• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.367-380
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• 2019

The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.3
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• pp.403-410
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• 2009

The aim of this research is to develop the Bees Algorithm named 'the dynamic allocated Bees Algorithm' for multi-objective problem, especially in order to be suit for Pareto optimality. In addition two new neighbourhood search methods have been developed to produce enhanced solutions for a multi-objective problem named 'random selection neighbourhood search' and 'weighted sum neighbourhood search' and they were compared with the basic neighbourhood search in the dynamic allocated Bees Algorithm. They were successfully applied to an Environmental/Economic (electric power) dispatch (EED) problem and simulation results presented for the standard IEEE 30-bus system and they were compared to those obtained using other approaches. The comparison shows the superiority of the proposed dynamic allocated Bees Algorithms and confirms its suitability for solving the multi-objective EED problem.

• Journal of Communications and Networks
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• v.17 no.4
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• pp.440-448
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• 2015

In this paper, we study the problem of selfish behavior of secondary users (SUs) based on cognitive radio (CR) with the presence of primary users (PUs). SUs are assumed to contend on a channel using the carrier sense multiple access with collision avoidance (CSMA/CA) and PUs do not consider transmission of SUs, where CSMA/CA protocols rely on the random deference of packets. SUs are vulnerable to selfish attacks by which selfish users could pick short random deference to obtain a larger share of the available bandwidth at the expense of other SUs. In this paper, game theory is used to study the systematic cheating of SUs in the presence of PUs in multichannel CR networks. We study two cases: A single cheater and multiple cheaters acting without any restraint. We identify the Pareto-optimal point of operation of a network with multiple cheaters and also derive the Nash equilibrium of the network. We use cooperative game theory to drive the Pareto optimality of selfish SUs without interfering with the activity of PUs. We show the influence of the activity of PUs in the equilibrium of the whole network.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.4
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• pp.613-624
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• 2021

This paper analyzes the relationship between income distribution and energy consumption from a Pareto optimal approach. For this purpose, the causality relationship between electricity consumption per capita (kWh) with respect to country groups and energy consumption per capita (kg of oil equivalent) along with gross domestic product per capita was analyzed. In addition to this purpose, a Pareto analysis was conducted to determine the countries with the highest per capita national income, how much of the world total energy they consume, and whether the law of power in the energy and electricity markets exists. Finally, the impact of official development assistance provided to low-income countries by high-income countries on the low-income countries' electricity and energy consumption was analyzed. In other words, it was questioned whether pareto redistribution policies serve the purpose or not. The Engle-Granger causality approach was used in the analysis of the causality relationship between variables. Our analysis indicated that, first, the energy data of the country groups may be inadequate in revealing income inequalities. Second, the existence of Pareto law of power and global income inequality can be explained based on energy data. Finally, Pareto optimal redistribution policies to eliminate income inequality remain inadequate in practice.

• Journal of Power Electronics
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• v.12 no.1
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• pp.104-112
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• 2012

In this paper a new method for the design of a simple PI controller is presented and it has been applied in the control of a Boost based PFC rectifier. The Strength Pareto evolutionary algorithm, which is based on the Pareto Optimality concept, used in Game theory literature is implemented as a multi-objective optimization approach to gain a good transient response and a high quality input current. In the proposed method, the input current harmonics and the dynamic response have been assumed as objective functions, while the PI controller's gains of the PFC rectifier (Kpi, Tpi) are design variables. The proposed algorithm generates a set of optimal gains called a Pareto Set corresponding to a Pareto Front, which is a set of optimal results for the objective functions. All of the Pareto Front points are optimum, but according to the design priority objective function, each one can be selected. Simulation and experimental results are presented to prove the superiority of the proposed design methodology over other methods.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.93.3-93
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• 2002

$\textbullet$ Co-evolutionary algorithms $\textbullet$ Nash Genetic Algorithms $\textbullet$ Multi-objective Optimization $\textbullet$ Distance dependent mutation $\textbullet$ Pareto Optimality

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.1
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• pp.26-35
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• 1987

As an attempt to make the multi-objection for the line design of the rope way, the resulted formulas from the catenary curve as exact ones were summarized, and it was found out that the Kuhn-Tucker's optimality conditions and regions of the objective functions can analytically be expressed with dimensionless parameters. The Pareto's optimum solution set was analytically obtained through the objective function-the minimum relation of $W^{*}$, and $W^{*}$ is a trade-off relation. From this, The dimension of a rope and the value of an initial tension that are the standard in design of the rope way were determined. It was concluded that $V^{*}$ should become minimum, and that the ratio of the dimension of rope to the value of and initial tension become larger than superposition factor corresponding to curve AB.to curve AB.

• Hwankyungkyoyuk
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• v.13 no.2
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• pp.38-50
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• 2000

We are evidently Home Economicus, egoistic rational utility maximiger, and all the capitalism economic situation make us adapt to such life, and recognize that it is rational to act like that. This can be demonstrated in Prisoner′s Dilemma(PD) which always select the non-cooperative choice for free rider in rational selection process of public goods. This paper notice the "what is problem\ulcorner"The problem is not in free rider itself but in free rider egoism. The practical behavior of free rider egoism can be explained by way of Prisoner′s Dilemma. In PD situation, the prisoner makes a rational choice, non-cooperative alternative, but he doesn′arrive at preto-optimality. It is dilemma. Why can′t he arrive \ulcorner Because he is isolated from other prisoner. So we call it prisoner′s dilemma. The PD situation can be compared with our real economic life, which, we think, have kept by rational choice of the public goods. We actually have made our life as an individual one although we organized communities of capitalism. Of course, we know each others as members of same society, but each individual being can′t secure the belief, which has composed basis of community. So, it is very similar and common between PD situation and our real economic life in the production of public goods. We conclude that this non-cooperative process of PD situation can be utilized as instrument of EE. So this non-cooperative process can show us the effectiveness of EE as follows. \circled1 Game situation life PD can be used as good instrument for explaining the rational selection dilemma(error) to Homo-Economicus, the rational agent, with the optimal and rational language. \circled2 We can show that the selection result is dilemma, not arrive pareto - optimality. \circled3 The dilemma can be resolved with accomplishing the good communal life based on the belief, not on the isolation.

• Management Science and Financial Engineering
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• v.13 no.2
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• pp.29-46
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• 2007

This paper makes an attempt to compare the two important methods for finding solutions of multi-item inventory problem with more than one conflicting objectives. Panda et al.[9] discusses a distance-based method to find the best possible compromise solution with variation of priority under the given weight structure. In this paper, the problem in [9] is revisited through the Pareto-optimal front of genetic algorithm with the help of a situation of retail stocking of FMCG business. The advantages of using the solutions from the perspective of the decision maker obtained through multi-objective optimization are highlighted in terms of population search, weighted goals and priority structure, cost, set of compromise solutions along with prevention of stock-out situation.