• International Journal of Control, Automation, and Systems
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• v.2 no.2
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• pp.247-255
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• 2004

The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known as Pareto-optimal solutions. The use of evolutionary algorithms Pareto GA, which was first introduced by Goldberg in 1989, has now become a sort of standard in solving Multiobjective Optimization Problems (MOPs). Though this approach was further developed leading to numerous applications, these applications are based on Pareto ranking and employ the use of the fitness sharing function to maintain diversity. Another scheme for solving MOPs has been presented by J. Nash to solve MOPs originated from Game Theory and Economics. Sefrioui introduced the Nash Genetic Algorithm in 1998. This approach combines genetic algorithms with Nash's idea. Another central achievement of Game Theory is the introduction of an Evolutionary Stable Strategy, introduced by Maynard Smith in 1982. In this paper, we will try to find ESS as a solution of MOPs using our game model based co-evolutionary algorithm. First, we will investigate the validity of our co-evolutionary approach to solve MOPs. That is, we will demonstrate how the evolutionary game can be embodied using co-evolutionary algorithms and also confirm whether it can reach the optimal equilibrium point of a MOP. Second, we will evaluate the effectiveness of our approach, comparing it with other methods through rigorous experiments on several MOPs.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2246-2251
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• 2003

This paper proposes shape design of frame structures for vibration suppression and weight reduction. The $H_{\infty}$ norm of the transfer function from disturbance sources to the output points where vibration should be suppressed, is adopted as the performance index to represent the magnitude of vibration transfer. The design parameters are the node positions of the frame structure, on which constraints are imposed so that the structure achieves given tasks. For computation of Pareto optimal solutions to the two-objective design problem, a number of linear combinations of the $H_{\infty}$ norm and the total weight of the structure are considered and minimized. For minimization of the scalared objective function, a Lagrange function is defined by the objective function and the imposed constraints on the design parameters. The solution for which the Lagrange function satisfies the Karush-Kuhn-Tucker condition, is searched by the sequential quadratic programming (SQP) method. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1219-1224
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• 2004

In this study the optimization of plate-fin type heat sink with vortex generator for thermal stability is conducted numerically. To acquire the optimal design variables, the CFD and mathematical optimization are integrated. The flow and thermal fields are predicted using the finite volume method. The optimization is carried out by means of the sequential quadratic programming (SQP) method. The results show that when the temperature rise is less than 40 K, the optimal design variables are as follows; $B_1=2.584mm$, $B_2=1.741mm$, and t = 7.914 mm. Comparing with the initial design, the temperature rise is reduced by 4.2 K, while the pressure drop is increased by 9.43 Pa. The Pareto optimal solutions are also presented between the pressure drop and the temperature rise.

• International Journal of Computer Science & Network Security
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• v.21 no.3
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• pp.304-310
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• 2021

The paper presents problems of optimization of the synthesis of embedded systems, in particular Pareto optimization. The model of such a system for its design for high-level of abstract is based on the classic approach known from the theory of task scheduling, but it is significantly extended, among others, by the characteristics of tasks and resources as well as additional criteria of optimal system in scope structure and operation. The metaheuristic algorithm operating according to this model introduces a new approach to system synthesis, in which parallelism of task scheduling and resources partition is applied. An algorithm based on a genetic approach with simulated annealing and Boltzmann tournaments, avoids local minima and generates optimized solutions. Such a synthesis is based on the implementation of task scheduling, resources identification and partition, allocation of tasks and resources and ultimately on the optimization of the designed system in accordance with the optimization criteria regarding cost of implementation, execution speed of processes and energy consumption by the system during operation. This paper presents examples and results for multi-criteria optimization, based on calculations for specifying non-dominated solutions and indicating a subset of Pareto solutions in the space of all solutions.

