Optimal solutions in weakly coupled multiple decision maker Markov chains with nonclassical information

2003 ◽  
Author(s):  
R. Srikant ◽  
T. Basar
Keyword(s):  
Markov Chains ◽  
Decision Maker ◽  
Optimal Solutions ◽  
Weakly Coupled ◽  
Nonclassical Information

scholarly journals A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Alberto Pajares ◽  
Xavier Blasco ◽  
Juan M. Herrero ◽  
Gilberto Reynoso-Meza
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Decision Maker ◽  
Pareto Front ◽  
Optimization Problem ◽  
Engineering Problem ◽  
Multiobjective Optimization Problem ◽  
Optimal Solutions ◽  
Multiobjective Genetic Algorithm ◽  
Pi Controllers

Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision-maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision-maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision-making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.

scholarly journals A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

2015 ◽  
Vol 10 (4) ◽  
pp. 508 ◽  
Author(s):  
Ernestas Filatovas ◽  
Dmitry Podkopaev ◽  
Olga Kurasova
Keyword(s):  
Multiobjective Optimization ◽  
Dimensionality Reduction ◽  
Decision Maker ◽  
Optimization Problem ◽  
Interactive Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Visualization Technique ◽  
Preference Information ◽  
Optimal Set

<pre>Interactive methods of <span>multiobjective</span> optimization repetitively derive <span>Pareto</span> optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the <span>Pareto</span> optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS.</pre>

A Preference-Based Multiobjective Evolutioary Algorithm for Finding Knee Solutions

2015 ◽  
Vol 781 ◽  
pp. 559-563 ◽  
Author(s):  
Sufian Sudeng ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Evolutionary Algorithm ◽  
Decision Maker ◽  
Test Problems ◽  
Optimal Solutions ◽  
View Point ◽  
Controller Parameter ◽  
Multi Objective

The aim of this paper is to develop a knee-based Multi-Objective Evolutionary Algorithm (MOEA) which is a method to find optimal solutions focusing on knee regions. The knee solutions are very interesting to the decision maker (DM) when he/she does not have an explicit preference. The proposed approach uses the extended angle-based dominance concept to guide the search towards knee regions. The extent of the obtained solutions can be controlled by the means of user-supplied density controller parameter. The approach is demonstrated with two and three-objective knee-based test problems. The results have shown that our approach is competitive to well-known knee-based MOEAs in convergence view point.

scholarly journals Towards Interactive Evolution: A Distributed Optimiser for Multi-Objective Water Distribution Network Design

10.29007/ltkb ◽  
2018 ◽  
Author(s):  
David Walker ◽  
Matthew Johns ◽  
Ed Keedwell ◽  
Dragan Savic
Keyword(s):  
Evolutionary Algorithms ◽  
Network Design ◽  
Decision Maker ◽  
Water Distribution ◽  
Water Distribution Network ◽  
Distribution Networks ◽  
Benchmark Problems ◽  
Optimal Solutions ◽  
Human Decision ◽  
Water Distribution Network Design

It is well known that water distribution networks can be optimised by evolutionary algorithms. However, while such optimisation can result in mathematically optimal solutions, the ability of the algorithm to generate novelty can often lead to solutions that are not practical for implementation. This work describes a distributed optimisation platform that will enable the inclusion of a human decision maker in the optimisation process. The architecture of the platform is described, and examples of its execution on benchmark problems is described, using an automated client that interacts with the platform in lieu of a human decision maker.

scholarly journals A Decision Making Approach for Multi-Objective Optimization Considering A Trade-off Method

2017 ◽  
Vol 11 (2) ◽  
pp. 178-189
Author(s):  
Tipwimol Sooktip ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Decision Maker ◽  
Optimization Problem ◽  
Benchmark Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Multi Objective ◽  
Component Allocation ◽  
Objective Value ◽  
Preferred Solutions

In multi-objective optimization problem, a set of optimal solutions is obtained from an optimization algorithm. There are many trade-off optimal solutions. However, in practice, a decision maker or user only needs one or very few solutions for implementation. Moreover, these solutions are difficult to determine from a set of optimal solutions of complex system. Therefore, a trade-off method for multi-objective optimization is proposed for identifying the preferred solutions according to the decision maker’s preference. The preference is expressed by using the trade-off between any two objectives where the decision maker is willing to worsen in one objective value in order to gain improvement in the other objective value. The trade-off method is demonstrated by using well-known two-objective and three-objective benchmark problems. Furthermore, a system design problem with component allocation is also considered to illustrate the applicability of the proposed method. The results show that the trade-off method can be applied for solving practical problems to identify the final solution(s) and easy to use even when the decision maker lacks some knowledge or not an expert in the problem solving. The decision maker only gives his/her preference information.  Then, the corresponding optimal solutions will be obtained, accordingly.

