Shift-Based Penalty for Evolutionary Constrained Multiobjective Optimization and its Application

Area of Science:

• Optimization
• Evolutionary Computation
• Applied Mathematics

Background:

• Constrained multiobjective optimization problems (CMOPs) are prevalent in engineering and science.
• Existing constraint-handling techniques (CHTs) face challenges in balancing feasibility and convergence.
• Effective CHTs are crucial for solving complex real-world optimization tasks.

Purpose of the Study:

• To introduce a new constraint-handling technique (CHT), named shift-based penalty (ShiP), for CMOPs.
• To demonstrate ShiP's ability to adaptively manage feasibility and convergence during evolutionary processes.
• To develop and evaluate an enhanced algorithm, ShiP+, based on the ShiP technique.

Main Methods:

• Developed the shift-based penalty (ShiP) method, involving shifting infeasible solutions towards feasible regions.
• Adaptively controlled the shift degree based on population feasibility.
• Penalized shifted infeasible solutions according to constraint violations.
• Integrated ShiP into existing multiobjective optimization frameworks and proposed ShiP+.

Main Results:

• ShiP demonstrated competitive performance against other representative CHTs on benchmark problems.
• The proposed ShiP+ algorithm outperformed two state-of-the-art constrained multiobjective evolutionary algorithms (CMOEAs).
• ShiP successfully applied to the practical problem of urban bus line vehicle scheduling.

Conclusions:

• ShiP offers an effective and adaptive approach to handling constraints in multiobjective optimization.
• The ShiP technique facilitates a transition from diversity/feasibility to diversity/convergence.
• ShiP provides a robust foundation for developing high-performing CMOEAs and solving real-world problems.