Fuzzy Random Noncooperative Two-level Linear Programming through Absolute Deviation Minimization Using Possibility and Necessity

This paper considers fuzzy random two-level linear programming problems under noncooperative behaviorof the decision makers. Having introduced fuzzy goals of decision makers together with the possibiliy and necessity measure, following absolute deviation minimization, fuzzy random two-level programin problems are transformed into deterministic ones. Extended Stackelberg solutions are introduced andcomputational methods are also presented

Computational Methodsfor Two-Level 0-1 Programming Problemsthrough Distributed Genetic Algorithms, Journal of Telecommunications and Information Technology, 2010, nr 2

In this paper, we consider a two-level 0-1 programming problem in which there is not coordination between the decision maker (DM) at the upper level and the decision maker at the lower level. We propose a revised computational method that solves problems related to computational methods for obtaining the Stackelberg solution. Specifically, in order to improve the computational accuracy of approximate Stakelberg solutions and shorten the computational time of a computational method implementing a genetic algorithm (GA) proposed by the authors, a distributed genetic algorithm is introduced with respect to the upper level GA, which handles decision variables for the upper level DM. Parallelization of the lower level GA is also performed along with parallelization of the upper level GA. The proposed algorithm is also improved in order to eliminate unnecessary computation during operation of the lower level GA, which handles decision variables for the lower level DM. In order to verify the effectiveness of the proposed method, we propose comparisons with existing methods by performing numerical experiments to verify both the accuracy of the solution and the time required for the computation

SOLVING TWO-LEVEL OPTIMIZATION PROBLEMS WITH APPLICATIONS TO ROBUST DESIGN AND ENERGY MARKETS

This dissertation provides efficient techniques to solve two-level optimization problems. Three specific types of problems are considered. The first problem is robust optimization, which has direct applications to engineering design. Traditionally robust optimization problems have been solved using an inner-outer structure, which can be computationally expensive. This dissertation provides a method to decompose and solve this two-level structure using a modified Benders decomposition. This gradient-based technique is applicable to robust optimization problems with quasiconvex constraints and provides approximate solutions to problems with nonlinear constraints. The second types of two-level problems considered are mathematical and equilibrium programs with equilibrium constraints. Their two-level structure is simplified using Schur's decomposition and reformulation schemes for absolute value functions. The resulting formulations are applicable to game theory problems in operations research and economics. The third type of two-level problem studied is discretely-constrained mixed linear complementarity problems. These are first formulated into a two-level mathematical program with equilibrium constraints and then solved using the aforementioned technique for mathematical and equilibrium programs with equilibrium constraints. The techniques for all three problems help simplify the two-level structure into one level, which helps gain numerical and application insights. The computational effort for solving these problems is greatly reduced using the techniques in this dissertation. Finally, a host of numerical examples are presented to verify the approaches. Diverse applications to economics, operations research, and engineering design motivate the relevance of the novel methods developed in this dissertation

Techniques for Optimum Design of Actively Controlled Structures Including Topological Considerations

The design and performance of complex engineering systems often depends on several conflicting objectives which, in many cases, cannot be represented as a single measure of performance. This thesis presents a multi-objective formulation for a comprehensive treatment of the structural and topological considerations in the design of actively controlled structures. The dissertation addresses three main problems. The first problem deals with optimum placement of actuators in actively controlled structures. The purpose of control is to reduce the vibrations when the structure is subjected to a disturbance. In order to mitigate the structural vibrations as quickly as possible, it is necessary to place the actuators at locations such that their ability to control the vibrations is maximized. Since the actuator locations are discrete (0-1) variables, a genetic algorithm based approach is used to solve the resulting optimization problem. The second problem this dissertation addresses is the multi-objective design of actively controlled structures. Structural weight, controller performance index and energy dissipated by the actuators are considered as the objective functions. It is assumed that a hierarchical structure exist between the actuator placement and structural-control design objective functions with the actuator placement problem considered being more important. The resulting multi-objective optimization problem is solved using Stackelberg game and cooperative game theory approaches. The exchange of information between different levels of the multi-level problem is done by constructing the rational reaction set of follower solution using design of experiments and response surface methods. The third problem addressed in this dissertation is the optimization of structural topology in the context of structural/control system design. Despite the recognition that an optimization of topology can significantly improve structural performance, most of the work in design of actively controlled structures has been done with structures of a known topology. The combined topology and sizing optimization of actively controlled structures is also considered in this thesis. The approach presented involves the determination of optimum topology followed by a sizing and control system optimization of the optimum topology. Using two numerical examples, it is shown that a simultaneous consideration of topological, control and structural aspects yields solutions that outperform designs when topological considerations are neglected

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Multi-parametric programming : novel theory and algorithmic developments

Imperial Users onl

Multilevel decision-making: A survey

© 2016 Elsevier Inc. All rights reserved. Multilevel decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a multiple level hierarchy. Significant efforts have been devoted to understanding the fundamental concepts and developing diverse solution algorithms associated with multilevel decision-making by researchers in areas of both mathematics/computer science and business areas. Researchers have emphasized the importance of developing a range of multilevel decision-making techniques to handle a wide variety of management and optimization problems in real-world applications, and have successfully gained experience in this area. It is thus vital that a high quality, instructive review of current trends should be conducted, not only of the theoretical research results but also the practical developments in multilevel decision-making in business. This paper systematically reviews up-to-date multilevel decision-making techniques and clusters related technique developments into four main categories: bi-level decision-making (including multi-objective and multi-follower situations), tri-level decision-making, fuzzy multilevel decision-making, and the applications of these techniques in different domains. By providing state-of-the-art knowledge, this survey will directly support researchers and practical professionals in their understanding of developments in theoretical research results and applications in relation to multilevel decision-making techniques

A reformulation strategy for mixed-integer linear bi-level programming problems

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature