Decomposition of satisficing decision problems

This paper intends to clarify the decomposition of satisficing (decision) problems. Many researchers have studied the several aspects of satisficing problems verbal-logically (e.g. Cyert and March [2]; Simon [12]; Simon, Smithburgh, and Thompson [13]) or mathematically (e.g. Charnes and Cooper [1]; Ijiri [4]), and a formulation of satisficing problems under true uncertainty was done about one decade ago by M. D. Mesarovic and his group (e.g. Mesarovic, Macko, and Takahara [9]; Mesarovic and Takahara [10]). Its fundamental properties have been studied qualitatively by Matsuda and Takatsu [6–8]. However, the decomposition of satisficing problems has not been explicitly mentioned anywhere, even though implicit discussions have been given. Without the decomposition principles, we cannot solve large-scale satisficing problems, and cannot analyze or design coordination processes of hierarchical systems with satisficing problems as overall decision problems. Our study is mainly concentrated on the decomposition. Our results are somewhat restricted, because we deal with satisficing problems of relatively manageable forms. However, we can develop more sophisticated decompositions by combining our decomposition principles or by adding the other assumptions to our formulations. The results will be a starting point of a more complete study of satisficing decision problem solving.     

Decomposition methods in multiobjective discrete-time dynamic problems

Decomposition methods for multicriteria dynamic (discrete-time) problems are derived. In these methods, the original problem is reduced to a series of multicriteria subproblems related to individual stages. Hence, the dimensionality of decision variables in each subproblem is smaller than in the original problem. The following decomposition procedures for such problems are developed: (1) a dynamic programming method, (2) a two-point boundary value problem method, (3) multilevel methods, and (4) the formulation of a temporal hierarchy. For completeness, methods for multicriteria dynamic problems are reviewed that, at the outset, transform a problem into a series of single-objective problems. Formulation of the multiobjective problem in the context of a multilayer temporal hierarchy is also presented. The temporal structure motivates problem simplification by decomposing the overall decision-making problem according to relative time scales.     

Decomposition of integrated scheduling and dynamic optimization problems using community detection

In this paper the decomposition of the integrated cyclic scheduling and dynamic optimization problem is analyzed using community detection. Different production systems are examined and based on the results of the community detection and the centrality of the constraint unipartite graph, a two level hierarchical structure is identified, with the scheduling problem in the first level and the dynamic optimization subproblems in the second level. The variables that link the two levels are continuous and obtained from the results of the community detection. Finally, Generalized Benders Decomposition is applied on the decomposed optimization problem obtained from the community detection and a solution is obtained faster than solving the problem monolithically.     

Group decision making problems in a linguistic and dynamic context

The aim of this paper is to present a new model of decision support system for group decision making problems based on a linguistic approach and dynamic sets of alternatives. The model incorporates a mechanism that allows to manage dynamic decision situations in which some information about the problem is not constant in time. We assume that the set of alternatives can change during the decision making process. The model is presented in a mobile and dynamic context where the experts’ preferences can be incomplete. The linguistic approach is used to represent both the experts’ preferences about the alternatives and the agreement degrees to manage the change of some alternatives. A prototype of such mobile decision support system in which the experts use mobile devices to provide their linguistic preferences at anytime and anywhere has been implemented. In such a way, we provide a new linguistic group decision making framework that is mobile and dynamic.     

An algorithmic approach to group decision making problems under fuzzy and dynamic environment

Our paper introduces a new methodology to solve group decision-making problems under fuzzy and dynamic environment. The methodology takes group members’ linguistically defined pair wise preferences of alternatives in different time intervals and aggregates them across the intervals to obtain each member's net preference levels. Each member's net preference levels are again aggregated across the members to obtain the group's preference. Our paper attaches higher importance to the members whose involvement in the decision process is more recent than the members who opined their views in the past. The fuzzy aggregation operator, IOWA (Induced Ordered Weighted Average) is used to aggregate their views in accordance to their importance in the group. The Ranked_List algorithm, introduced in our paper, inputs the aggregated views of the members in pair wise form and produces the set of sequences of ranked list of alternatives representing the group's consensus view as output. The Ranked_List algorithm is validated and analyzed through a series of synthetic data sets and its results are compared with a movie selection case study. The methodology is illustrated with a numerical example.     

