Multi-Objective PSO (MOPSO) Algorithm Overview

This algorithm is a hybrid Multi-Objective Particle Swarm Optimization (MOPSO) with simulated annealing–like temperature control and a mode switch from single-objective to multi-objective optimization.

Main Workflow

1. Main Loop The algorithm iterates until the temperature (temp) drops below a minimum value:
   • Evaluate each particle using the objective function(s).
   • Before switching mode:
     • Use a single-objective function (combinte path length, obstacle advoidance, etc.) to update p_best and g_best.
   • After switching mode:
     • Apply a multi-objective evaluation (e.g., path length, smoothness, obstacle avoidance).
     • Perform fast non-dominated sorting and crowding distance to select diverse Pareto-optimal solutions.
     • Combine results to update the new p_best and calculate global best base on the Patero front rank.
2. Velocity and Position Update
   • Update each particle’s velocity using:

     v = w*v + c1*r1*(p_best - x) + c2*r2*(g_best - x)
     

     or a weighted mean term in multi-objective mode.

   • Clamp positions within the map limits to avoid going outside boundaries.
3. Temperature Reduction
   • After each generation, reduce the temperature:

     T <- alpha * T
     

     (acts like a cooling schedule to stabilize convergence).

4. Result Extraction
   • Perform final non-dominated sorting to obtain the Pareto front (best trade-off solutions).
   • Save the trajectories and visualize convergence (fitness curves, paths).

Key Features

• Two-phase optimization: single-objective → multi-objective.
• Adaptive simulated-annealing acceptance for worse solutions.
• Fast Non-Dominated Sorting (NSGA-II style) for Pareto selection.
• Crowding distance for solution diversity.
• Designed for path planning with obstacle avoidance in a 2D map.

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