A Scalar Projection and Angle-Based Evolutionary Algorithm for Many-Objective Optimization Problems.

Area of Science:

• Optimization Algorithms
• Evolutionary Computation
• Multi-objective Optimization

Background:

• Decomposition-based multiobjective evolutionary algorithms rely heavily on search directions and reference points for performance.
• Scalarizing functions in these algorithms utilize ideal or nadir points, impacting their effectiveness.

Purpose of the Study:

• To propose a novel decomposition-based many-objective optimizer.
• To enhance the performance of evolutionary algorithms in multi-objective optimization problems.

Main Methods:

• The proposed optimizer uses adaptive search directions and two reference points (ideal and nadir).
• It employs two novel fitness functions based on differences between PBI and inverted PBI functions.
• An angle-based elimination procedure is used for solution diversification.

Main Results:

• The algorithm demonstrates flexibility in handling irregular Pareto-optimal fronts.
• Experimental results show promising improvements in solution set quality and algorithmic efficiency.
• Performance was validated against seven state-of-the-art algorithms on 32 test problems with up to 15 objectives.

Conclusions:

• The new optimizer effectively handles diverse Pareto-optimal front shapes using adaptive strategies.
• Simultaneous use of ideal and nadir points leverages complementary strengths for concave and convex fronts.
• The algorithm offers a robust and efficient approach for many-objective optimization challenges.