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Existing research on dynamic multi-objective optimization problems involving changes in the number of objectives has received little attention, but it is widespread in practical applications. This problem would cause the expansion or contraction of the manifold in the objective space. If it is accompanied by changes in Pareto set/front (PS/PF), the problem becomes more complex. However, several dynamic response techniques have been developed to handling this kind of dynamics. Faced with these issues, a multi-spatial information joint guidance evolutionary algorithm is proposed. To more accurately identify the optimal solutions after the change, a space adaptive transfer strategy is introduced, which adopts the geodesic flow kernel method to extract spatial information at different times. Afterwards it adaptively transfers the space via different changes to generate new individuals. In order to improve the diversity after the change, a dual space multi-dimensional joint sampling strategy is proposed. It fully combines the individual information in the objective and the decision space. Then the promising solutions are sampled in multiple dimensions near the representative individuals. Comprehensive experiments are conducted on 15 benchmark functions with a varying number of objectives and PS/PF. Simulation results verify the capability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Multi-tasking optimization algorithm attracts much attention because the knowledge transfer between tasks enables the algorithm to process multiple related tasks simultaneously. However, negative knowledge transfer occasionally occurs, which may weaken the performance of the algorithm. To reduce the impact of negative knowledge transfer, a multi-objective multi-tasking optimization algorithm (IM-MFEA) based on inverse model mapping and an objective transformation strategy is proposed. First, correlation analysis is applied in an inverse mapping strategy to improve the accuracy of the inverse mapping model. Then, following the pattern of using the source domain solutions to assist the optimization of the target domain, the adaptive transformation strategy is used to improve the quality of the source domain solution in the objective space. These transformed solutions are reconstructed through the inverse mapping strategy. Finally, these reconstructed source domain solutions are mated with the target domain solutions to generate competitive offspring individuals for the target domain. To verify the effectiveness of the IM-MFEA, comprehensive experiments were conducted on nine multi-objective multi-factorial optimization (MFO) benchmark problems. Empirical results demonstrate that IM-MFEA is superior to other algorithms in 90% of test instances by inverted generational distance (IGD) and hypervolume (HV) value indicators. • An adaptive transformation strategy for scaling solutions is proposed. • An inverse mapping strategy is proposed to improve offspring individual's quality. • Algorithm IM-MFEA is proposed to reduce the impact of the difference between tasks. [ABSTRACT FROM AUTHOR]

In practical applications and daily life, dynamic multiobjective optimization problems (DMOPs) are ubiquitous. The purpose of dealing with DMOPs is to track moving Pareto Front (PF) and find a series of Pareto Set (PS) at different times. Prediction-based strategies improve the performance of multiobjective evolutionary algorithms in dynamic environments. However, how to ensure the accuracy of prediction models is always a challenge. In this study, a dual prediction strategy with inverse model (DPIM) is developed, to alleviate the negative impact of inaccurate prediction. When a change is confirmed, DPIM responses to it by predicting the individuals in the objective space. Furthermore, the inverse model is established to connect the decision space with the objective space, which can guide the search for promising decision areas. Specifically, the inverse model is also predicted to minimize the error in the process of mapping the population from the objective space back to the decision space. The effectiveness of the proposed DPIM is proved by comparison with four effective DMOEAs on 14 benchmark problems with various real-word scenarios. The experimental results show that DPIM can obtain high-quality populations with good convergence and distribution in dynamic environments. • The individuals are predicted in the objective space. • The inverse model is introduced to establish the relation between decision space and objective space. • Different prediction methods are adopted for population individuals and inverse model. The dual prediction strategy improves the accuracy of prediction. [ABSTRACT FROM AUTHOR]

The performance of traditional penalty boundary intersection (PBI) decomposition-based evolutionary algorithm is totally determined by the penalty factor. The fixed penalty factor causes the imbalance between the convergence and the diversity when solving many-objective problems. So, an adaptive decomposition evolutionary algorithm based on environmental information (MaOEA/ADEI) is proposed to solve the imbalance. The penalty factor of PBI decomposition is determined by the environmental information (include distribution information of weight vectors and population). Furthermore, the parent individual selection strategy is introduced to select promising individuals for variation and the weight vectors adaption strategy is used to handle problems with scaled objectives. Comparisons with 4 algorithms on 24 benchmark instances are used to test the property of MaOEA/ADEI. The experimental results show MaOEA/ADEI performs best on 14 test instances. • A convergence (CW) function is used to construct a mating pool in order to get offspring with good convergence performance. • The adaptive decomposition method based on environmental information is proposed to dynamically adjust the penalty factor of PBI. • The weight vectors adaptation strategy is used to produce uniformly distributed individuals specially the disparately scaled objectives. [ABSTRACT FROM AUTHOR]

