Evolutionary Multi-criterion Optimization Research Articles

MOEA/D with customized replacement neighborhood and dynamic resource allocation for solving 3L-SDHVRP

Split delivery heterogeneous vehicle routing problem with three-dimensional loading (3L-SDHVRP) is a critical issue in manufacturing logistics. Current mainstream research formulates this problem as a single objective optimization problem, which fails to reveal the relationship among multiple conflicting objectives and cannot provide various trade-off solutions for decision-makers in real-world logistics scenarios. This paper concentrates on a multi-objective 3L-SDHVRP and proposes a multi-objective evolutionary algorithm based on decomposition with customized replacement neighborhood and dynamic resource allocation (called MOEA/D-RD) to deal with it. The numerical experiments on the dataset from the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021) show the superior performance of the proposed method over some state-of-the-art ones. The source code of MOEA/D-RD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEAD-RD.

First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001) 報告

First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001) 報告

進化型多目的最適化における探索履歴を活用した局所解脱出と集中探索メカニズム

進化型多目的最適化における探索履歴を活用した局所解脱出と集中探索メカニズム

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.

3次元距離画像センサを用いた進化論的多目的最適化に基づく上肢関節角度推定

In this research, we have developed a rehabilitation support system for analysis of upper body motion using 3D image sensor. Such a sensor has embedded systems to detect and track joint positions, but it is difficult to directly apply the data to calculation of inverse kinematics to estimate the joint angles because of errors in measurement. To solve the issue, some researchers have proposed methods of joint angle estimation using kinematic model and search technique. In these works, objective functions were defined to evaluate the similarity of posture between a person and kinematic model, and the problem was typically considered as a single-objective optimization problem. However, the data basically includes not only feature of personal behavior patterns but also noise. Therefore, we address a multi-objective optimization problem in order to scale back the influence of noise. This paper proposes a method of joint angle estimation of upper limb base on Evolutionary Multi-criterion Optimization (EMO). Furthermore, we apply a feedforward neural network to motion pattern modeling to realize a predictive search, combining with the EMO.

A Proposal on Analysis Support System Based on Association Rule Analysis for Non-dominated Solutions

This paper presents a new analysis support system for analyzing non-dominated solutions (NDSs) derived by evolutionary multi-criterion optimization (EMO). The main features of the proposed system are to use association rule analysis and to perform a multi-granularity analysis based on a hierarchical tree of NDSs. The proposed system applies association rule analysis to the whole NDSs and derives association rules related to NDSs. And a hierarchical tree is created through our original association rule grouping that guarantees to keep at least one common features. Each node of a hierarchical tree corresponds to one group consisting of association rules and is fixed in position according to inclusion relations between groups. Since each group has some kinds of common features, the designer can analyze each node with previous knowledge of these common features. To investigate the characteristics and effectiveness of the proposed system, the proposed system is applied to the concept design problem of hybrid rocket engine (HRE) which has two objectives and six variable parameters. HRE separately stores two different types of thrust propellant unlike in the case of usual other rockets and the concept design problem of HRE has been provided by JAXA. The results of this application provided possible to analyze the trends and specifics contained in NDSs in an organized way unlike analysis approaches targeted at the whole NDSs.

A Proposal on an Approach Based on Evolutionary Multi-criterion Optimization for Nurse Scheduling Problem

A Proposal on an Approach Based on Evolutionary Multi-criterion Optimization for Nurse Scheduling Problem

計算論的システムリハビリテーションにおける動作解析のための進化型多目的最適化

本研究では,リハビリテーション評価支援のための動作解析システムを提案することを目的とする.まず本稿では,計算論的システムリハビリテーションの基本的な概念,方法論について説明する.次に,3次元距離画像センサを用いた上肢の動作解析システムの概要を示す-さらに,私たちは遺伝的アルゴリズムとニューラルネットワークに基づく人間の動作解析手法を提案する.最後に,実験結果を通じて提案手法の有効性について議論する。

HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization

In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator's potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume--so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/.

Differential EvolutionによるSAWフィルタの多目的最適設計

The structural design of Surface Acoustic Wave (SAW) filters is formulated as a constrained multi-objective optimization problem. Then three Evolutionary Multi-criterion Optimization (EMO) algorithms based on Differential Evolution (DE), namely, Multi-Objective DE (MODE), Non-dominated Sorting DE (NSDE), and Generalized DE 3 (GDE3), are applied to the three- and two-objective optimization problems of a balanced SAW filter. In order to compare the performances of the above EMO algorithms, several criteria including hypervolume are evaluated. As a result, it is shown that the performance of the EMO algorithm depends on the number of objective functions. Besides, in order to clarify the tradeoff relationship among the objective functions of the three-objective optimization problem, Principal Component Analysis (PCA) is employed.

Development of a design support system that can efficiently utilize non-dominated solutions

This paper proposes a new design support approach, which efficiently utilizes the information of many non-dominated solutions obtained from evolutionary multi-criterion optimization (EMO). The proposed approach consists of four mechanisms: grouping (clustering), reducing the number of candidates (selecting the representative solutions), dimensionality reduction, and estimation. Non-dominated solutions can be regarded as a beneficial subspace in whole search space, which have the feature of being non-inferior to other solutions. Therefore, we think the proposed approach can be used to estimate the characteristics of a problem through the interaction with the designer.In this paper, we examine the characteristics and effectiveness of the proposed approach through computational experiments on a design problem of a counter rotating axial fan turbojet engine. A counter rotating axial fan turbojet engine with two spools is chosen for the design target of the present study. We handle this task as a seven-objective design problem.

Development of a Design Support System that Can Efficiently Utilize Non-dominated Solutions Through an Example of Turbojet Engine Design

This paper proposes a new design support approach, which efficiently utilizes the information of many non-dominated solutions obtained from evolutionary multi-criterion optimization (EMO). The proposed approach consists of four mechanisms: grouping (clustering), reducing the number of candidates (selecting the representative solutions), dimensionality reduction, and estimation. Non-dominated solutions can be regarded as a beneficial subspace in whole search space, which have the feature of being non-inferior to other solutions. Therefore, we think the proposed approach can be used to estimate the characteristics of a problem through the interaction with the designer.In this paper, we examine the characteristics and effectiveness of the proposed approach through computational experiments on a design problem of a counter rotating axial fan turbojet engine. A counter rotating axial fan turbojet engine with two spools is chosen for the design target of the present study. We handle this task as a seven-objective design problem.