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A multi-objective optimization problem (MOP) can be stated as follows: maximize f (x)=(f1 (x), f2 (x),..., fp (x)) T(1) subject to x∈ S where x=(x1,..., xn) T is the decision variable vector. fi: Rn→ R, i= 1,..., p are objectives functions. Let x, y∈ S, x is said to be dominated by y if fi (y)≥ fi (x) for all i= 1,..., p and fj (y)> fj (x) for at least one index j. A solution x∗∈ S is said to be pareto-optimal to (1) if there does not exist another solution x such that x∗ is dominated by x. f (x∗) is then called a pareto-optimal objective vector. The set of all the pareto-optimal objective vectors is called the pareto-optimal front.

A number of multiobjective evolutionary algorithms (MOEAs) have recently been proposed. Compared with classical multi-objective optimization algorithms, MOEAs are able to find multiple nondominated solutions in a single run. Decomposition is a basic strategy used in conventional multiobjective optimization. This strategy is rarely adopted in MOEAs. In this paper, we propose a new multi-objective evolutionary strategy based on decomposition, called MOES/D. The proposed algorithm decomposes a MOP into a number of scalar optimization subproblems based on Tchebycheff scalarizing approach. It optimizes these subproblems simultaneously. Each subproblem can have several neighboring subproblems. Information collected from optimization of a subproblem is used for optimization of its neighbors.