Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.7.2025.3.08
Volume 7, Issue 3, 1 December 2025, Pages 421-458

 

Abstract. Decomposition techniques are proven highly effective in addressing complexity of optimization problems. For multiobjective optimization problems (MOPs), a variety of objective-space decomposition approaches are developed and applied in practice, while decision-space decomposition remains rather underexplored. We develop a line-decomposition algorithm for computing an approximation of the efficient set of strictly convex MOPs. The feasible region is decomposed into lines whose efficient sets are used to reconstruct the overall efficient set. Because the algorithm relies on solving a collection of single objective line search problems, it is immediately applicable to single-objective optimization with no modifications. We prove the algorithm convergence and provide a preliminary error analysis. The algorithm is implemented in Python and tested on biobjective and single objective problems with bounded variables. Numerical results are also included.

 

How to Cite this Article:
E. Soriano, M. Mitkovski, M. M. Wiecek, A line decomposition algorithm for multiobjective optimization, J. Appl. Numer. Optim. 7 (2025), 421-458.