Pareto optimal policies for harvesting with multiple objectives

1980 ◽  
Vol 51 (3-4) ◽  
pp. 213-224 ◽  
Author(s):  
Roy Mendelssohn
Keyword(s):  
Multiple Objectives ◽  
Pareto Optimal ◽  
Optimal Policies

Model-Based Multi-Objective Reinforcement Learning by a Reward Occurrence Probability Vector

2020 ◽  
pp. 269-295
Author(s):  
Tomohiro Yamaguchi ◽  
Shota Nagahama ◽  
Yoshihiro Ichikawa ◽  
Yoshimichi Honma ◽  
Keiki Takadama
Keyword(s):  
Reinforcement Learning ◽  
Experimental Results ◽  
Previous Model ◽  
Pareto Optimal ◽  
Occurrence Probability ◽  
Contrast Model ◽  
Multi Objective ◽  
Model Based ◽  
Model Free ◽  
Optimal Policies

This chapter describes solving multi-objective reinforcement learning (MORL) problems where there are multiple conflicting objectives with unknown weights. Previous model-free MORL methods take large number of calculations to collect a Pareto optimal set for each V/Q-value vector. In contrast, model-based MORL can reduce such a calculation cost than model-free MORLs. However, previous model-based MORL method is for only deterministic environments. To solve them, this chapter proposes a novel model-based MORL method by a reward occurrence probability (ROP) vector with unknown weights. The experimental results are reported under the stochastic learning environments with up to 10 states, 3 actions, and 3 reward rules. The experimental results show that the proposed method collects all Pareto optimal policies, and it took about 214 seconds (10 states, 3 actions, 3 rewards) for total learning time. In future research directions, the ways to speed up methods and how to use non-optimal policies are discussed.

An Interactive Multistage ε-Inequality Constraint Method For Multiple Objectives Decision Making

1998 ◽  
Vol 120 (4) ◽  
pp. 678-686 ◽  
Author(s):  
N. Palli ◽  
S. Azarm ◽  
P. McCluskey ◽  
R. Sundararajan
Keyword(s):  
Decision Making ◽  
Optimal Solution ◽  
Inequality Constraint ◽  
Multiple Objectives ◽  
Feasible Region ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Pareto Optimal Set ◽  
Constraint Method ◽  
Multiple Objectives Decision Making

Multiple objectives decision making (MODM) in engineering design refers to obtaining a preferred optimal solution in the context of conflicting design objectives. Problems with multiple objectives do not have a unique optimal solution but a set of Pareto optimal solutions. This paper presents a new interactive multistage MODM method which captures a decision maker’s preference structure in order to obtain a preferred Pareto solution even for non-convex problems. Representative subsets of an entire Pareto optimal set are generated and expanded based on the decision maker’s preference. The ε-constraint method is used to constrain the multiple objectives problem based on the decision maker’s feedback. In addition, ideas from an interactive weighted Tchebycheff approach are applied to reduce the feasible region at each stage, ensuring that the process eventually converges to a preferred solution. The method is demonstrated with two examples: (i) a simple two-bar truss design, and (ii) a more complicated problem in power electronic module design.

An Interactive Multistage ε-Inequality Constraint Method for Multiple Objectives Decision Making

1998 ◽  
Author(s):  
N. Palli ◽  
P. McCluskey ◽  
S. Azarm ◽  
R. Sundararajan
Keyword(s):  
Decision Making ◽  
Optimal Solution ◽  
Inequality Constraint ◽  
Multiple Objectives ◽  
Feasible Region ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Pareto Optimal Set ◽  
Constraint Method ◽  
Multiple Objectives Decision Making

Abstract Multiple objectives decision making (MODM) in engineering design involves obtaining a preferred optimal solution in the context of conflicting design objectives. Problems with multiple objectives do not have a unique optimal solution but a set of Pareto optimal solutions. This paper presents a new interactive multistage MODM method which captures a decision maker’s preference structure in order to obtain a preferred Pareto solution even for non-convex problems. Representative subsets of an entire Pareto optimal set are generated and expanded based on the decision maker’s preference. The ε-constraint method is used to constrain the multiple objectives problem based on the decision maker’s feedback. In addition, ideas from an interactive weighted Tchebycheff approach are applied to reduce the feasible region at each stage, ensuring that the process eventually converges to a preferred solution. The method is demonstrated with two examples: (i) a simple two-bar truss design, and (ii) a more complicated problem of power electronic module design.

Grillage Optimization with Multiple Objectives

2006 ◽  
Vol 306-308 ◽  
pp. 517-522
Author(s):  
Ki Sung Kim ◽  
Kyung Su Kim ◽  
Ki Sup Hong
Keyword(s):  
Structural Optimization ◽  
Structural Design ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Pareto Optimal Solution ◽  
Multiple Objectives ◽  
Pareto Optimal ◽  
Design Environment ◽  
Design Problems ◽  
Solution Methods

The structural design problems are acknowledged to be commonly multicriteria in nature. The various multicriteria optimization methods are reviewed and the most efficient and easy-to-use Pareto optimal solution methods are applied to structural optimization of grillages under lateral uniform load. The result of the study shows that Pareto optimal solution methods can easily be applied to structural optimization with multiple objectives, and the designer can have a choice from those Pareto optimal solutions to meet an appropriate design environment.

Bicriterion Optimization of an M/G/1 Queue with A Removable Server

1996 ◽  
Vol 10 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Dong J. Kim
Keyword(s):  
Operating Cost ◽  
Operating Costs ◽  
Pareto Optimal ◽  
Removable Server ◽  
Optimal Policies ◽  
Average Operating ◽  
Bicriterion Optimization ◽  
Number Of Customers

This paper studies bicriterion optimization of an M/G/1 queue with a server that can be switched on and off. One criterion is an average number of customers in the system, and another criterion is an average operating cost per unit time. Operating costs consist of switching and running costs. We describe the structure of Pareto optimal policies for a bicriterion problem and solve problems of optimization of one of these criteria under a constraint for another one.

Pareto Optimality in Electoral Competition

1971 ◽  
Vol 65 (4) ◽  
pp. 1141-1145 ◽  
Author(s):  
Peter C. Ordeshook
Keyword(s):  
Pareto Optimality ◽  
Pareto Optimal ◽  
Mixed Strategies ◽  
Zero Sum Games ◽  
The Core ◽  
Equilibrium Strategies ◽  
Optimal Policies ◽  
Optimal Allocations ◽  
Zero Sum ◽  
Pareto Optimal Allocations

The core of welfare economics consists of the proof that, for certain classes of goods, perfectly competitive markets are efficient in that they provide Pareto optimal allocations of these goods. In this paper, the efficiency of competitive elections is examined. Elections are modeled as two-candidate zero-sum games, and three kinds of equilibria for such games are identified: pure, risky, and mixed strategies. It is shown, however, that regardless of which kind of equilibrium prevails, if candidates adopt equilibrium strategies, an election is efficient in the sense that the candidates advocate Pareto optimal policies. But one caveat to this analysis is that while an election is Pareto optimal, citizens can unanimously prefer markets to elections as a mechanism for selecting future policies.

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