Decompositionbased

Decomposition-based optimization refers to a family of approaches for solving complex optimization problems by partitioning the problem into a set of smaller subproblems. In multiobjective optimization, the subproblems are usually constructed by decomposing the objective space into subregions using a collection of weight vectors or reference points, turning the original problem into a set of scalarized subproblems.

Each subproblem is optimized with evolutionary operators or other solvers, and information is shared among neighboring subproblems to promote convergence and diversity. The canonical example is MOEA/D, which maintains a population of solutions associated with fixed weight vectors and uses neighborhood relations to exchange information.

Common scalarizing functions include weighted sum, Tchebycheff, and penalty-based boundary intersection; the choice affects front coverage and convergence. Advantages of decomposition-based methods include scalability to many objectives and potential for parallel execution, while challenges include selecting a suitable set of subproblems, determining neighborhood size, and handling nonconvex fronts.

Applications of decomposition-based optimization span engineering design, logistics and supply chain, energy systems, finance, and hyperparameter optimization in machine learning. Variants and extensions include constrained, dynamic, stochastic, and surrogate-assisted versions, as well as techniques for automatic weight vector generation and adaptive management of subproblems.