scholarly journals Dynamic multicriteria games' solutions: classical and untraditional approaches

2020 ◽  
Vol 12 (1) ◽  
pp. 19-32
Author(s):  
Анна Реттиева ◽  
Anna Rettieva
Keyword(s):  
Management Problem ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Classical Scheme

In this paper the approaches to obtain an optimal behavior in dynamic multicriteria games are constructed. Classical scheme with weighted sum of the criteria and new conceptions of optimal solutions' construction are presented. Dynamic multicriteria bioresorce management problem is considered. Parameters of the model where the equilibria obtained applying traditional or dynamic approaches coincide are obtained.

scholarly journals Dynamic Multicriteria Games with Finite Horizon

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 156 ◽  
Author(s):  
Anna Rettieva
Keyword(s):  
Nash Equilibrium ◽  
Finite Horizon ◽  
Nash Bargaining ◽  
Management Problem ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Cooperative Equilibrium

The approaches to construct optimal behavior in dynamic multicriteria games with finite horizon are presented. To obtain a multicriteria Nash equilibrium, the bargaining construction (Nash product) is adopted. To construct a multicriteria cooperative equilibrium, a Nash bargaining scheme is applied. Dynamic multicriteria bioresource management problem with finite harvesting times is considered. The players’ strategies and the payoffs are obtained under cooperative and noncooperative behavior.

scholarly journals COALITION FORMATION IN DYNAMIC MULTICRITERIA GAMES

2019 ◽  
Vol 10 (2) ◽  
pp. 40-61
Author(s):  
Анна Реттиева ◽  
Anna Rettieva
Keyword(s):  
Nash Equilibrium ◽  
Characteristic Function ◽  
Coalition Formation ◽  
Information Structure ◽  
Planning Horizon ◽  
Nash Bargaining ◽  
Management Problem ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Bargaining Procedure

In this paper new approaches to obtain optimal behavior in dynamic multicriteria games are constructed. The multicriteria Nash equilibrium is obtained via the Nash bargaining design (Nash products), and the cooperative equilibrium is determined by the Nash bargaining procedure for the entire planning horizon. Coalition formation process in dynamic multicriteria games is investegated. To construct the characteristic function the Nash bargaining scheme is applied where the multicriteria Nash equilibrium plays the role of the status-quo points. Two variants of characteristic function's determination that take into account information structure of the game are presented (models without information and with informed players). Dynamic multicriteria bioresorce management problem is considered. The players' strategies and the size of the resource are compared under cooperative and noncooperative behavior and for different variants of characteristic function determination.

Meta-Heuristic Structure for Multiobjective Optimization Case Study

2014 ◽  
pp. 38-58
Author(s):  
T. Ganesan ◽  
I. Elamvazuthi ◽  
K. Z. KuShaari ◽  
P. Vasant
Keyword(s):  
Performance Metrics ◽  
Heuristic Algorithms ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Green Sand ◽  
Weighted Sum Method ◽  
Real World Problem ◽  
Green Sand Mould System

In engineering optimization, one often encounters scenarios that are multiobjective (MO) where each of the objectives covers different aspects of the problem. It is hence critical for the engineer to have multiple solution choices before selecting of the best solution. In this chapter, an approach that merges meta-heuristic algorithms with the weighted sum method is introduced. Analysis on the solution set produced by these algorithms is carried out using performance metrics. By these procedures, a novel chaos-based metaheuristic algorithm, the Chaotic Particle Swarm (Ch-PSO) is developed. This method is then used generate highly diverse and optimal solutions to the green sand mould system which is a real-world problem. Some comparative analyses are then carried out with the algorithms developed and employed in this work. Analysis on the performance as well as the quality of the solutions produced by the algorithms is presented in this chapter.