When dealing with multi-objective optimization, the proportion of non-dominated solutions increase rapidly with the increase of optimization objective. Pareto-dominance-based algorithms suffer the low selection pressure towards the true Pareto front. Decomposition-based algorithms may fail to solve the problems with highly irregular Pareto front. Based on the analysis of the two selection mechanism, a dynamic reference-vector-based many-objective evolutionary algorithm(RMaEA) is proposed. Adaptive-adjusted reference vector is used to improve the distribution of the algorithm in global area, and the improved non-dominated relationship is used to improve the convergence in a certain local area. Compared with four state-of-art algorithms on DTLZ benchmark with 5-, 10- and 15-objective, the proposed algorithm obtains 13 minimum mean IGD values and 8 minimum standard deviations among 15 test problem. [ABSTRACT FROM AUTHOR]

High-speed cold tandem rolling process control system consists of complex mechanical and electrical equipments. The coupling association of these equipments makes multi-objective rolling process complicated to be predicted and controlled. In order to achieve higher prediction precision, a multi-parameter depth perception model is established based on a deep belief network. To get higher control precision in real time, a multi-objective rolling optimization method is introduced, which is supported by many-objective evolutionary algorithm. Five objectives are selected as rolling schedule optimization objective: equal relative power margin, slippage prevent, good flatness, total energy consumption and energy consumption per ton. Simulation results show that many-objective evolutionary algorithm based on decomposition and Gaussian mixture model achieves a set of balance solutions on these objectives. The proposed method could not only predict rolling force and rolling power in real time, but also give the solutions for many-objective reduction schedule. • The relationships between different control variables and optimization objectives are analyzed. • The model combined deep learning network and mechanism model is used to improve the prediction of rolling parameter. • Tension and speed, which effect rolling power and quality, are considered for rolling schedule. • Many-objective evolutionary algorithm is employed to optimize rolling schedule. [ABSTRACT FROM AUTHOR]

Dynamic multi-objective optimization problems (DMOPs) which contain various Pareto-optimal front (PF) and Pareto-optimal set (PS) have gained much attention. Accurate environmental change detection reveals the change degree of DMOPs and contributes the algorithm to quickly respond to the environment changes. In order to fully detect environmental changes and efficiently track front, a double-space environmental change detection and response strategy (DSDRS) is proposed. It could detect whether the environment has changed while explore the change intensity of PF and PS, respectively. Moreover, different response strategies are implemented for PF and PS. For PF environmental changes, a multiple knee points-guided evolutionary strategy (MKGES) is proposed, which is driven by front shape information and adaptively responds to different PF change intensities. For PS environmental changes, a knowledge guided memory strategy (KGMS) is proposed, which guides population evolution based on environmental information. The effectiveness of DSDRS is confirmed by comparison with five evolutionary algorithms on 20 dynamic multiobjective benchmark functions. Simulation results demonstrate that the performance of proposed algorithm is outstanding on test functions with complex changing PF and PS. [ABSTRACT FROM AUTHOR]

In multi-objective evolutionary optimization, maintaining a good balance between convergence and diversity is particularly crucial to decision makers, especially when tackling problems with complicated Pareto sets. According to the analysis of dominance-based and decomposition-based selection mechanisms in multi-objective evolutionary algorithms, a multi-objective evolutionary algorithm based on the combination of local non-dominated rank and global decomposition is presented. The Gauss distribution model and differential evolution based on history information are employed as evolutionary operators. Various comparative experiments are conducted on 19 unconstraint test MOPs, and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types. [ABSTRACT FROM AUTHOR]

Proximity and diversity are two basic issues in multi-objective optimization problems. However, it is hard to optimize them simultaneously, especially when tackling problems with complicated Pareto fronts and Pareto sets. To make a better performance of multi-objective optimization evolutionary algorithm, the environmental information and history information are used to generate better offsprings. The conception of locality and reference front is introduced to improve the diversity. Adaptation mechanism of evolutionary operator is proposed to solve searching issue during different stages in evolutionary process. Based on these improvement, an improved multi-objective evolutionary algorithm based on environmental and history information (MOEA-EHI) is presented. The performance of our proposed method is validated based inverted generation distance (IGD) and compared with three state-of-the-art algorithms on a number of unconstrained benchmark problems. Empirical results fully demonstrate the superiority of our proposed method on complicated benchmarks. [ABSTRACT FROM AUTHOR]