Emerging Techniques for Evolutionary Single- and Multi-objective Optimization with Application to Humanoid Robot Gait Generation

This chapter presents emerging techniques in evolutionary computation that address critical challenges such as fair algorithm comparison, dynamic performance evaluation, and knee-based multi-objective optimization. These techniques are applied to a real-world problem of gait generation for bipedal locomotion. For single-objective optimization, a novel statistical comparison methodology is proposed that employs multiple independent runs to gain insight into algorithm consistency and reliability. The Particle swarm optimization (PSO) algorithm demonstrates superior convergence characteristics and reduced performance variability compared to a genetic algorithm (GA) across different initial conditions. In multi-objective optimization, the study introduces running performance metrics for a dynamic assessment without requiring knowledge of the true Pareto-optimal front (PF). The running Inverted Generational Distance Plus (IGD+) indicator reveals that elitist non-dominated sorting GA (NSGA-II) is superior to multi-objective PSO (MOPSO) in handling constraints. Furthermore, knee-based optimization techniques focusing on PF regions are discussed to reduce decision-maker burden. The angle-based knee detection method is validated on a DO2DK benchmark problem generation wise and later applied to humanoid robot gait optimization, demonstrating its effectiveness in identifying critical trade-off regions. The single-support phase exhibits one distinct knee region while the double-support phase reveals two, reflecting the underlying behavior of bipedal locomotion. These applications demonstrate the usefulness of evolutionary single- and multi-objective optimization algorithms in solving a complex real-world optimization problem with multiple objectives.