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In this paper, we investigate a robust nonsmooth multiobjective optimization problem related to a multiobjective optimization with data uncertainty. We firstly introduce two kinds of generalized convex functions, which are not necessary to be convex. Robust necessary optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are established by a generalized alternative theorem and the robust constraint qualification. Further, robust sufficient optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are also derived. The Mond–Weir-type dual problem and Wolfe-type dual problem are formulated. Finally, we obtain the weak, strong and converse robust duality results between the primal one and its dual problems under the generalized convexity assumptions.

The dynamic multiobjective evolutionary algorithm (DMOEA) is an efficient solver for dynamic multiobjective optimization problems (DMOPs). It is challenging for algorithms to converge quickly and maintain diversity in new environments. However, existing DMOEAs incorporate strategies only in the environment response stage, which may limit the further improvement of the algorithm performance. To address this problem, different strategies have been proposed in the environment response stage and static optimization stage to balance convergence and diversity throughout the optimization process. In the static optimization stage, nondominated solutions-guided evolution leaves the individuals that are closer to the nondominated individuals among the original individuals and the opposition individuals generated by opposition-based learning, which can accelerate the convergence of each generation. In the environment response stage, based on the individual dominance relationship before environmental change, the fine prediction strategy performs difference prediction and opposition-based learning prediction for nondominated and dominated individuals, respectively, which results in an initial population with good convergence and diversity in the new environment. The performance of proposed algorithm was evaluated on 22 instances and compared to eight state-of-the-art algorithms. The results show that proposed algorithm outperforms its competitors on most problems. Additionally, proposed algorithm performs better in early environmental changes and is relatively insensitive to different severity changes.

Biased multiobjective optimization problems pose a challenge for evolutionary algorithms in obtaining high-accuracy solutions, and as the number of decision variables increases, this challenge becomes increasingly difficult to overcome. To address this issue, we propose a three-particle-based local search method (TPS) for multiobjective evolutionary algorithms (MOEAs). The main concept is to use three particles to maintain three equidistant values of a decision variable and gradually approach the local optimal value by adaptively adjusting their differences. Specifically, the TPS maintains a population with three particles and uses five proposed population state-transition operations to gradually move these three particles to a better state. A local optimal value can be obtained when these three particles become indistinguishable. The TPS is then embedded into an MOEA to form a new algorithm, called MOEA/TPS. To enable the TPS to search along the convergence and diversity directions, the two aggregation functions of the target problem are alternately used. Compared with twelve competitive MOEAs on various biased test problems with 30 to 2000 decision variables, our proposed algorithm demonstrates significant advantages in obtaining high-accuracy solutions.

Advanced control system design for large wind turbines is becoming increasingly complex, and high-level optimization techniques are receiving particular attention as an instrument to fulfil this significant degree of design requirements. Multiobjective optimal (MOO) control, in particular, is today a popular methodology for achieving a control system that conciliates multiple design objectives that may typically be incompatible. Multiobjective optimization was a matter of theoretical study for a long time, particularly in the areas of game theory and operations research. Nevertheless, the discipline experienced remarkable progress and multiple advances over the last two decades. Thus, many high-complexity optimization algorithms are currently accessible to address current control problems in systems engineering. On the other hand, utilizing such methods is not straightforward and requires a long period of trying and searching for, among other aspects, start parameters, adequate objective functions, and the best optimization algorithm for the problem. Hence, the primary intention of this work is to investigate old and new MOO methods from the application perspective for the purpose of control system design, offering practical experience, some open topics, and design hints. A very challenging problem in the system engineering application of power systems is to dominate the dynamic behavior of very large wind turbines. For this reason, it is used as a numeric case study to complete the presentation of the paper.

Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring the properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time.

