Multi-Objective Neural Evolutionary Algorithm for Combinatorial Optimization Problems.

Area of Science:

• Artificial Intelligence
• Computational Optimization
• Evolutionary Computation

Background:

• Deep reinforcement learning (DRL) optimization has seen success using neural evolutionary algorithms.
• Existing algorithms primarily address single-objective optimization problems (SOPs).
• Combinatorial optimization problems often involve multiple, conflicting objectives.

Purpose of the Study:

• Introduce an end-to-end multi-objective neural evolutionary algorithm based on decomposition and dominance (MONEADD).
• Develop a method to evolve neural networks for combinatorial optimization without extensive re-engineering.
• Enhance the efficiency and performance of DRL models in solving complex optimization tasks.

Main Methods:

• MONEADD utilizes genetic operations and reward signals for neural network evolution.
• A set of non-dominated neural networks is maintained per generation using dominance and decomposition principles.
• Three multi-objective search strategies are incorporated to improve inference-time performance.

Main Results:

• MONEADD demonstrates competitive and robust performance on bi-objective Traveling Salesman Problems (TSP).
• The algorithm shows effectiveness on Knapsack problems with up to 200 instances.
• Empirical results confirm MONEADD's scalability when distributed across multiple GPUs.

Conclusions:

• MONEADD offers an efficient, end-to-end solution for multi-objective combinatorial optimization using DRL.
• The proposed method provides a significant advantage over conventional heuristic approaches by enabling direct problem-solving at inference time.
• MONEADD presents a scalable and robust framework for evolving neural networks in complex optimization scenarios.