• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.11 s.254
• /
• pp.1358-1368
• /
• 2006

This paper proposes a Pareto artificial life algorithm for solving multi-objective optimization problems. The artificial life algorithm for optimization problem with a single objective function is improved to handle Pareto optimization problem through incorporating the new method to estimate the fitness value for a solution and the Pareto list to memorize and to improve the Pareto optimal set. The proposed algorithm was applied to the optimum design of a journal bearing which has two objective functions. The Pareto front and the optimal solution set for the application were presented to give the possible solutions to a decision maker or a designer. Furthermore, the relation between linearly combined single-objective optimization problem and Pareto optimization problem has been studied.

• Smart Structures and Systems
• /
• v.22 no.4
• /
• pp.469-479
• /
• 2018

The present research study utilizes a multi-objective optimization method for Pareto optimization of an eight-degree of freedom full vehicle vibration model, adopting a non-dominated sorting genetic algorithm II (NSGA-II). In this research, a full set of ride comfort as well as ride safety parameters are considered as objective functions. These objective functions are divided in to two groups (ride comfort group and ride safety group) where the ones in one group are in conflict with those in the other. Also, in this research, a special optimizing technique and combinational method consisting of weighted sum method and Pareto optimization are applied to transform Pareto double-objective optimization to Pareto full-objective optimization which can simultaneously minimize all objectives. Using this technique, the full set of ride parameters of three dimensional vehicle model are minimizing simultaneously. In derived Pareto front, unique trade-off design points can selected which are non-dominated solutions of optimizing the weighted sum comfort parameters versus weighted sum safety parameters. The comparison of the obtained results with those reported in the literature, demonstrates the distinction and comprehensiveness of the results arrived in the present study.

• Journal of Distribution Science
• /
• v.15 no.2
• /
• pp.15-20
• /
• 2017

Purpose - This paper aims to suggest a delivery constrained internet shopping optimization problem (DISOP) which must be solved for online recommendation system to provide a customized service considering cost and delivery conditions at the same time. Research design, data, and methodology - To solve a (DISOP), we propose a multi-objective formulation and a solution approach. By using a commercial optimization software (LINDO), a (DISOP) can be solved iteratively and a pareto optimal set can be calculated for real-sized problem. Results - We propose a new research problem which is different with internet shopping optimization problem since our problem considers not only the purchasing cost but also delivery conditions at the same time. Furthermore, we suggest a multi-objective mathematical formulation for our research problem and provide a solution approach to get a pareto optimal set by using numerical example. Conclusions - This paper proposes a multi-objective optimization problem to solve internet shopping optimization problem with delivery constraint and a solution approach to get a pareto optimal set. The results of research will contribute to develop a customized comparison and recommendation system to help more easy and smart online shopping service.

• Journal of the Society of Naval Architects of Korea
• /
• v.46 no.4
• /
• pp.409-416
• /
• 2009

The structural design problems are acknowledged to be commonly multi-criteria in nature. The various multi-criteria optimization methods are reviewed and the most efficient and easy-to-use Pareto optimal solution methods are applied to structural optimization of a truss and a beam. 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.

• Structural Engineering and Mechanics
• /
• v.70 no.3
• /
• pp.367-380
• /
• 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 the Institute of Electronics Engineers of Korea SP
• /
• v.44 no.2 s.314
• /
• pp.108-115
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.6
• /
• pp.987-992
• /
• 2002

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. This algorithm is based on Continuous Evolutionary Algorithms to solve single objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method fur fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto-optimal tradeoff surface. Finally, the validity of this method has been demonstrated through a numerical example.

• The KIPS Transactions:PartB
• /
• v.11B no.2
• /
• pp.213-220
• /
• 2004

Evolutionary algorithms are well-suited for multi-objective optimization problems involving several. often conflicting objective. Pareto-based evolutionary algorithms, in particular, have shown better performance than other multi-objective evolutionary algorithms in comparison. Recently, pareto-based evolutionary algorithms uses a density information in fitness assignment scheme for generating uniform distributed global pareto optimal front. However, the usage of density information is not Important elements in a whole evolution path but plays an auxiliary role in order to make uniform distribution. In this paper, we propose an evolutionary algorithms for multi-objective optimization which assigns the fitness using pareto dominance rank and density weighting, and thus pareto dominance rank and density have similar influence on the whole evolution path. Furthermore, the experimental results, which applied our method to the six multi-objective optimization problems, show that the proposed algorithms show more promising results.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.30 no.11 s.254
• /
• pp.1084-1092
• /
• 2006

Shape optimization of airfoil in WIG craft has been performed by considering the ground effect. The WIG craft should satisfy various aerodynamic characteristics such as lift, lift to drag ratio, and static height stability. However, they show a strong trade-off phenomenon so that it is difficult to satisfy aerodynamic properties simultaneously. Optimization is carried out through the multi-objective genetic algorithm. A multi-objective optimization means that each objective is considered separately instead of weighting. Due to the trade-off, pareto sets and non-dominated solutions can be obtained instead of the unique solution. NACA0015 airfoil is considered as a baseline model, shapes of airfoil are parameterized and rebuilt with four-Bezier curves. There are eighteen design variables and three objective functions. The range of design variables and their resolutions are two primary keys for the successful optimization. By two preliminary optimizations, the variation can be reduced effectively. After thirty evolutions, the non-dominated pareto individuals of twenty seven are obtained. Pareto sets are all the set of possible and excellent solution across the design space. At any selections of the pareto set, these are no better solutions in all design space.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.44 no.2
• /
• pp.36-42
• /
• 2021

This paper deals with a vehicle routing problem with resource repositioning (VRPRR) which is a variation of well-known vehicle routing problem with pickup and delivery (VRPPD). VRPRR in which static repositioning of public bikes is a representative case, can be defined as a multi-objective optimization problem aiming at minimizing both transportation cost and the amount of unmet demand. To obtain Pareto sets for the problem, famous multi-objective optimization algorithms such as Strength Pareto Evolutionary Algorithm 2 (SPEA2) can be applied. In addition, a linear combination of two objective functions with weights can be exploited to generate Pareto sets. By varying weight values in the combined single objective function, a set of solutions is created. Experiments accomplished with a standard benchmark problem sets show that Variable Neighborhood Search (VNS) applied to solve a number of single objective function outperforms SPEA2. All generated solutions from SPEA2 are completely dominated by a set of VNS solutions. It seems that local optimization technique inherent in VNS makes it possible to generate near optimal solutions for the single objective function. Also, it shows that trade-off between the number of solutions in Pareto set and the computation time should be considered to obtain good solutions effectively in case of linearly combined single objective function.