Decomposition of heterogeneous classification problems

In some classification problems the feature space is heterogeneous in that the best features on which to base the classification are different in different parts of the feature space. In some other problems the classes can be divided into subsets such that distinguishing one subset of classes from another and classifying examples within the subsets require very different decision rules, involving different sets of features. In such heterogeneous problems, many modeling techniques (including decision trees, rules, and neural networks) evaluate the performance of alternative decision rules by averaging over the entire problem space, and are prone to generating a model that is suboptimal in any of the regions or subproblems. Better overall models can be obtained by splitting the problem appropriately and modeling each subproblem separately.This paper presents a new measure to determine the degree of dissimilarity between the decision surfaces of two given problems, and suggests a way to search for a strategic splitting of the feature space that identifies regions with different characteristics. We illustrate the concept using a multiplexor problem, and apply the method to a DNA classification problem.     

Three-level Stackelberg decision problems

Three-level Stackelberg decision problems are studied by using the inducible region concept. Through a systematic derivation, it is identified that the leader's control has dual purposes, which in general are not separable. A special class of problems is then considered, where explicit results are obtained.     

信号灯控制的多阶段决策模型及其前向动态规划算法

为研究路口交通信号灯的实时最优控制问题,提出一种以最小化等待时间为目标的多阶段决策模型.该模型利用最短绿灯和红灯时间的结构特征,通过合理选择系统状态和控制变量压缩了模型规模,进而提出了前向动态规划算法以高效得到最优解.数值实验显示,对比于固定时长的周期性控制可以节省路口车辆的等待时间;对比基于混合整数规划的求解方法,可以提高求解效率,满足实时控制的要求.     

动态影响图模型研究

部分可观察马尔可夫决策过程在策略空间和状态空间上的计算复杂性,使求解其一个最优策略成为NP-hard难题.为此,提出一种动态影响图模型来建模不确定环境下的Agent动态决策问题.动态影响图模型以有向无环图表示系统变量之间的复杂关系.首先,动态影响图利用动态贝叶斯网络表示转移模型和观察模型以简化系统的状态空间;其次,效用函数以效用结点的形式清晰地表示出来,从而简化系统效用函数的表示;最后,通过决策结点表示系统的行为来简化系统的策略空间.通过实例从3个方面和POMDP模型进行了比较,研究的结果表明,动态影响图模型为大型的POMDP问题提供了一种简明的表示方式,最后在Robocup环境初步验证了该模型.     

Cognitive biases and time stress in team decision making

This experiment investigates the impart of time stress on the decision making performance of command and control teams. Two person teams were trained to execute a set of simple decision procedures. Some of these procedures required subjects to make judgments that were inconsistent with normal heuristic decision processing. The principal hypothesis was that these decision procedures would be vulnerable-to-bias, and would therefore be more vulnerable to the effects of time stress than other decision procedures. The results support this hypothesis. In addition, the results suggest that the subjects adapted inappropriately to time stress. As time stress increased, they began to use a decision processing strategy that was less effective than the strategy they were trained to use     

Ultrafuzzy team decisions in a dynamic environment

In this paper, the concept of fuzzy sets of type 2 is introduced and the team decision processes which contain ultrafuzzy states, ultrafuzzy information structures, ultrafuzzy information signals, ultrafuzzy decision rules, and ultrafuzzy actions are formulated. After some definitions of fuzzy relations of type 2, fuzzy sets of type 2 induced by mappings, composition, Cartesian product, ultrafuzzy mappings, and ultrafuzzy functions, a model of ultrafuzzy team decision in a dynamic environment is proposed. The team decision problem under ultrafuzzy constraints is dealt with. Some results on fuzzy sets of type 2 induced by mappings are given.     

