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In system modeling arises a fundamental question about the level of difficulty one may encounter when designing a model on a basis of some training data. In this study, we advocate that such level of difficulty inherently depends upon the variability of the available function (data). If for a pair of input data which exhibits small differences, the differences of the corresponding outputs are substantial then building a model in the presence of such data becomes more challenging than in cases of data where the differences in the output data are far more limited. Dwelling on this observation, we introduce a variability index quantifying the nature of data in terms of variability observed in input and output data, respectively. The proposed index is model‐neutral (model agnostic), namely describes and quantifies the modeling challenge implied by the data irrespectively of the specific model to be constructed. In case of functions, we show that the Lipschitz constant plays a similar role as the variability index computed for experimental data. An original way of reducing values of the variability index through a nonlinear transformation of original data completed by a fuzzy rule‐based model is introduced. It is shown that such rule‐based architecture gives rise to a piecewise linear transformation (multipoint linear approximation) exhibiting required contraction‐dilation characteristics. The optimization of this transformation is carried out with the use of a Particle Swarm Optimization algorithm. We also demonstrate that the index can be used to quantify a concept of adversarial data. Along this line, we introduce a granular characterization of adversarial feature of individual data points. A series of experiments is provided to offer a thorough illustration and detailed insight into the nature and a thorough characterization of publicly available data. [ABSTRACT FROM AUTHOR]

Sorting solutions play a key role in using evolutionary algorithms (EAs) to solve many-objective optimization problems (MaOPs). Generally, different solution-sorting methods possess different advantages in dealing with distinct MaOPs. Focusing on this characteristic, this article proposes a general voting-mechanism-based ensemble framework (VMEF), where different solution-sorting methods can be integrated and work cooperatively to select promising solutions in a more robust manner. In addition, a strategy is designed to calculate the contribution of each solution-sorting method and then the total votes are adaptively allocated to different solution-sorting methods according to their contribution. Solution-sorting methods that make more contribution to the optimization process are rewarded with more votes and the solution-sorting methods with poor contribution will be punished in a period of time, which offers a good feedback to the optimization process. Finally, to test the performance of VMEF, extensive experiments are conducted in which VMEF is compared with five state-of-the-art peer many-objective EAs, including NSGA-III, SPEA/R, hpaEA, BiGE, and grid-based evolutionary algorithm. Experimental results demonstrate that the overall performance of VMEF is significantly better than that of these comparative algorithms. [ABSTRACT FROM AUTHOR]

With the continuous expansion of civilian field, unmanned aerial vehicle (UAV), also known as drone, has received much attention. Nevertheless, the flight range of a rotary wing drone is restricted due to limited battery endurance. To conquer this shortage, the coordination of ground vehicles (GVs) and drones to finish complex tasks has attracted much attention recently. Especially, the coordination of trucks and drones has been investigated to realize the last-mile parcel delivery. By contrast, in this study, we propose to coordinate GVs and drones to monitor urban road networks more efficiently. The GV serves as a mobile carrier for launching, recovering, and charging the drones, while the drones are used to inspect some concerned sections of the road networks. To obtain high-quality routes for the GV and drones, a novel GV-drone arc routing problem (GVD-ARP) is specifically investigated. A mathematical model is constructed to describe the GVD-ARP and solved by the Gurobi optimizer. In addition, a hybrid optimization algorithm that combines the randomized variable neighborhood descent search, which is incorporated with the simulated annealing algorithm (RVND-SA), is developed to solve the model. Extensive experiments on instances with different scales are conducted and the results show the superiority of RVND-SA comparing with four other algorithms. Moreover, experiments on patrolling the real-world road networks are conducted, which further demonstrates the effectiveness of the model and RVND-SA. [ABSTRACT FROM AUTHOR]

Recently, evolutionary algorithms (EAs) have shown their strong competitiveness in handling many-objective optimization problems (MaOPs) with different Pareto fronts (PFs). However, maintaining convergence and diversity simultaneously in high-dimensional problems can be further explored. This paper suggests an adaptive convergence-diversity balanced evolutionary algorithm (ACDB-EA) to handle the above issue, which maintains balance between convergence and diversity adaptively during the evolutionary process. In the proposed algorithm, a novel diversity maintenance mechanism based on the global and local diversities is developed to promote the diversity by considering them collaboratively. To be specific, the average similarity and the maximal similarity represent respectively the global and local diversities of the solution, where the similarity between two solutions is defined as the cosine similarity between their objective vectors. In the environmental selection, the proposed adaptive convergence-diversity balanced strategy is used to adjust weights of convergence (defined as the L 2 norm in the objective space), global diversity and local diversity according to the population adaptively. Under this strategy, each solution produces a score and the solution with the highest score will enter the next generation, which means it acquires the optimal performance in terms of convergence and diversity. In each iteration, scores of candidate solutions will be recalculated to continuously search for the most suitable one, which strengthens the selection pressure toward the true PFs. We conduct experimental study on 111 benchmark testing instances with 2-20 objectives. The proposed method is shown to be superior to seven state-of-the-art algorithms in maintaining balance between convergence and diversity. [ABSTRACT FROM AUTHOR]

In this paper, we study on how to achieve balance between minimizing the objectives, satisfying the constraints, and avoiding the population to stuck at locally optimal or locally feasible regions. We propose a new constraints handling technique based on diversity distance measure for constrained multiobjective optimization problems. We innovatively measure all effects of the constraints on the objectives by the interaction effects and direct effects of constraints on the objectives. The interactive effects of constraints on the objective functions are firstly expressed and quantified by using Mahalanobis distance and computing the value of the distance measure by involving a Lebesgue measure. Based on interactive and direct effects, we propose a new modified mechanism of objective space, called objective space modified mechanism based on diversity distance measure, so that the good infeasible solution could be more effectively used to find the optimal solution. The Pull and Push search is used to adaptively adjust the location of the Pareto front, which could preclude the population from being stuck at some locally optimal or locally feasible regions and could decrease time complexity. Comprehensive experiments completed for several benchmark problems demonstrate the competitiveness of the proposed algorithm, in comparison to the existing state-of-art constrained evolutionary multiobjective optimization. [ABSTRACT FROM AUTHOR]