Improved Solution Search Performance of Constrained MOEA/D Hybridizing Directional Mating and Local Mating

In this study, we propose an improvement to the direct mating method, a constraint handling approach for multi-objective evolutionary algorithms, by hybridizing it with local mating. Local mating selects another parent from the feasible solution space around the initially selected parent. The direct mating method selects the other parent along the optimal direction in the objective space after the first parent is selected, even if it is infeasible. It shows better exploration performance for constraint optimization problems with coupling NSGA-II, but requires several individuals along the optimal direction. Due to the lack of better solutions dominated by the optimal direction from the first parent, direct mating becomes difficult as the generation proceeds. To address this issue, we propose a hybrid method that uses local mating to select another parent from the neighborhood of the first selected parent, maintaining diversity around good solutions and helping the direct mating process. We evaluate the proposed method on three mathematical problems with unique Pareto fronts and two real-world applications. We use the generation histories of the averages and standard deviations of the hypervolumes as the performance evaluation criteria. Our investigation results show that the proposed method can solve constraint multi-objective problems better than existing methods while maintaining high diversity.Comment: Revised paper presented at ISMSI2023, 9pages, 8 figures (Online

実行不可能解を活用する進化型制約付き多目的最適化

本研究では，進化計算による制約付き多目的最適化において，従来法では単に排除される制約条件を満たさない実行不可能解を解探索に有効活用する方法について探求し，その有効性を計算機実験によって検証することを目的とする．この目的を達成するために，まず，本研究の基礎となる二段階の非支配ソートと指向性交配を用いるTNSDM (Two-stage Non-dominated Sorting and Directed Mating) アルゴリズムを提案する．二段階の非支配ソートでは，制約違反量に基づいて解集団をいくつかのグループに分類した後，各グループを目的関数値に基づいて再分類することによって解をランキングする．指向性交配では，実行可能解を第一の親とし，それより目的関数値が良い実行不可能解集合を選出する．その中から，二段階の非支配ソートで求めた解のランキングに従って第二の親を選択し，子を生成する．制約条件を満たさない実行不可能解の中には，解集団中の実行可能解より良い目的関数値(評価値) を示す場合があるため，それを解探索の手掛かりに活用する．まず，(1) 基礎となるTNSDM の指向性交配において，実行可能解より高い目的関数値を持つ解を解探索に活用することによって最適化性能が改善されることを示す．次に，(2)指向性交配による解探索効果が問題の性質に依存することを解決するために，有用な実行不可能解の選出領域を制御するTNSDM-CS (TNSDM with Controlling Selection area) を提案する．これにより，解探索中に生じる実行不可能解が少ない問題では，選出領域を拡大して指向性交配を実行しやすく，多い問題では縮小して良い親を選べるようになる．また，(3) 指向性交配で活用する実行可能解は，良い目的関数値を持つが実行不可能であるがゆえ，世代ごとに解集団から消失される．この問題を解決するため，有用な実行不可能解を解集団中にアーカイブし，解探索の手掛かりとして繰り返し活用するTNSDM-A(TNSDM with Archive) を提案する．さらに，(4) TNSDM-CS とTNSDM-A を組み合わせたTNSDM-CSA (TNSDM with Controlling Selection area and Archive) を提案する．TNSDM-CS において，有用な実行不可能解の選出領域を縮小すると，解探索の指向性が高まるため解探索性能が改善される利点があるが，同時に，選出領域に解が存在せずに指向性交配を実行できないケースが生じる欠点がある．この問題に対して，有用な実行不可能解のアーカイブを導入すると，選出領域を縮小しても選出領域に解が得られやすくなり，選出領域を縮小する欠点を補える．また，(5) 指向性交配で選択する有用な実行不可能解から子に複写される遺伝子(変数) の量を操作するTNSDM-CG (TNSDM with Controlling crossed Genes) を提案する．実行不可能解から子に複写される遺伝子量を減少させると，子は実行可能解になりやすいが有用な遺伝子情報を得にくい．逆に増加させると，子は実行不能解になりやすいが有用な遺伝子情報を得やすくなる．このバランスを操作することによって，指向性交配の解探索効果を高める．