• Journal of Electrical Engineering and Technology
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• v.9 no.2
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• pp.423-432
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• 2014

Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied for solving Combined Economic Emission Dispatch (CEED) problem with valve-point loading of thermal generators. This CEED problem with valve-point loading is a nonlinear, constrained multi-objective optimization problem, with power balance and generator capacity constraints. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a nonsmooth optimization problem. To validate its effectiveness of NSGA-II, two benchmark test systems, IEEE 30-bus and IEEE 118-bus systems are considered. To compare the Pareto-front obtained using NSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Comparison with other optimization techniques showed the superiority of the NSGA-II approach and confirmed its potential for solving the CEED problem. Numerical results show that NSGA-II algorithm can provide Pareto-front in a single run with good diversity and convergence. An approach based on Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) is applied on non-dominated solutions obtained to determine Best Compromise Solution (BCS).

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.2 s.314
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• pp.108-115
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• 2007

This paper proposes a new optimization algorithm prescribed by GBNSGA(Goal-Pareto Based Non-dominated Sorting Genetic Algorithm) whose result satisfies the user's needs and goals to enhance the performance of optimization. Typically, lots of real-world engineering problems encounter simultaneous optimization subject to satisfying prescribed multiple objectives. Unfortunately, since these objectives might be mutually competitive, it is hardly to find a unique solution satisfying every objectives. Instead, many researches have been investigated in order to obtain an optimal solution with sacrificing more than one objectives. This paper introduces a novel optimization scheme named by GBNSGA obeying both goals as well as objectives as possible as it can via allocating candidated solutions on Pareto front, which enhances the performance of Pareto based optimization. The performance of the proposed GBNSGA will be compared with that of the conventional NSGA and weighted-sum approach.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.491-496
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• 2002

Multi-objective Optimization Problems(MOPs) are occur more frequently than generally thought when we try to solve engineering problems. In the real world, the majority cases of optimization problems are the problems composed of several competitive objective functions. In this paper, we introduce the definition of MOPs and several approaches to solve these problems. In the introduction, established optimization algorithms based on the concept of Pareto optimal solution are introduced. And contrary these algorithms, we introduce theoretical backgrounds of Nash Genetic Algorithm(Nash GA) and Evolutionary Stable Strategy(ESS), which is the basis of Co-evolutionary algorithm proposed in this paper. In the next chapter, we introduce the definitions of MOPs and Pareto optimal solution. And the architecture of Nash GA and Co-evolutionary algorithm for solving MOPs are following. Finally from the experimental results we confirm that two algorithms based on Evolutionary Game Theory(EGT) which are Nash GA and Co-evolutionary algorithm can search optimal solutions of MOPs.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.1
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• pp.39-45
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• 2008

This paper considers the multi-objective optimization of a multi-service arrayed waveguide grating-based single-hop WDM network with the two conflicting objectives of maximizing throughput while minimizing delay. This paper presents a genetic algorithm based methodology for finding the optimal throughput-delay tradeoff curve, the so-called Pareto-optimal frontier. Genetic algorithm based methodology provides the network architecture parameters and the Medium Access Control protocol parameters that achieve the Pareto-optima in a computationally efficient manner. The numerical results obtained with this methodology provide the Pareto-optimal network planning and operation solution for a wide range of traffic scenarios. The presented methodology is applicable to other networks with a similar throughput-delay tradeoff.

• The KSFM Journal of Fluid Machinery
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• v.14 no.5
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• pp.31-38
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• 2011

Optimization using a hybrid multi-objective evolutionary algorithm coupled with response surface approximation has been performed to improve the performance of a transonic axial compressor with circumferential casing grooves. In order to optimize the operating stability and peak adiabatic efficiency of the compressor with circumferential casing grooves, tip clearance, angle distribution at blade tip and the depth of the circumferential casing grooves are selected as design variables. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by finite volume approximations. The trade-off between two objectives with the interaction of blade and casing treatment is determined and discussed with respect to the representative clusters in the Pareto-optimal solutions compared to the axial compressor without the casing treatment.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.1
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• pp.72-78
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• 2009

This paper considers a multiagent scheduling problem under public information where a machine is shared by multiple agents. Each agent has a local objective among the minimization of total completion time and the minimization of maximum. In this problem, it is assumed that scheduling information is public. Therefore an agent can access to complete information of other agents and pursue efficient schedules in a centralized manner. We propose an enumeration scheme to find Pareto optimal schedules and a multiobjective genetic algorithm as a heuristic approach. Experimental results indicate that the proposed genetic algorithm yields close-to Pareto optimal solution under a variety of experimental conditions.