By Masatoshi Sakawa
ISBN-10: 3662003864
ISBN-13: 9783662003862
ISBN-10: 3790818518
ISBN-13: 9783790818512
Simultaneous concerns of multiobjectiveness, fuzziness and block angular buildings interested in the real-world determination making difficulties lead us to the hot box of interactive multiobjective optimization for big scale programming difficulties below fuzziness. the purpose of this publication is to introduce the newest advances within the new box of interactive multiobjective optimization for big scale programming difficulties less than fuzziness at the foundation of the author's carrying on with study. detailed tension is put on interactive determination making points of fuzzy multiobjective optimization for human-centered structures in so much practical occasions whilst facing fuzziness. The publication is meant for graduate scholars, researchers and practitioners within the fields of operations learn, business engineering, administration technology and desktop science.
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Extra resources for Large Scale Interactive Fuzzy Multiobjective Programming: Decomposition Approaches
Sample text
The basic idea behind the RPM is that the DM can specify reference values for the objective functions and change the reference objective levels interactively due to learning or improved understanding during the solution process. In this procedure, when the DM specifies a reference point, the corresponding scalarization problem is solved for generating the Pareto optimal solution which is, in a sense, dose to the reference point or better than that if the reference point is attainable. Then the DM either chooses the current Pareto optimal solution or modifies the reference point to find a satisficing solution.
Since the relative cost coefficients of the nonbasic variables I-'~: 50 mo 3. The Dantzig-Wolfe Decomposition Method Ipl···p~lql···tlrpi···p~qi···~21··· I 0 ···0 1 ... 1 0 ···0 I 11 ... p 11 ... 10 ... 3. Structure of master problem for unbounded subproblems. 36) w7 are always negative, the eolumns in the form of ((AiW7)T,OT)T, eorresponding to p,7, are eandidates to enter the basis. 5 Restricted master problem As diseussed thus far, the Dantzig-Wolfe deeomposition method solves p independent linear programming problems in the subproblems, but in the master problem only a single pivot operation is performed.
For example, consider a production planning problem in a manufacturing company having a number of divisions, where each division has its own limited amounts of internal resources and the divisions are coupled by limited amounts of shared resources. 1). 1) by the revised simplex method using the Ef=o mi x Ef=o mi basis matrix. 1 Linear programming problems with block angular structures minimize subject to CiXi Bixi = Xi ~ 43 } bi O. 1) into one master problem and p independent subproblems, obtains the optimal solution by solving the master problem and these subproblems alternatingly.
Large Scale Interactive Fuzzy Multiobjective Programming: Decomposition Approaches by Masatoshi Sakawa
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