Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives.

Area of Science:

• Optimization
• Computational Mathematics

Background:

• Many-objective optimization problems often feature redundant objectives, complicating the identification of the Pareto front.
• Existing objective reduction algorithms rely on correlation or dominance structures, which can be insufficient for degenerate Pareto fronts.

Purpose of the Study:

• To propose novel objective reduction algorithms, LHA and NLHA, for linearly and nonlinearly degenerate Pareto fronts.
• To introduce a new framework for objective reduction incorporating magnitude adjustment and a performance metric.

Main Methods:

• LHA and NLHA approximate the Pareto front structure using hyperplanes with non-negative sparse coefficients.
• NLHA employs a power transformation to convert nonlinearly degenerate fronts into nearly linearly degenerate ones, minimizing approximation error.
• The proposed algorithms were compared against correlation-based (LPCA, NLMVUPCA) and dominance-structure-based (PCSEA, greedy MOSS) methods.

Main Results:

• Comparative experiments on DTLZ5(I,M), MAOP(I,M), and WFG3(I,M) benchmark problems demonstrated the effectiveness of LHA and NLHA.
• The proposed algorithms showed superior performance compared to the tested correlation-based and dominance-structure-based methods.

Conclusions:

• LHA and NLHA offer a more effective approach to objective reduction in many-objective optimization, particularly for degenerate Pareto fronts.
• The hyperplane approximation strategy provides a robust alternative to existing methods for handling objective redundancy.