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This gives rise to a multiple objective problem.
The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve.
The multi-objective optimization problem is transformed into a single objective problem using a weight factor.
The resulting objective problem is solved using a simple lexicographic method.
This work presents a two objective problem considering both effectiveness and costs of alternative environmental policies.
In these methods the bi-objective problem is transformed into a single objective problem which is easier to solve.
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Thus, a multi-objective problem must be solved.
The equivalence between the original multi-objective problem and the new single-objective one is proved.
This type of bi-objective problem has not been modeled in previous studies.
The optimization is virtually a multi-objective problem with several important parameters on regeneration recycling involved.
The multi-objective problem with four decision variables is translated into two subproblems.
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