As urban areas expand, energy demands are escalating, necessitating the development of urban energy systems (UES) to achieve energy conservation and emission reduction goals. Although small‐scale regional integrated energy supply technologies have reached a level of maturity, urban‐scale integrated energy supply solutions are still in development. In response, this study introduces an architecture for the UES and an economic and low‐carbon operation strategy. The approach begins by constructing a highly reliable and robust integrated energy system (IES) within each independent region to accommodate a variety of energy needs, followed by the establishment of an operational architecture for large‐scale urban energy systems. The study then examines the energy flow and the mathematical model of multiple energies within urban energy systems, simplifying the complex model for practical application. Subsequently, a multiobjective optimization model is developed to facilitate the large‐scale consumption of clean energy, with considerations for economic and low‐carbon operations, and is formatted into a linear programming model. The model's accuracy is empirically tested through numerical simulation in a city divided into three regions. The simulation results demonstrate substantial improvements in clean energy consumption, a reduction in carbon emissions, and a decrease in operational costs. Specifically, the proposed strategy can boost the clean energy consumption rate to 96.41%, cut operational costs by up to 50.13%, and lower carbon dioxide emissions by up to 57.59% compared to traditional technologies. These findings robustly validate the methodology's effectiveness, paving the way for more sustainable urban energy management practices. Multiple integrated energy systems (IESs) are interconnected to form a urban energy system (UES), which is more suitable for the backbone of the UES. The system takes the power grids as the core skeleton to construct UESs.

Decomposition is an effective and popular strategy used by evolutionary algorithms to solve multiobjective optimization problems (MOPs). It can reduce the difficulty of directly solving MOPs, increase the diversity of the obtained solutions, and facilitate parallel computing. However, with the increase of the number of decision variables, the performance of multiobjective evolutionary algorithms (MOEAs) often deteriorates sharply. The advantages of the decomposition strategy are not fully exploited when solving such large-scale MOPs (LSMOPs). To this end, this paper proposes a parallel MOEA based on two-space decomposition (TSD) to solve LSMOPs. The main idea of the algorithm is to decompose the objective space and decision space into multiple subspaces, each of which is expected to contain some complete Pareto-optimal solutions, and then use multiple populations to conduct parallel searches in these subspaces. Specifically, the objective space decomposition approach adopts the traditional reference vector-based method, whereas the decision space decomposition approach adopts the proposed method based on a diversity design subspace (DDS). The algorithm uses a message passing interface (MPI) to implement its parallel environment. The experimental results demonstrate the effectiveness of the proposed DDS-based method. Compared with the state-of-the-art MOEAs in solving various benchmark and real-world problems, the proposed algorithm exhibits advantages in terms of general performance and computational efficiency.

The purpose of this study is to improve the P-I controllers of the voltage-source converters (VSC)-based multiterminal high voltage direct-current (MT-HVDC) networks. Since the VSCs are the non-linear elements of the MT-HVDC stations, the classical optimization methods, which approximately implement the linear model to optimize the P-I controllers of the VSCs, do not generate optimal results. Therefore, this paper presents a novel technique to optimize the VSC-based MT-HVDC grids’ P-I controllers by embedding the artificial bee colony (ABC) algorithm. The voltage-droop control method is employed at on-shore grids to ensure the active and reactive power balance within MT-HVDC networks. During an evaluation, achieved via a detailed four-terminal MT-HVDC model designed in PSCAD/EMTDC, the improved results obtained under different dynamic situations such as unbalance wind power generation, change in load demand at the on-shore side grids, and eventual VSC disconnection, respectively.

In many multiobjective optimization problems, the Pareto Fronts and Sets contain a large number of solutions and this makes it difficult for the decision maker to identify the preferred ones. A possible way to alleviate this difficulty is to present to the decision maker a subset of a small number of solutions representatives of the Pareto Front characteristics. In this paper, a two-steps procedure is presented, aimed at identifying a limited number of representative solutions to be presented to the decision maker. Pareto Front solutions are first clustered into \"families\", which are then synthetically represented by a \"head-of-the-family\" solution. Level Diagrams are then used to represent, analyse and interpret the Pareto Front reduced to its head-of-the-family solutions. The procedure is applied to a reliability allocation case study of literature, in decision-making contexts both without or with explicit preferences by the decision maker on the objectives to be optimized.

In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower shell and upper shell. We worked there under the assumption that for a given problem an upper shell exists. As it is not always the case, in this paper we give some sufficient conditions for the existence of upper shells. We also investigate how to constructively search infeasible sets to derive upper shells. We approach this issue by means of problem relaxations. We formally show that under certain conditions some subsets of lower shells to relaxed multiobjective optimization problems are upper shells in the respective unrelaxed problems. Results are illustrated by a numerical example representing a small but real mechanical problem. Practical implications of the results are discussed.