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Ratio error (RE) estimation of the voltage transformers (VTs) plays an important role in modern power delivery systems. Existing RE estimation methods mainly focus on periodical calibration but ignore the time-varying property. Consequently, it is difficult to efficiently estimate the state of the VTs in real time. To address this issue, we formulate a time-varying RE estimation (TREE) problem into a large-scale multiobjective optimization problem, where the multiple objectives and inequality constraints are formulated by statistical and physical rules extracted from the power delivery systems. Furthermore, a set of TREE problems from different substations is systematically formulated into a benchmark test suite for characterizing their different properties. The formulation of these TREE problems not only transfers an expensive RE estimation task to a relatively cheaper optimization problem but also promotes the research in large-scale multiobjective optimization by providing a real-world benchmark test suite with complex variable interactions and correlations to different objectives. To the best of our knowledge, this is the first time to formulate a real-world problem into a benchmark test suite for large-scale multiobjective optimization, and it is also the first work proposing to solve TREE problems via evolutionary multiobjective optimization.

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Although quality indicators play a crucial role in benchmarking evolutionary multiobjective optimization algorithms, their properties are still unclear. One promising approach for understanding quality indicators is the use of the optimal distribution of objective vectors that optimizes each quality indicator. However, it is difficult to obtain the optimal distribution for each quality indicator, especially, when its theoretical property is unknown. Thus, optimal distributions for most quality indicators have not been well investigated. To address these issues, first, we propose a problem formulation of finding the optimal distribution for each quality indicator on an arbitrary Pareto front. Then, we approximate the optimal distributions for nine quality indicators using the proposed problem formulation. We analyze the nine quality indicators using their approximated optimal distributions on eight types of Pareto fronts of three-objective problems. Our analysis demonstrates that uniformly distributed objective vectors over the entire Pareto front are not optimal in many cases. Each quality indicator has its own optimal distribution for each Pareto front. We also examine the consistency among the nine quality indicators.

Prospective authors are requested to submit new, unpublished manuscripts for inclusion in the upcoming event described in this call for papers.

In this article, a new hypervolume-based evolutionary multiobjective optimization algorithm (EMOA), namely, R2HCA-EMOA (R2-based hypervolume contribution approximation EMOA), is proposed for many-objective optimization. The core idea of the algorithm is to use an R2 indicator variant to approximate the hypervolume contribution. The basic framework of the proposed algorithm is the same as SMS-EMOA. In order to make the algorithm computationally efficient, a utility tensor structure is introduced for the calculation of the R2 indicator variant. Moreover, a normalization mechanism is incorporated into R2HCA-EMOA to enhance the performance of the algorithm. Through experimental studies, R2HCA-EMOA is compared with three hypervolume-based EMOAs and several other state-of-the-art EMOAs on 5-, 10-, and 15-objective DTLZ, WFG problems, and their minus versions. Our results show that R2HCA-EMOA is more efficient than the other hypervolume-based EMOAs, and is superior to all the compared state-of-the-art EMOAs.

Context-free grammars are useful tools for modeling the solution space of problems that can be solved by optimization algorithms. For a given solution space, there exists an infinite number of grammars defining that space, and there are clues that changing the grammar may impact the effectiveness of the optimization. In this article, we investigate theoretically and experimentally the possibility of specializing a grammar in a problem, that is, of systematically improving the quality of the grammar for the given problem. To this end, we define the quality of a grammar for a problem in terms of the average fitness of the candidate solutions generated using that grammar. Theoretically, we demonstrate the following findings: 1) that a simple mutation operator employed in a (1 + 1)-EA setting can be used to specialize a grammar in a problem without changing the solution space defined by the grammar and 2) that three grammars of equal quality for a grammar-based version of the ONEMAX problem greatly vary in how they can be specialized with that (1 + 1)-EA, as the expected time required to obtain the same improvement in quality can vary exponentially among grammars. Then, experimentally, we validate the theoretical findings and extend them to other problems, grammars, and a more general version of the mutation operator.

Multiobjective multitasking optimization (MTO) is an emerging research topic in the field of evolutionary computation. In contrast to multiobjective optimization, MTO solves multiple optimization tasks simultaneously. MTO aims to improve the overall performance of multiple tasks through knowledge transfer among tasks. Recently, MTO has attracted the attention of many researchers, and several algorithms have been proposed in the literature. However, one of the crucial issues, finding useful knowledge, has been rarely studied. Keeping this in mind, this article proposes an MTO algorithm based on incremental learning (EMTIL). Specifically, the transferred solutions (the form of knowledge) will be selected by incremental classifiers, which are capable of finding valuable solutions for knowledge transfer. The training data are generated by the knowledge transfer at each generation. Furthermore, the search space of the tasks will be explored by the proposed mapping (among tasks) approach, which helps these tasks to escape from their local Pareto Fronts. Empirical studies have been conducted on 15 MTO problems to assess the effectiveness of EMTIL. The experimental results demonstrate that EMTIL works more effectively for MTO compared to the existing algorithms.

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Decomposition-based evolutionary algorithms using predefined reference points have shown good performance in many-objective optimization. Unfortunately, almost all experimental studies have focused on problems having regular Pareto fronts (PFs). Recently, it has been shown that the performance of such algorithms is deteriorated when facing irregular PFs, such as degenerate, discontinuous, inverted, strongly convex, and/or strongly concave fronts. The main issue is that the predefined reference points may not all intersect with the PF. Therefore, many researchers have proposed to update the reference points with the aim of adapting them to the discovered Pareto shape. Unfortunately, the adaptive update does not really solve the issue for two main reasons. On the one hand, there is a considerable difficulty to set the time and the frequency of updates. On the other hand, it is not easy to define how to update the search directions for an unknown PF shape. This article proposes to approximate irregular PFs using a set of predefined normal-boundary intersection (NBI) directions. The main motivation behind this article is that when using a set of well-distributed NBI directions, all these directions intersect with the PF regardless of its shape, except for the case of discontinuous and/or degenerate fronts. To handle the latter cases, a simple interaction mechanism between the decision maker (DM) and the algorithm is used. In fact, the DM is asked if the number of NBI directions needs to be increased in some stages of the evolutionary process. If so, the resolution of the NBI directions that intersect the PF is increased to properly cover discontinuous and/or degenerate PFs. Our experimental results on benchmark problems with regular and irregular PFs, having up to fifteen objectives, show the merits of our algorithm when compared to eight of the most representative state-of-the-art algorithms.

Overall constraint violation functions are commonly used in multiobjective evolutionary algorithms (MOEAs) for handling constraints. Constraints could cause these algorithms stuck in two stagnation states: 1) since the feasible region of a multiobjective optimization problem can consist of several disconnected feasible subregions, the search can be easily trapped in a feasible subregion which does not contain all the global Pareto optimal solutions and 2) an overall constraint violation function may have many nonzero minimal points, it can make the search stuck in an unfeasible area. To address these two issues, this article proposes a strategy to detect whether or not the search is stuck in these two stagnation states and then escape from them. Our proposed detect-and-escape strategy uses the feasible ratio and the change rate of overall constraint violation to detect stagnation, and adjusts the weight of the constraint violation for guiding the search to escape from stagnation states. We develop and implement a decomposition-based constrained MOEA with this strategy. Extensive experiments on a number of benchmark problems demonstrate the competitiveness of our proposed algorithm when compared to five other state-of-the-art constrained evolutionary algorithms.