Constraint Handling Guided by Landscape Analysis in Combinatorial and Continuous Search Spaces

Area of Science:

• Optimization Theory
• Heuristic Algorithms
• Computational Intelligence

Background:

• Fitness landscapes characterize heuristic algorithm performance on optimization problems.
• Practical problems often involve constraints, necessitating constraint-handling techniques (CHTs) to navigate infeasible search spaces.
• The interaction between fitness and violation landscapes complicates algorithm behavior.

Purpose of the Study:

• To characterize constrained optimization landscapes using violation metrics.
• To evaluate the performance of six CHTs across diverse constrained problems.
• To establish relationships between landscape properties and the efficacy of different CHTs.

Main Methods:

• Applied violation landscape metrics to continuous and combinatorial optimization problems.
• Assessed the relative performance of six established constraint-handling techniques.
• Correlated landscape characteristics with CHT performance.

Main Results:

• For problems with sampled feasible solutions, a bi-objective approach excelled, though other techniques were better for disjoint feasible areas.
• For problems lacking measurable feasibility, feasibility ranking was generally superior, but other CHTs performed better with high fitness-violation correlation.
• Specific landscape properties favor particular constraint-handling strategies.

Conclusions:

• The structure of constrained optimization landscapes significantly impacts the performance of heuristic algorithms.
• Understanding violation landscapes is crucial for selecting appropriate constraint-handling techniques.
• Tailoring CHTs to specific landscape properties can enhance optimization efficiency.