penalty clause or liquidated damage which is formerly agreed between parties is legally examined and accepted as a rule. although judge could in some circumstances modify this stipulation. yet its economic analysis which is focused on economic efficiency can be considered as a “major unexplained puzzle in the economic theory of law”. this article compares the major legal systems in the case of ...

In recent studies on evolutionary multiobjective optimization, MOEA/D has been frequently used due to its simplicity, high computational efficiency, and high search ability. A multiobjective problem in MOEA/D is decomposed into a number of single-objective problems, which are defined by a single scalarizing function with evenly specified weight vectors. The number of the single-objective proble...

Kalyanmoy Deb and Samir Agrawal Kanpur Genetic Algorithms Laboratory (KanGAL), Department of Mechanical Engineering, Indian Institute of Technology Kanpur, PIN 208 016, India E-mail: deb,samira @iitk.ac.in Abstract Most applications of genetic algorithms (GAs) in handling constraints use a straightforward penalty function method. Such techniques involve penalty parameters which must be set righ...

To formulate a single-leg seat inventory control problem in an airline ticket sales system, the concept and techniques of revenue management are applied in this research. In this model, it is assumed the cabin capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two groups of early-reserving and late-purchasing customers demanding t...

This article proposes the use of a penalty function for pruning feedforward neural network by weight elimination. The penalty function proposed consists of two terms. The first term is to discourage the use of unnecessary connections, and the second term is to prevent the weights of the connections from taking excessively large values. Simple criteria for eliminating weights from the network ar...

This section begins with the motivation and general form of penalty functions as used in evolutionary computation. The main types of penalty function—constant, static, dynamic, and adaptive—are described within a common notation framework. References from the literature concerning these exterior penalty approaches are presented. The section concludes with a brief discussion of promising areas o...

We study a nonlinear exact penalization for optimization problems with a single constraint. The penalty function is constructed as a convolution of the objective function and the constraint by means of IPH (increasing positively homogeneous) functions. The main results are obtained for penalization by strictly IPH functions. We show that some restrictive assumptions, which have been made in ear...

Evolutionary algorithms are becoming increasingly valuable in solving large-scale, realistic engineering multiobjective optimization problems, which typically require consideration of conflicting and competing design issues. A criticism of Evolutionary Algorithms might be the lack of efficient and robust generic methods to handle constraints. The most widespread approach for constrained search ...

In this paper an exact penalty line search is introduced for solving constrained nonlinear programing. By this method it is possible to solve some problems with combining penalty method and SQP method, and in any iteration for producing new stepone can uses linear search and solves unconstrained optimization by exact penalty function. In this method a linear programming subproblem with trust ar...

First, this paper introduces a notion of a sharp penalty mapping which can replace more common exact penalty function for convex feasibility problems. Second, it uses it for solution of variational inequalities with monotone operators or pseudo-varitional inequalities with oriented operators. Appropriately scaled the sharp penalty mapping can be used as an exact penalty in variational inequalit...