Control of weakly-coupled Markov chains

1980 ◽  
Author(s):  
D. Teneketzis ◽  
S. Javid ◽  
B. Sridhar
Keyword(s):  
Markov Chains ◽  
Weakly Coupled

GraphMDP: A NEW DECOMPOSITION TOOL FOR SOLVING MARKOV DECISION PROCESSES

2001 ◽  
Vol 10 (03) ◽  
pp. 325-343 ◽  
Author(s):  
PIERRE LAROCHE
Keyword(s):  
Approximate Solution ◽  
Markov Decision Processes ◽  
Mobile Robotics ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Decomposition Techniques ◽  
Weakly Coupled ◽  
Markov Decision ◽  
Local Solutions ◽  
Reduced Time

In this paper, we present a new tool for solving weakly-coupled Markov Decision Processes using decomposition techniques. Using a predefined partition of the MDP, a directed graph is built to decompose the global MDP into small local MDPs which are independently solved. An approximate solution for the global MDP is obtained by combining local solutions. Our approach has been tested on a mobile robotics application. It allows near-optimal solutions to be obtained in significantly reduced time. We also present preliminary results concerning a parallel implantation of our tool.

scholarly journals New Reference-Neighbourhood Scalarization Problem for Multiobjective Integer Programming

2013 ◽  
Vol 13 (1) ◽  
pp. 104-114 ◽  
Author(s):  
Krasimira Genova ◽  
Leonid Kirilov ◽  
Vasil Guljashki
Keyword(s):  
Integer Programming ◽  
Decision Maker ◽  
Multicriteria Optimization ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Additional Information ◽  
Multicriteria Problems ◽  
Computing Complexity

Abstract Scalarization is a frequently used approach for finding efficient solutions that satisfy the preferences of the Decision Maker (DM) in multicriteria optimization. The applicability of a scalarization problem to solve integer multicriteria problems depends on the possibilities it provides for the decrease of the computing complexity in finding optimal solutions of this class of problems. This paper presents a reference-neighbourhood scalarizing problem, possessing properties that make it particularly suitable for solving integer problems. One of the aims set in this development has also been the faster obtaining of desired criteria values, defined by the DM, requiring no additional information by him/her. An illustrative example demonstrates the features of this scalarizing problem.

scholarly journals An Improved Parallelized Multi-Objective Optimization Method for Complex Geographical Spatial Sampling: AMOSA-II

2020 ◽  
Vol 9 (4) ◽  
pp. 236
Author(s):  
Xiaolan Li ◽  
Bingbo Gao ◽  
Zhongke Bai ◽  
Yuchun Pan ◽  
Yunbing Gao
Keyword(s):  
Markov Chains ◽  
Optimization Problems ◽  
Optimization Method ◽  
Spatial Sampling ◽  
Computational Time ◽  
Test Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Complex geographical spatial sampling usually encounters various multi-objective optimization problems, for which effective multi-objective optimization algorithms are much needed to help advance the field. To improve the computational efficiency of the multi-objective optimization process, the archived multi-objective simulated annealing (AMOSA)-II method is proposed as an improved parallelized multi-objective optimization method for complex geographical spatial sampling. Based on the AMOSA method, multiple Markov chains are used to extend the traditional single Markov chain; multi-core parallelization technology is employed based on multi-Markov chains. The tabu-archive constraint is designed to avoid repeated searches for optimal solutions. Two cases were investigated: one with six typical traditional test problems, and the other for soil spatial sampling optimization applications. Six performance indices of the two cases were analyzed—computational time, convergence, purity, spacing, min-spacing and displacement. The results revealed that AMOSA-II performed better which was more effective in obtaining preferable optimal solutions compared with AMOSA and NSGA-II. AMOSA-II can be treated as a feasible means to apply in other complex geographical spatial sampling optimizations.

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