最後に，(6)TNSDM-CS とTNSDM-A，TNSDM-CG それぞれの指向性交配の効果を高める手法を組み合わせたTNSDM-CSACG(TNSDM with Controlling Selection area, Archive and Controlling crossed Genes) を提案し，その効果を検証する．提案法の効果を検証するため，離散問題のm 目的k ナップザック問題，連続問題のSRN，OSY，TNK，mCDTLZ，実問題の3 段式ハイブリッドロケットの概念設計最適化問題を用いる．また，比較アルゴリズムとして，代表的なCNSGA-II とRTS アルゴリズムを用いる．実験の結果，本研究で提案するいずれのアルゴリズムも，従来法より高い解探索性能を示すことが明らかになった．その詳細について順に述べると，まず，(1)TNSDM が従来法より高い解探索性能を示すことがわかった．これより，目的関数値の高い実行不可能解を活用する指向性交配によって，制約条件を有する多目的最適化問題における進化計算の解探索性能が改善されることが明らかになった．次に，(2) TNSDM-CSにおいて有用な実行不可能解の選出領域を制御することによって，指向性交配による解探索効果がさらに高まることが明らかになった．選出領域が拡大されると指向性交配の実行回数が増加する効果があり，縮小されると解探索の指向性が高まる効果があるため，解探索性能が改善される．また，(3) TNSDM-A において有用な実行不可能解を解集団中にアーカイブすることによっても，指向性交配による解探索効果がさらに高まることが明らかになった．これは，TNSDM では世代ごとに消失してしまう有用な実行不可能解を繰り返し指向性交配に活用できるためである．さらに，(4) TNSDM-CSA において有用な実行不可能解の選出領域制御法にアーカイブ法を組み合わせると，指向性交配を実行できないケースが減るため，より選出領域を縮小して解探索の指向性を高めた場合に，TNSDM-CS とTNSDM-A より高い解探索性能を達成できることが明らかになった．また，(5) TNSDM-CG において有用な実行不可能解から子へ複写される遺伝子(変数) 量を操作することによって，子の実行可能解へのなりやすさと，子に複写される解探索に有用な遺伝子情報の量を操作できるようになり，指向性交配の効果が高まることが明らかになった．最後に，(6)TNSDM-CSACG において，有用な実行不可能解の選出領域制御法とアーカイブ法，交叉量操作法を組み合わせると，上記(1)～(5) のアルゴリズムと比べ，最も高い解探索性能を示すことが明らかになった．(4) において示される有用な実行不可能解の選出領域制御法にアーカイブ法の組み合わせによる効果に加え，交叉量操作により親として選択された実行不可能解から子に複写する遺伝子量を制御することによって解探索性能が高まる．電気通信大学201

Explicit Building-Block Multiobjective Genetic Algorithms: Theory, Analysis, and Developing

This dissertation research emphasizes explicit Building Block (BB) based MO EAs performance and detailed symbolic representation. An explicit BB-based MOEA for solving constrained and real-world MOPs is developed the Multiobjective Messy Genetic Algorithm II (MOMGA-II) which is designed to validate symbolic BB concepts. The MOMGA-II demonstrates that explicit BB-based MOEAs provide insight into solving difficult MOPs that is generally not realized through the use of implicit BB-based MOEA approaches. This insight is necessary to increase the effectiveness of all MOEA approaches. In order to increase MOEA computational efficiency parallelization of MOEAs is addressed. Communications between processors in a parallel MOEA implementation is extremely important, hence innovative migration and replacement schemes for use in parallel MOEAs are detailed and tested. These parallel concepts support the development of the first explicit BB-based parallel MOEA the pMOMGA-II. MOEA theory is also advanced through the derivation of the first MOEA population sizing theory. The multiobjective population sizing theory presented derives the MOEA population size necessary in order to achieve good results within a specified level of confidence. Just as in the single objective approach the MOEA population sizing theory presents a very conservative sizing estimate. Validated results illustrate insight into building block phenomena good efficiency excellent effectiveness and motivation for future research in the area of explicit BB-based MOEAs. Thus the generic results of this research effort have applicability that aid in solving many different MOPs

