Cooperative Game Theoretic Approach Research Articles

A multiobjective decision support system for multiresource forest management

A multiobjective and/or multiperson decision support system for analyzing multiresource forest management problems is developed in this paper. The procedure includes formulating the problem in a multiobjective and group decision making framework, and solving it using two solution techniques which consist of a distance-based compromise programming (CP) and a cooperative game theoretic approach of the Nash equilibrium type. The problem consists of five forest resources management objective functions to be maximized. Solving the problem using the two solution techniques enables determining a satisfactory compromise solution of the five forest resource management objectives. Sensitivity analysis of the two techniques shows compromise programming to be more sensitive to changes in the weight and the p-parameter of the technique while the cooperative game theoretic approach is relatively robust with respect to changes in the worst utility set.

Optimization of truss topology using tabu search

AbstractA design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross‐sections are assumed to be continuous, the topological optimization problem has mixed discrete‐continuous variables. This non‐linear programming problem is solved using a memory‐based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.

Single and multiobjective structural optimization in discrete‐continuous variables using simulated annealing

AbstractA multivariable optimization technique based on the Monte‐Carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems. This procedure, known as simulated annealing, draws an analogy between energy minimization in physical systems and objective function minimization in structural systems. The search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. Numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete‐continuous variables are presented. The influence of cooling schedule parameters on the optimum solutions obtained is discussed. Simulation results indicate that, in several instances, the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient‐based and discrete optimization techniques. The results also indicate that simulated annealing has substantial potential for additional applications in optimization, especially for problems with mixed discrete‐continuous variables.

DISCRETE AND CONTINUOUS VARIABLE STRUCTURAL OPTIMIZATION USING TABU SEARCH

A memory-based combinatorial optimization technique is adapted into a search procedure for solving single and multiobjective structural optimization problems. This approach, known as tabu search, employs two complementary mechanisms, namely tabu restrictions and aspiration criteria for constraining and guiding the search in the design space. A non-Markovian function utilizing recent search history is used to constrain the search by classifying certain moves as forbidden or tabu whereas a short term memory function, providing strategic forgetting, is used to free up the search process. Numerical results obtained using three different tabu search strategies for single and multiobjective design of structures with discrete-continuous variables are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that, in several instances, the optimum solutions obtained using tabu search outperform the optimum solutions obtaine...

A cooperative fuzzy game theoretic approach to multiple objective design optimization

The utility and applicability of cooperative game theory in an engineering design process is examined. It is shown how game theory may be used as a tool for solving multiple objective optimization (MOO) problems. The concepts in cooperative game theory and fuzzy set theory are combined to yield a new optimization method referred to herein as cooperative fuzzy games. The concept of cooperative fuzzy games can be applied to solve not only well- and ill-structured single and MOO problems, but also preliminary decision making and design problems where only a feasible solution is sought and no objective functions are specified. A completely general formulation capable of solving decision making problems with partly crisp and partly fuzzy objective functions, as well as partly crisp and partly fuzzy constraints is presented. It is shown that existing techniques for solving crisp and fuzzy mathematical programming problems are special cases of this general formulation. The computational procedure is illustrated via an application to a MOO problem dealing with the design of high speed mechanisms.

ROBUST DESIGN OF ACTIVELY CONTROLLED STRUCTURES USING COOPERATIVE FUZZY GAMES

Abstract The combined structural and control optimization problem for flexible space structures is formulated as a multiple objective optimization (MOO) problem. An improvement in robustness of active controlled structures through structural modifications is also addressed. The structural weight, controlled system energy, and robustness indices are considered as objective functions of the integrated structure/control design problem with cross-sectional areas of members treated as design variables. To model vague and imprecise information in the problem formulation, the tools of fuzzy set theory are employed. A new methodology for solving the resulting MOO problem, referred to herein as a cooperative fuzzy game theoretic approach is presented. It is shown that existing techniques for solving crisp and fuzzy optimization problems are special cases of the fuzzy game theoretic formulation. The computational procedure is demonstrated via an application to a twelve member ACOSS-FOUR space structure. The qualita...

A cooperative game of information trading: The core, the nucleolus and the kernel

A certain trade of the information about a technological innovation between the initial owner of the information andn identical producers is studied by means of a cooperative game theoretic approach. The information trading situation is modelled as a cooperative (n+1)-person game with side payments. The symmetrical strong ɛ-cores (including the core), the nucleolus and the kernel of the cooperative game model are determined. Interpretations of these game theoretic solutions and their implications for the information trading problem are given.