Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)[Formula: see text] via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)[Formula: see text] are obtained through a new nonlinear scalarization technical. Then, under [Formula: see text]-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)[Formula: see text] is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)[Formula: see text] under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

Global Well Posedness for the Thermally Radiative Magnetohydrodynamic Equations in 3D

In this paper, we study the thermally radiative magnetohydrodynamic equations in 3D, which describe the dynamical behaviors of magnetized fluids that have nonignorable energy and momentum exchange with radiation under the nonlocal thermal equilibrium case. By using exquisite energy estimate, global existence and uniqueness of classical solutions to Cauchy problem in ℝ3 or T3 are established when initial data is a small perturbation of some given equilibrium. We can further prove that the rates of convergence of solution toward the equilibrium state are algebraic in ℝ3 and exponential in T3 under some additional conditions on initial data. The proof is based on the Fourier multiplier technique.

p-Optimality-Based Multiobjective Root System Growth Algorithms for Multiobjective Applications

In this paper, a multiobjective root system growth algorithm-based p-optimality (p-MORSGA) is proposed. The proposed p-MORSGA extended original root system growth algorithm with multiobjective nondomination strategy. To enhance its effect of convergence of solution groups, the p-optimality criterion is employed to determine the solutions of last nondominated front into the next generation group. In the evolution process, global general (GG), concerning the margin information and population density, is selected as the suitable optimality criterion of evaluating the performance of solutions. Application of the new p-MORSGA on several multiobjective benchmark functions shows a marked improvement in performance over the modified classical MOEAs with such criterion. Finally, the proposed p-MORSGA is applied to solve two real-world problems, multiobjective portfolio optimization problems (MOPOPs) and multiobjective optimal power flow (OPF) problems. The experimental results demonstrate that p-MORSGA is extremely effective for real-world application problems.

A Comparative Study on Evolutionary Multi-objective Optimization Algorithms Estimating Surface Duct

The problem of atmospheric duct inversion is usually solved as a single objective optimization problem. Based on ground-based Global Positioning System (GPS) phase delay and propagation loss, this paper develops a multi-objective method including the effect of source frequency and receiving antenna height. The diversity and convergence of solution sets are evaluated for seven multi-objective evolutionary algorithms with three performance metrics: Hypervolume (HV), Inverted Generational Distance (IGD), and the averaged Hausdorff distance (Δ2). The inversion results are compared with the simulation results, and the experimental comparison is conducted on three groups of test situations. The results demonstrate that the ranking of algorithm performance varies because of the different methods used to calculate performance metrics. Moreover, when the algorithms show overwhelming performance using performance metrics, the inversion result is not more close to the real value. In the comparison of computational experiments, it was found that, as the retrieved parameter dimension increases, the inversion result becomes more unstable. When the observed data are sufficient, the inversion result seems to be improved.

Study on Numerical Methodologies for Assessing Ultimate Bending Moment of Ship Hull Girder

Nonlinear finite element analysis is usually used to assess the ultimate strength of hull girder, which includes implicit analysis and explicit dynamic analysis. So far, most of researchers use the implicit analysis to assess the ultimate strength of various vessels or stiffened plates. Comparing with the implicit analysis, the explicit dynamic analysis may be more stable since this method doesn’t need to consider the convergence of solution, and can consider the transient influence of time. However, the accuracy of solution results and time in the explicit dynamic method is very important. This depends on modelling configurations, such as the loading time, geometric ranges of finite element models, element types and applying methods of loading. The purpose of the present paper is to investigate the influences of these factors, and then to figure out a reliable numerical method which meets permitted accuracy and consumes acceptable computer resource in explicit dynamic analysis.