Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained evolutionary algorithms (CMaOEAs), they always give priority satisfy constraints, while ignoring the maintenance of population diversity dealing with conflicting o...

In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

1 Sub-Problems and Objectives Divide and conquer techniques in problem solving are familiar and intuitive; first find the solution to sub-problems and then re-use these to find solutions to the whole problem. For example, we may decompose the problem of designing a vehicle into designing the engine and designing the body. It is acknowledged that most real-world problems (vehicles included) do n...

CST method is a powerful parameterization method because of its simplicity, robustness, and its ability to be generalized into various possible shapes of aerodynamic bodies. The geometry from CST itself is mainly determined by the formula of class and shape function. Application of CST to transonic airfoil optimization is still rare and more studies are needed. This work studies the application...

Satisficing, as an approach to decision-making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision-making include the P-model of Charnes and Cooper (1963), where satisficing is the objective, as well as chance-constrained and robust optimization problems, where sat...

nowadays, the environmental impact of transportation project and, especially air pollution impacts, are major concerns in evaluating transportation projects. based on this concern, beside definition of traditional objective functions like total travel time and total investment cost, different type of environmental related function is considered as objective function in urban network design. in ...