The sewer layout in flat areas significantly influences the construction and operational costs as well as reliability of the network performance. To find an optimum design of sewer networks for flat areas, this study presents a multi-objective optimization problem with the objective functions of 1- the cost and 2- the reliability. The reliability criterion is defined as the effect of a clogging in a sewer on its upstream population. To solve the problem, the NSGA-II Algorithm is coupled to two self-adaptive design algorithms for generating the layout and sizing of sewers. A case study is solved using the proposed model to demonstrate its application and advantages.

A Multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval Multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

Generally, an engineering design problem has multiple objective functions. Some of these problems can be formulated as Multiobjective geometric programming models. On the other hand, often in the real world, coefficients of the objective functions are not known precisely. Coefficients may be interpreted as fuzzy numbers, which lead to a Multiobjective geometric programming with fuzzy parameters. In this paper, we solve the Multiobjective geometric programming problem with fuzzy parameters by applying a linear ranking function. The linear ranking function is used to compare fuzzy numbers. Finally, a numerical example is given.