" (SDR) is proposed, which outperforms the existing dominance relations in balancing convergence and diversity. In this article, two points that influence the performance of SDR are studied and a new dominance relation, which is mainly based on SDR, is proposed (CSDR). An adaptation strategy is presented to dynamically adjust the dominance relation according to the current generation number. The CSDR is embedded into NSGA-II to substitute the Pareto dominance, labeled as NSGA-II/CSDR. The performance of our proposed method is validated by comparing it with five state-of-the-art algorithms on commonly used benchmark problems. NSGA-II/CSDR outperforms other algorithms in the most test instances considering both convergence and diversity.

This article develops a novel mission-motion planner for unmanned underwater vehicles (UUVs) when dispatching them to visit a set of marine stations in a vast and time-varying environment. Specifically, a tri-level optimization model is built for the planner to finish the task with less energy cost. The lower-level is a motion planner, which provides safe and efficient paths with local environmental information. The middle-level is a mission planner, which designs a balanced station allocation mode as well as economical visitation sequences for each UUV concerning global information. The upper-level is a commander, which manages and synchronizes the two levels, so that UUVs can autonomously decide the next destination and corresponding paths in real-time. Thereafter, different heuristic algorithms are chosen according to each level property, and their initialization processes are modified to solve the optimization efficiently. Finally, the proposed model and algorithms present their outstanding performance in complex and large-scale cases.

This paper proposes a radial basis functions (RBFs) assisted evolutionary algorithm for solving expensive many-objective problems where only a small number of real fitness evaluations are permitted. Two kinds of RBFs are applied in this algorithm, and the differences between the two kinds of RBFs are figured out to provide the estimated errors. By doing this, the estimated individual which has the maximum difference will be evaluated by real functions to strengthen the RBF models. In addition, for each objective, a more suitable RBF is selected for the purpose of making a more accurate approximation of the real functions. The simulation results demonstrate that the proposed algorithm not only performs well on many-objective problems with 10 decision variables, but also shows high efficiency. Besides, the proposed algorithm has good performance on problems with up to 30 decision variables.

In order to improve the performance of Water Cycle Algorithm (WCA), an alternative adaptation approach for enhancing the global searching ability is proposed. The proposed algorithm, named WCA-ALR, uses a new diversity enhancement approach to effectively improve the exploration capability of the WCA. The proposed approach consists of two major modifications: (1) an active selection method for choosing learning targets; (2) a promising position sifting and returning strategy. The benefits prove that actively selecting a learning target performs better than that of learning from a fixed one. A promising position sifting and returning strategy can also enhance the exploration ability. In order to verify the performance, numerical experiments on five basic benchmark problems are conducted. Then, a set of benchmark problems from the CEC2017 on 10 and 30 dimensions are used to prove the effectiveness of WCA-ALR. Experimental results affirm that the proposed approach can obtain better results, compared to the original WCA.

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring's objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent's position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness.