Interactive reference point procedure based on the conic scalarizing function.

Area of Science:

• Operations Research
• Mathematical Optimization
• Decision Sciences

Background:

• Multiobjective optimization commonly uses scalarizing functions to convert multiple objectives into a single one.
• Conic scalarizing functions characterize Benson proper efficient solutions for non-convex problems via scalar Lagrangian saddle points, preserving convexity.
• These functions are effective in a posteriori and a priori methods for real-world applications.

Purpose of the Study:

• To propose a novel conic scalarizing function-based interactive reference point procedure.
• To enable active decision-maker participation in directing the optimization search based on preferences.
• To present an algorithmic framework for interactive multiobjective optimization.

Main Methods:

• Development of a conic scalarizing function tailored for interactive reference point procedures.
• Integration of decision-maker preferences to guide the search process.
• Formulation of an algorithmic framework for interactive solution of multiobjective optimization problems.

Main Results:

• The proposed method facilitates active decision-maker involvement in the optimization process.
• The conic scalarizing function approach preserves the convexity property.
• The algorithmic framework is demonstrated through illustrative examples.

Conclusions:

• The developed interactive reference point procedure effectively incorporates decision-maker preferences.
• Conic scalarizing functions offer a robust method for Benson proper efficient solutions in non-convex multiobjective problems.
• The presented framework provides a practical approach for solving complex multiobjective optimization problems interactively.