Sentence examples for both objective functions and from inspiring English sources

The main difference lies in that they allow both objective functions and constraints of each player to depend on the strategies of other players.

It is well known that, in the conventional bilevel programming problem, the coefficients in both objective functions and constraints are deterministic or crisp.

Then the interval bilevel linear programming problem with interval coefficients in both objective functions and constraints was transformed into a deterministic bilevel optimization problem.

This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers.

Here, it is important to realize that the meaning of minimizing both objective functions and inequality constraints is not clear at all owing to the presence of interval coefficients in problem (1).

Under the above consideration, from a point of decision makers' preferences, our objective is to propose an alternative way based on preference-based index to deal with the interval bilevel linear programming problem in which all coefficients in both objective functions and constraints are intervals.

This development poses new challenges for both objective function and penalty function definitions.

This confirms that both objective function and constraints of model (8) are convex.

In other words, pharmacological treatment has a significant positive impact on patients' both objective functioning and subjective well-being [ 16].

This approach is advocated by Muldoon et al [ 52], who suggest that QOL scales should measure both objective functioning and subjective well-being.

The linear bilevel multiobjective programming (LBMP) problem, i.e., both the objective functions and the constraint functions are linear functions, has attracted more and more attention.