Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization.

Area of Science:

• Optimization Algorithms
• Computational Intelligence
• Evolutionary Computation

Background:

• Constrained optimization problems (COPs) are prevalent in various scientific and engineering domains.
• Multiobjective evolutionary algorithms (EAs) are commonly used to address COPs by transforming them into unconstrained multiobjective optimization problems.
• Existing methods face challenges in efficiently solving COPs, particularly those with complex landscapes like "wide gap" problems.

Purpose of the Study:

• To propose a novel multiobjective method for solving constrained optimization problems (COPs).
• To enhance the efficiency of evolutionary algorithms in handling difficult optimization landscapes.
• To theoretically and empirically validate the effectiveness of the proposed method.

Main Methods:

• A new multiobjective method is proposed, converting COPs into problems with "helper" and "equivalent" objectives.
• The transformed multiobjective problem is decomposed into subproblems using a weighted sum approach with dynamic weight adjustment.
• Theoretical analysis of computational time complexity is performed on "wide gap" problems.
• An algorithm implementing the helper and equivalent objective method is developed and tested.

Main Results:

• The helper and equivalent objective method is theoretically proven to shorten the time required to cross "wide gap" problem landscapes.
• Experimental results demonstrate superior performance of the proposed method compared to eight other state-of-the-art EAs.
• The algorithm achieved the top rank on IEEE CEC2017 benchmarks for constrained optimization.

Conclusions:

• The proposed helper and equivalent objective method offers a significant advancement in solving constrained optimization problems.
• This approach effectively addresses the computational challenges posed by difficult optimization landscapes.
• The method shows strong potential for practical applications in scientific and engineering fields requiring efficient constrained optimization.