Analysis and Modeling of Supply Chain Management of Fresh Products Based on Genetic Algorithm in E-commerce Environment

2020 ◽  
Author(s):  
Yaoting Chen
Keyword(s):  
Genetic Algorithm ◽  
Supply Chain ◽  
Weighted Sum ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Optimal Process ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Proposed Model ◽  
Fresh Products

Abstract BackgroundSupply chain provides the chance to enhance chain performances by decrease these uncertainties. It is a demand for some level of co-ordination of activities and processes within and between organization in the supply chain to decrease uncertainties and increase more cost for customers. Partner selection is an important issue in the supply chain management of fresh products in E-commerce environment. In this paper, we utilized a multi-objective genetic algorithm for evaluation supply chain of fresh products in E-commerce environment. ResultsThe proposed multi-objective genetic algorithm is to search the set of Pareto-optimal solutions for these conflicting objectives using by weighted sum approach. The proposed model suitable for fresh products in E-commerce environment to optimize supply chain are derived. The value of objective 1 (f1) performs approximately nonlinearly with the increasing the value of objective 2,3 and 4 (f2,f3 and f4). At the value of objective 1 of 3.2*105, f2, f3 and f4 is about 4.3*105, 86 and 5.6*104. When the value of objective 1 is increased to 7.6*105, the minimum f2, f3 and f4 is about 3.0*105, 38 and 2.56*104. It is noted that the value of objective 1 is increased from 6.4*105 to 7.6*105, the variation of f2, f3 and f4 is 11.7%, 17.4% and 3.4% respectively. It is pointed out that the variation of f2 and f3 with f1 and f4 is kept within obvious ranges. This practical result highlights the fact that the effects of the fact that effects of f2 and f3 are important factors affecting the performance supply chain network of fresh product in E-commerce environment.ConclusionsIn this paper, we utilized a multi-objective genetic algorithm for evaluation supply chain of fresh products in E-commerce environment. Four objectives for optimal process are included in the proposed model: (1) maximization of green appraisal score, (2) minimization of transportation time and total time comprised of product time, (3) maximization of average product quality, (4) minimization of transportation cost and total cost comprised of product cost. In order to evaluate optimal process, set of Pareto-optimal solutions is obtained based on the weighted sum method.

scholarly journals Heuristics and optimal solutions to the breadth–depth dilemma

2020 ◽  
Vol 117 (33) ◽  
pp. 19799-19808
Author(s):  
Rubén Moreno-Bote ◽  
Jorge Ramírez-Ruiz ◽  
Jan Drugowitsch ◽  
Benjamin Y. Hayden
Keyword(s):  
Risky Choice ◽  
Information Gathering ◽  
Square Root ◽  
Optimal Solutions ◽  
Limited Information ◽  
Finite Sample ◽  
Sharp Transition ◽  
Trade Off ◽  
Optimal Behavior ◽  
Capacity Model

In multialternative risky choice, we are often faced with the opportunity to allocate our limited information-gathering capacity between several options before receiving feedback. In such cases, we face a natural trade-off between breadth—spreading our capacity across many options—and depth—gaining more information about a smaller number of options. Despite its broad relevance to daily life, including in many naturalistic foraging situations, the optimal strategy in the breadth–depth trade-off has not been delineated. Here, we formalize the breadth–depth dilemma through a finite-sample capacity model. We find that, if capacity is small (∼10 samples), it is optimal to draw one sample per alternative, favoring breadth. However, for larger capacities, a sharp transition is observed, and it becomes best to deeply sample a very small fraction of alternatives, which roughly decreases with the square root of capacity. Thus, ignoring most options, even when capacity is large enough to shallowly sample all of them, is a signature of optimal behavior. Our results also provide a rich casuistic for metareasoning in multialternative decisions with bounded capacity using close-to-optimal heuristics.

Activity scheduling and resource allocation with uncertainties and learning in activities

2019 ◽  
Vol 119 (6) ◽  
pp. 1289-1320 ◽  
Author(s):  
Felix T.S. Chan ◽  
Zhengxu Wang ◽  
Yashveer Singh ◽  
X.P. Wang ◽  
J.H. Ruan ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Project Management ◽  
Manufacturing Industry ◽  
Learning Rate ◽  
Management Problem ◽  
Optimal Solutions ◽  
Resource Constrained ◽  
Nsga Ii ◽  
Content Type ◽  
Activity Schedule

