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Copyright © 2021 The Author(s). In this paper, a novel proportion-integral-derivative-like particle swarm optimization (PIDLPSO) algorithm is presented with improved terminal convergence of the particle dynamics. A derivative control term is introduced into the traditional particle swarm optimization (PSO) algorithm so as to alleviate the overshoot problem during the stage of the terminal convergence. The velocity of the particle is updated according to the past momentum, the present positions (including the personal best position and the global best position), and the future trend of the positions, thereby accelerating the terminal convergence and adjusting the search direction to jump out of the area around the local optima. By using a combination of the Routh stability criterion and the final value theorem of the Z-transformation, the convergence conditions are obtained for the developed PIDLPSO algorithm. Finally, the experiment results reveal the superiority of the designed PIDLPSO algorithm over several other state-of-the-art PSO variants in terms of the population diversity, searching ability and convergence rate. National Natural Science Foundation of China under Grants 61873148, 61933007 and 620730070; AHPU Youth Top-notch Talent Support Program of China under Grant 2018BJRC009; Natural Science Foundation of Anhui Province of China under Grant 2108085MA07; Royal Society of the UK; Alexander von Humboldt Foundation of Germany.

In this paper, we address the problem of optimal measurement budget allocation to estimate the state of a linear discrete-time dynamical system over a finite horizon. More precisely, our aim is to select the measurement times in order to minimize the variance of the estimation error over a finite horizon. In addition, we investigate the closely related problem of finding a trade-off between number of measurements and signal to noise ratio.First, the optimal measurement budget allocation problem is reduced to a deterministic combinatorial program. Then, we propose a genetic algorithm implementing a count preserving crossover to solve it. On the theoretical side, we provide a one-dimensional analysis that indicates that the benefit of using irregular measurements grows when the system is unstable or when the process noise becomes important. Then, using the duality between estimation and control, we show that the problem of selecting optimal control times for a linear quadratic regulator can be reduced to our initial problem.Finally, numerical implementations demonstrate that using measurement times optimized by our genetic algorithm gives better estimate than regularly spaced measurements. Our method is applied to a discrete version of a continuous-time system and the impact of the discretization time step is studied. It reveals good convergence properties, showing that our method is well suited to both continuous-time and discrete-time setups.

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of $$\varGamma $$ Γ -convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition, a careful treatment of the Maxwell system in the deformed film is required.

This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an $$L^{2}$$ L 2 -penalization in the phase field variable, driven by a viscous parameter $$\delta >0$$ δ > 0 , and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t. time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for $$\delta >0$$ δ > 0 and then consider the vanishing viscosity limit $$\delta \rightarrow 0$$ δ → 0 .

We consider a dynamic approach to games in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite sequential games the corresponding restriction of better-response dynamics will converge to a Nash equilibrium in quadratic time. Convergence happens on a per-player basis, and even in the presence of players with cyclic preferences, the players with acyclic preferences will stabilize. Thus, we obtain a candidate notion for rationality in the presence of irrational agents. Moreover, the restriction of convertibility can be justified by a conservative updating of beliefs about the other players strategies. For infinite games in extensive form we can retain convergence to a Nash equilibrium (in some sense), if the preferences are given by continuous payoff functions; or obtain a transfinite convergence if the outcome sets of the game are $$\Delta ^0_2$$-sets.

We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to concentrate in relatively small regions of the state space. The proposed scheme pushes some particles toward specific regions where the likelihood is expected to be high, an operation known as nudging in the geophysics literature. We reinterpret nudging in a form applicable to any particle filtering scheme, as it does not involve any changes in the rest of the algorithm. Since the particles are modified, but the importance weights do not account for this modification, the use of nudging leads to additional bias in the resulting estimators. However, we prove analytically that nudged particle filters can still attain asymptotic convergence with the same error rates as conventional particle methods. Simple analysis also yields an alternative interpretation of the nudging operation that explains its robustness to model errors. Finally, we show numerical results that illustrate the improvements that can be attained using the proposed scheme. In particular, we present nonlinear tracking examples with synthetic data and a model inference example using real-world financial data.

Until now, the theories about the convergence analysis, the almost surely and mean square exponential stability of the numerical solution for neutral stochastic functional differential equations with Markovian switching (NSFDEwMSs) have been well established, but there are very few research works concentrating on the stability in distribution of numerical solution. This paper will pay attention to the stability in distribution of numerical solution of NSFDEwMSs. The strong mean square convergence analysis is also discussed.

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method., Comment: Technical Report. 34 pages, 5 figures

Carbon fiber production is a large-scale system which comprises a large number of production processes. Among the various complex production conditions, the drawing process is one of the most influential factors that affect the quality of carbon fiber. How to obtain the fittest process parameters of the drawing process is a typical multi-objective optimization problem. To address the drawbacks of mathematical programming techniques available for solving optimization problems, we propose a new synergetic immune clonal selection algorithm (SICSA) to obtain the optimal process parameters, such as the linear density, strength, and breaking elongation ratio. The main operators of the SICSA are synergetic evolution, clonal operation and non-uniform mutation. The synergetic evolution between populations adopts a “division-parallel-recombination” mode, the clonal operation searches for optimal solutions globally, and the non-uniform mutation explores optimal solutions locally and enhances the diversity of the solutions. As a result, optimal solutions which lead to reasonable distribution of the drawing ratio are obtained. We also compare the proposed SICSA with an immune algorithm and a genetic algorithm for optimizing the parameter in the drawing process. Our results show that the SICSA has the best performance in precision and convergence time. These results can serve as references and provide guidance for real production of carbon fiber.