where f : Rn → R and g : Rn → Rp are nonlinear continuous functions and Ω = {x ∈ Rn : −∞ < l ≤ x ≤ u < ∞}. Problems with equality constraints, h(x) = 0, can be reformulated into the above form by converting into a couple of inequality constraints h(x)− β ≤ 0 and −h(x)− β ≤ 0, where β is a small positive relaxation parameter. Since we do not assume that the objective function f is convex, the pr...

Recently, we proposed a new threshold based penalty function. The threshold dynamically controls the penalty to infeasible solutions. This paper implants the two different forms of the proposed penalty function in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework to solve constrained multiobjective optimization problems. This led to a new algorithm, denoted by ...

EQUALITY CONSTRAINED OPTIMIZATION Masao Fukushima Kyoto University Hisashi Mine Kansai University Eiki Yamakawa Kyoto University (Received November 12, 1984: Revised June 12, 1985) This paper is concerned with a differentiable exact penalty function derived by modifying the Wolfe dual of an equality constrained problem. It may be considered that this penalty function belongs to a class of gener...

In many evolutionary algorithms, as fitness functions, penalty functions play an important role. In order to solve zero-one nonlinear optimization problems, a new objective penalty function is defined in this paper and some of its properties for solving integer nonlinear optimization problems are given. Based on the objective penalty function, an algorithm with global convergence for integer no...

Wu X, Li S. On the discounted penalty function in a discrete time renewal risk model with general interclaim times. Scandinavian Actuarial Journal. In this paper a discrete time renewal risk model with arbitrary interclaim times is discussed. We show that the expected discounted penalty function satisfies a recursive formula. In particular, the probability generating function of the time of rui...

Using Metaheuristics models and Evolutionary Algorithms for solving portfolio problem has been considered in recent years.In this study, by using particles swarm optimization and tabu search algorithms we  optimized two-sided risk measures . A standard exact penalty function transforms the considered portfolio selection problem into an equivalent unconstrained minimization problem. And in final...

Constrained optimization is a computationally difficult task, particularly if the constraint functions are non-linear and nonconvex. As a generic classical approach, the penalty function approach is a popular methodology which degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sen...

1. Abstract A well-known approach for solving constrained optimization problems is based on penalty functions. A penalty technique transforms the constrained problem into an unconstrained problem by penalizing the objective function when constraints are violated and then minimizing the penalty function using methods for unconstrained problems. In this paper, we analyze the implementation of a s...