Theory and practice of uncertain programming
type: Item
instance of: scholarly article
title: Theory and practice of uncertain programming
zbMATH Open document ID: 1029.90084
author: Baoding Liu
published in: Studies in Fuzziness and Soft Computing
publication date: 2003-05-22T00:00:00Z
review text: Real-life decisions are usually made in the state of uncertainty (randomness, fuzziness, roughness, etc.). How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas and various applications in transportation problem, inventory system, feed mixture problem, production process, water supply problem, facility location and allocation, capital budgeting, topological optimization, vehicle routing problem, redundancy optimization, critical path problem, and parallel machine scheduling. Numerous intelligent algorithms such as genetic algorithm, neural network, simulated annealing, and tabu search have been developed by researchers of different backgrounds. A natural idea is to integrate these intelligent algorithms to produce more effective and powerful hybrid intelligent algorithms. In order to solve uncertain programming models, a spectrum of hybrid intelligent algorithms are documented in this book. Part I, Fundamentals, offers the basic concepts of mathematical programming, genetic algorithms and neural networks. Part II, Stochastic Programming, lists various methods of generating random numbers, and deals with the law of large numbers, stochastic simulation, expected value model, chance-constrained programming, dependent-chance programming, hybrid intelligent algorithms, and applications in various decision problems. Part III, Fuzzy Programming, introduces possibility space, fuzzy variable, possibility measure, necessity measure, credibility measure, expected value operator, fuzzy simulation, and fuzzy programming theory. Part IV, Rough Programming, is devoted to rough space, rough variable, trust measure, expected value operator, rough simulation, and rough programming. As a byproduct, interval programming is also discussed. Part V, Fuzzy Random Program…
reviewed by: Nikolay Yakovlevich Tikhonenko
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90B06
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 90B35
Mathematics Subject Classification ID: 68T37
zbMATH DE Number: 1914869
zbMATH Keywords: uncertain programming
zbMATH Keywords: mathematical programming
zbMATH Keywords: linear programming
zbMATH Keywords: nonlinear programming
zbMATH Keywords: multiobjective programming
zbMATH Keywords: goal programming
zbMATH Keywords: integer programming
zbMATH Keywords: dynamic programming
zbMATH Keywords: multilevel programming
zbMATH Keywords: genetic algorithms
zbMATH Keywords: neural networks
zbMATH Keywords: stochastic programming
zbMATH Keywords: stochastic simulations
zbMATH Keywords: parallel machine scheduling
zbMATH Keywords: capital budgeting
zbMATH Keywords: vehicle routing problem
zbMATH Keywords: facility location and allocation
zbMATH Keywords: water supply problem
zbMATH Keywords: production process
zbMATH Keywords: mark six lottery
zbMATH Keywords: fuzzy programming
zbMATH Keywords: fuzzy programming with fuzzy decisions
zbMATH Keywords: rough programming
zbMATH Keywords: fuzzy random programming
zbMATH Keywords: random fuzzy programming
zbMATH Keywords: multifold uncertainty
zbMATH Keywords: graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1914869