Penalty method for fuzzy linear programming with trapezoidal numbers

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints

Developing an Overbooking Fuzzy-Based Mathematical Optimization Model for Multi-Leg Flights

Overbooking is one of the most vital revenue management practices that is used in the airline industry. Identification of an overbooking level is a challenging task due to the uncertainties associated with external factors, such as demand for tickets, and inappropriate overbooking levels which may cause revenue losses as well as loss of reputation and customer loyalty. Therefore, the aim of this paper is to propose a fuzzy linear programming model and Genetic Algorithms (GAs) to maximize the overall revenue of a large-scale multi-leg flight network by minimizing the number of empty seats and the number of denied passengers. A fuzzy logic technique is used for modeling the fuzzy demand on overbooking flight tickets and a metaheuristics-based GA technique is adopted to solve large-scale multi-leg flights problem. As part of model verification, the proposed GA is applied to solve a small multi-leg flight linear programming model with a fuzzified demand factor. In addition, experimentation with large-scale problems with different input parameters’ settings such as penalty rate, show-up rate and demand level are also conducted to understand the behavior of the developed model. The validation results show that the proposed GA produces almost identical results to those in a small-scale multi-leg flight problem. In addition, the performance of the large-scale multi-leg flight network represented by a number of KPIs including total booking, denied passengers and net-overbooking profit towards changing these input parameters will also be revealed

Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them

Generating Interpretable Fuzzy Controllers using Particle Swarm Optimization and Genetic Programming

Autonomously training interpretable control strategies, called policies, using pre-existing plant trajectory data is of great interest in industrial applications. Fuzzy controllers have been used in industry for decades as interpretable and efficient system controllers. In this study, we introduce a fuzzy genetic programming (GP) approach called fuzzy GP reinforcement learning (FGPRL) that can select the relevant state features, determine the size of the required fuzzy rule set, and automatically adjust all the controller parameters simultaneously. Each GP individual's fitness is computed using model-based batch reinforcement learning (RL), which first trains a model using available system samples and subsequently performs Monte Carlo rollouts to predict each policy candidate's performance. We compare FGPRL to an extended version of a related method called fuzzy particle swarm reinforcement learning (FPSRL), which uses swarm intelligence to tune the fuzzy policy parameters. Experiments using an industrial benchmark show that FGPRL is able to autonomously learn interpretable fuzzy policies with high control performance.Comment: Accepted at Genetic and Evolutionary Computation Conference 2018 (GECCO '18

Development of an experiment-based robust design paradigm for multiple quality characteristics using physical programming

The well-known quality improvement methodology, robust design, is a powerful and cost-effective technique for building quality into the design of products and processes. Although several approaches to robust design have been proposed in the literature, little attention has been given to the development of a flexible robust design model. Specifically, flexibility is needed in order to consider multiple quality characteristics simultaneously, just as customers do when judging products, and to capture design preferences with a reasonable degree of accuracy. Physical programming, a relatively new optimization technique, is an effective tool that can be used to transform design preferences into specific weighted objectives. In this paper, we extend the basic concept of physical programming to robust design by establishing the links of experimental design and response surface methodology to address designers’ preferences in a multiresponse robust design paradigm. A numerical example is used to show the proposed procedure and the results obtained are validated through a sensitivity study