Dynamic Multi-Objective Lion Swarm Optimization with Multi-strategy Fusion: An application in 6R robot trajectory planning

TL;DR

MF-DMOLSO addresses dynamic multi-objective optimization by integrating Tent chaotic mapping for uniform initialization, adaptive cold-hot start strategies, and a multi-strategy swarm update framework with Pareto-based and reference-point guided selection. It combines Levy flight mutation, crowding-degree sorting, and a tailored external archive to balance convergence speed and Pareto-front diversity, achieving high accuracy across 2- and 3-objective benchmarks ($< GD$ improvements reaching up to $97\%$ and $>90\%$ success rates) and outperforming MOPSO, NSGA-II, NSGA-III, MOLSO, RMOLSO, and MC-DCMOEA. The method is applied to 6R robot trajectory planning, delivering shorter running times ($8.3\mathrm{s}$) and lower maximum accelerations ($54^\circ$/s$^2$) with a substantial Pareto-front coverage increase ($70.97\%$ vs $2\%$ for MOPSO). These results demonstrate MF-DMOLSO’s practical impact for real-time dynamic optimization and safe, efficient robotic motion planning.

Abstract

The advancement of industrialization has spurred the development of innovative swarm intelligence algorithms, with Lion Swarm Optimization (LSO) notable for its robustness, parallelism, simplicity, and efficiency. While LSO excels in single-objective optimization, its multi-objective variants face challenges such as poor initialization, local optima entrapment, and so on. This study proposes Dynamic Multi-Objective Lion Swarm Optimization with Multi-strategy Fusion (MF-DMOLSO) to address these limitations. MF-DMOLSO comprises three key components: initialization, swarm position update, and external archive update. The initialization unit employs chaotic mapping for uniform population distribution. The position update unit enhances behavior patterns and step size formulas for cub lions, incorporating crowding degree sorting, Pareto non-dominated sorting, and Levy flight to improve convergence speed and global search capabilities. Reference points guide convergence in higher-dimensional spaces, maintaining population diversity. An adaptive cold-hot start strategy generates a population responsive to environmental changes. The external archive update unit re-evaluates solutions based on non-domination and diversity to form the new population. Evaluations on benchmark functions showed MF-DMOLSO surpassed multi-objective particle swarm optimization, non-dominated sorting genetic algorithm II, and multi-objective lion swarm optimization, exceeding 90% accuracy for two-objective and 97% for three-objective problems. Compared to non-dominated sorting genetic algorithm III, MF-DMOLSO showed a 60% improvement. Applied to 6R robot trajectory planning, MF-DMOLSO optimized running time and maximum acceleration to 8.3s and 0.3pi rad/s^2, achieving a set coverage rate of 70.97% compared to 2% by multi-objective particle swarm optimization, thus improving efficiency and reducing mechanical dither.

Figures (8)

• Figure 1: MF-DMOLSO architecture. MF-DMOLSO comprises three units: initialization unit, swarm position update unit, and external archive update unit.
• Figure 2: Two start-up methods: (a) weak association – cold start mode, and (b) strong association – hot start mode.
• Figure 3: Reference point mechanism. We generally show how population individuals relate to reference points.
• Figure 4: Optimal location selection and external archive update results based on congestion degree: (a) Optimization result of a certain iteration, and (b) Optimization result after a few more iterations. The dot circled represented the global optimal position that lay within the sparsely distributed region of the PF's optimal solution.
• Figure 5: Work process of MF-DMOLSO. Here we show the full flow of the algorithm. It is worth noting that whether the crowding degree sort operation uses the crowding distance sort or the sort based on reference points depends on the target space dimension. Crowded distance sort is used only in two target spaces, and in other cases another way is used.

Theorems & Definitions (5)

• Definition 1
• Theorem 1
• proof
• Theorem 2
• proof