The dynamic linear exponential Gaussian team problem

The dynamic team problem for a linear system with Gaussian noise, exponential of a quadratic performance index, and one-step delayed sharing information pattern is considered. It is shown, via dynamic programming, that the multistage problem can be decomposed into a series of static team problems. Moreover, the optimal policy of theith team member at timekis an affine function of both the one-step predicted Kalman filter estimate and theith team member's observation at timek. Efficient algorithms are available for determining the gains of this affine controller. This model and solution are applied to an approximate resource allocation problem associated with a defense network, and a numerical example is discussed.     

A multimodel approach to stochastic team problems

This paper develops decentralized team strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.     

Nonlinear robust control and minimax team problems

The problem of robust stabilization of a linear system leads to the classical ℋ︁_∞ control problem. The same analysis applied to a nonlinear system leads to the problem of ensuring via output feedback that a nonlinear operator be Lipshitz continuous, with a prescribed Lipshitz modulus. We show that, in the same way as the ℋ︁_∞ control problem is equivalent to a minimax control problem, the Lipshitz modulus control problem can be approached via a minimax team decision problem. This motivates us to re-visit a class of the so-called ‘static’ team decision problems for nonlinear dynamical control systems. Because of the ‘static’ character, signaling plays no role in that case, which is important for the equivalence with the Lipshitz modulus control problem. We show that under some conditions, a certainty equivalence principle applies that yields a practical solution to the team problem at hand. To reach that conclusion we must first investigate a ‘partial team’ problem where one of the team members has all the information. Copyright © 1999 John Wiley & Sons, Ltd.     

Multi-objective optimization and decision making approaches to cricket team selection

Selection of players for a sports team within a finite budget is a complex task which can be viewed as a constrained multi-objective optimization and a multiple criteria decision making problem. The task is specially challenging for the game of cricket where a team requires players who are efficient in multiple roles. In the formation of a good and successful cricket team, batting strength and bowling strength of a team are major factors affecting its performance and an optimum trade-off needs to be reached. We propose a novel gene representation scheme and a multi-objective approach using the NSGA-II algorithm to optimize the overall batting and bowling strength of a team with 11 players as variables. Fielding performance and a number of other cricketing criteria are also used in the optimization and decision-making process. Using the information from the trade-off front obtained, a multi-criteria decision making approach is then proposed for the final selection of team. Case studies using a set of players auctioned in Indian Premier League (IPL) 4th edition are illustrated and players’ current statistical data is used to define performance indicators. The proposed computational techniques are ready to be extended according to individualistic preferences of different franchises and league managers in order to form a preferred team within the budget constraints. It is also shown how such an analysis can help in dynamic auction environments, like selecting a team under player-by-player auction. The methodology is generic and can be easily extended to other sports like American football, baseball and other league games.     

A decentralized team decision problem with an exponential cost criterion

A static decentralized team is represented by the nodes of a network working together to optimize the expected value of an exponential of a quadratic function of the state and control variables. The information consists of known linear functions of the normally distributed state corrupted by additive Gaussian noise. For certain ranges of the system parameters, the stationary condition for optimality is satisfied by a linear decision rule operating on the available information. These stationary conditions reduce to a set of algebraic matrix equations and a matrix inequality condition from which the values of the decision gains are determined. Although the stationary conditions are necessary for the linear control law to be minimizing in the class of nonlinear control laws, sufficiency is obtained for our linear controller to be minimizing in the class of linear control laws. Since the quadratic performance criterion produces the only previously known closed form decentralized decision rule, the exponential criterion is an important generalization.     

Continuous logic and combinatorial problems decision

A class of combinatorial problems equivalent to mutual arrangement of N interval sequences is described. It is shown that a finite dynamic automaton without memory is an adequate mathematic model of the solution of the posed problem, and continuous logic is an appropriate mathematic tool. The solution algorithms are constructed. An example is given.