Purpose The purpose of this paper is to develop a model which schedules activities and allocates resources in a resource constrained project management problem. This paper also considers learning rate and uncertainties in the activity durations. Design/methodology/approach An activity schedule with requirements of different resource units is used to calculate the objectives: makespan and resource efficiency. A comparisons between non-dominated sorting genetic algorithm – II (NSGA-II) and non-dominated sorting genetic algorithm – III (NSGA-III) is done to calculate near optimal solutions. Buffers are introduced in the activity schedule to take uncertainty into account and learning rate is used to incorporate the learning effect. Findings The results show that NSGA-III gives better near optimal solutions than NSGA-II for multi-objective problem with different complexities of activity schedule. Research limitations/implications The paper does not considers activity sequencing with multiple activity relations (for instance partial overlapping among different activities) and dynamic events occurring in between or during activities. Practical implications The paper helps project managers in manufacturing industry to schedule the activities and allocate resources for a near-real world environment. Originality/value This paper takes into account both the learning rate and the uncertainties in the activity duration for a resource constrained project management problem. The uncertainty in both the individual durations of activities and the whole project duration time is taken into consideration. Genetic algorithms were used to solve the problem at hand.

Comparison of Two Random Weight Generators for Multi-Objective Optimization

2016 ◽  
pp. 222-237
Author(s):  
Victor M. Carrillo ◽  
German Almanza
Keyword(s):  
Decision Maker ◽  
Optimal Solution ◽  
Multiple Objective ◽  
Heuristic Methods ◽  
Weighted Sum ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Mathematical Methods ◽  
Weighted Sum Method ◽  
Random Weight

There exist two general approaches to solve multiple objective problems. The first approach belongs to the classical mathematical methods: The weighted sum method, goal programming, or utility functions methods pertain to this approach. The output of mathematical methods is a single optimal solution. In the second approach are the heuristic methods, like the multiple objective evolutionary algorithms that offer the decision maker a set of optimal solutions usually called non- dominated or, Pareto-optimal solutions. This set is usually very large and the decision maker faces the problem of reducing the size of this set to a manageable number of solutions to analyze. In this paper the second approach is used to reduce the Pareto front using two weights generator for the non-numerical ranking preferences method and their performance is compared.

scholarly journals Rational Behavior in Dynamic Multicriteria Games

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1485
Author(s):  
Anna Rettieva
Keyword(s):  
Game Model ◽  
Bargaining Solution ◽  
Rational Behavior ◽  
Management Problem ◽  
Multicriteria Games ◽  
Cooperative Solution ◽  
Cooperative Equilibrium ◽  
Irrational Behavior ◽  
Common Resource ◽  
Behavior Condition

We consider a dynamic, discrete-time, game model where n players use a common resource and have different criteria to optimize. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To design a multicriteria cooperative equilibrium, a modified bargaining scheme that guarantees the fulfillment of rationality conditions is applied. The concept of dynamic stability is adopted for dynamic multicriteria games. To stabilize the multicriteria cooperative solution a time-consistent payoff distribution procedure is constructed. The conditions for rational behavior, namely irrational-behavior-proofness condition and each step rational behavior condition are defined for dynamic multicriteria games. To illustrate the presented approaches, a dynamic bi-criteria bioresource management problem with many players is investigated.

scholarly journals A Runtime Analysis of Typical Decomposition Approaches in MOEA/D Framework for Many-objective Optimization Problems

2021 ◽  
Author(s):  
Zhengxin Huang ◽  
Yuren Zhou ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Theoretical Analysis ◽  
Pareto Front ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Good Choice ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Penalty Parameter ◽  
Decomposition Approach ◽  
Popular Method

Decomposition approach is an important component in multi-objective evolutionary algorithm based on decomposition (MOEA/D), which is a popular method for handing many-objective optimization problems (MaOPs). This paper presents a theoretical analysis on the convergence ability of using the typical weighted sum (WS), Tchebycheff (TCH) or penalty-based boundary intersection (PBI) approach in a basic MOEA/D for solving two benchmark MaOPs. The results show that using WS, the algorithm can always find an optimal solution for any subproblem in polynomial expected runtime. In contrast, the algorithm needs at least exponential expected runtime for some subproblems if using TCH or PBI. Moreover, our analyses discover an obvious shortcoming of using WS, that is, the optimal solutions of different subproblems are easily corresponding to the same solution. In addition, this analysis indicates that if using PBI, a small value of the penalty parameter is a good choice for faster converging to the Pareto front, but it may lose the diversity. This study reveals some optimization behaviors of using three typical decomposition approaches in the well-known MOEA/D framework for solving MaOPs.

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