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One of the most challenging robotic manipulator designs is finding an appropriate balance between the shaking force and shaking moment because this reduces vibrations. Several approaches have been introduced in the last decades; nevertheless, some assumptions must be established to make such a balance. In this paper, a dynamic balancing approach is proposed. The main novelty is the no dependence on specific trajectories to be executed by the manipulator, which allows finding a design with a similar tradeoff in the balancing under robot configuration changes. Also, the proposal incorporates mass distribution and link shape in a single design procedure. The proposal is stated as a constrained nonlinear optimization problem and applied to a hybrid serial-parallel robotic manipulator. The use of different bio-inspired algorithms and one gradient one in the solution of the balancing problem reveals that differential evolution finds the most suitable design. Besides, comparative simulation results of the obtained design with other design approaches show that the obtained design presents the most suitable tradeoff between the shaking force and the shaking moment when the manipulator executes tasks with different operating velocities. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

Many metaheuristic methods have been proposed and have shown promising performance in solving multi-objective optimization problems (MOPs). As a representative example, the competitive swarm optimizer (CSO) exhibits excellent performance in solving large-scale MOPs. However, CSO performs poorly when used straightforwardly for constrained MOPs with complex constraints or objective spaces. In this paper, we propose a dual-swarm-based CSO framework that co-evolves two swarms with different orientations: (i) CSO is improved using genetic algorithms, namely CSO-GA to form a convergence-directed swarm without considering constraints to accelerate the convergence. (ii) CSO is further improved by differential evolution, namely CSO-DE to form a search-directed swarm by considering constraints to enhance diversity and improving the search for the constrained Pareto front. Moreover, a new constraint relaxation method is proposed that combines the particle swarm feasible rate and current evolutionary generation to dynamically adjust the factor for decreasing or increasing constraint relaxation. Extensive experiments with 37 benchmark instances and nineteen real-world constrained MOPs demonstrate that our proposed algorithm yields significantly better or at least more competitive results than ten state-of-the-art methods. • A dual-swarm-based CSO framework is proposed for CMOPs. • Two swarms co-evolve to form different orientations. • A new constraint relaxation method is presented. • Results demonstrate the superiority of our approach. [ABSTRACT FROM AUTHOR]

Traditional differential evolution (DE) algorithms have functional limitations in effectively addressing increasingly intricate numerical optimization problems. The key to responding to this challenge is to strike a suitable balance between exploration and exploitation. Exploration is used to find the global optimal solution, and exploitation is used to improve the accuracy of the global optimal solution. Therefore, this study introduces a novel differential evolution algorithm with a stage stratification method and a dual balanced mutation strategy framework, named SbmDE. To enhance the balance between convergence and diversity, the population is stratified into exploration and exploitation layers based on the size of the fitness value and evolutionary period. In the exploitation layer, a hybridization mutation is applied as the first mutation. A novel dual improved mutation operation is proposed and applied to the exploration layer. For the first mutation, the hybridization mutation is used in the same manner as for the exploitation layer. For the secondary mutation, two improved mutation strategies are proposed to alleviate premature convergence at the early stage of evolution and to enhance the local neighborhood search at a later stage, named DE/ranking-to-rand/1 and DE/best-current-dev/1. Experiments were conducted on the CEC2017 benchmark suite, which contains 29 single-objective real-parameter numerical optimization problems, to evaluate the performance of the proposed algorithm. Compared with 11 state-of-the-art algorithms, the results demonstrate the superiority of the proposed algorithm, which does not increase the time complexity. Additionally, based on the four engineering design problems, the proposed algorithm is fully competent in solving practical constrained optimization problems. • A stage stratification method is proposed to divide population. • Dual mutation is proposed and applied to the exploration layer. • Proposed two improved mutation strategies applied to the secondary mutation. • SbmDE obtains better values than the other algorithms in the paper. • SbmDE is applied to four engineering design problems. [ABSTRACT FROM AUTHOR]

As we move to increasingly complex cyber–physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4. 5 ms while respecting workspace constraints and switching between a 'left' and 'right' bend in the elbow joint. [ABSTRACT FROM AUTHOR]