Development and Integration of Geometric and Optimization Algorithms for Packing and Layout Design

The research work presented in this dissertation focuses on the development and application of optimization and geometric algorithms to packing and layout optimization problems. As part of this research work, a compact packing algorithm, a physically-based shape morphing algorithm, and a general purpose constrained multi-objective optimization algorithm are proposed. The compact packing algorithm is designed to pack three-dimensional free-form objects with full rotational freedom inside an arbitrary enclosure such that the packing efficiency is maximized. The proposed compact packing algorithm can handle objects with holes or cavities and its performance does not degrade significantly with the increase in the complexity of the enclosure or the objects. It outputs the location and orientation of all the objects, the packing sequence, and the packed configuration at the end of the packing operation. An improved layout algorithm that works with arbitrary enclosure geometry is also proposed. Different layout algorithms for the SAE and ISO luggage are proposed that exploit the unique characteristics of the problem under consideration. Several heuristics to improve the performance of the packing algorithm are also proposed. The proposed compact packing algorithm is benchmarked on a wide variety of synthetic and hypothetical problems and is shown to outperform other similar approaches. The physically-based shape morphing algorithm proposed in this dissertation is specifically designed for packing and layout applications, and thus it augments the compact packing algorithm. The proposed shape morphing algorithm is based on a modified mass-spring system which is used to model the morphable object. The shape morphing algorithm mimics a quasi-physical process similar to the inflation/deflation of a balloon filled with air. The morphing algorithm starts with an initial manifold geometry and morphs it to obtain a desired volume such that the obtained geometry does not interfere with the objects surrounding it. Several modifications to the original mass-spring system and to the underlying physics that governs it are proposed to significantly speed-up the shape morphing process. Since the geometry of a morphable object continuously changes during the morphing process, most collision detection algorithms that assume the colliding objects to be rigid cannot be used efficiently. And therefore, a general-purpose surface collision detection algorithm is also proposed that works with deformable objects and does not require any preprocessing. Many industrial design problems such as packing and layout optimization are computationally expensive, and a faster optimization algorithm can reduce the number of iterations (function evaluations) required to find the satisfycing solutions. A new multi-objective optimization algorithm namely Archive-based Micro Genetic Algorithm (AMGA2) is presented in this dissertation. Improved formulation for various operators used by the AMGA2 such as diversity preservation techniques, genetic variation operators, and the selection mechanism are also proposed. The AMGA2 also borrows several concepts from mathematical sciences to improve its performance and benefits from the existing literature in evolutionary optimization. A comprehensive benchmarking and comparison of AMGA2 with other state-of-the-art optimization algorithms on a wide variety of mathematical problems gleaned from literature demonstrates the superior performance of AMGA2. Thus, the research work presented in this dissertation makes contributions to the development and application of optimization and geometric algorithms

New approaches to optimization in aerospace conceptual design

Aerospace design can be viewed as an optimization process, but conceptual studies are rarely performed using formal search algorithms. Three issues that restrict the success of automatic search are identified in this work. New approaches are introduced to address the integration of analyses and optimizers, to avoid the need for accurate gradient information and a smooth search space (required for calculus-based optimization), and to remove the restrictions imposed by fixed complexity problem formulations. (1) Optimization should be performed in a flexible environment. A quasi-procedural architecture is used to conveniently link analysis modules and automatically coordinate their execution. It efficiently controls a large-scale design tasks. (2) Genetic algorithms provide a search method for discontinuous or noisy domains. The utility of genetic optimization is demonstrated here, but parameter encodings and constraint-handling schemes must be carefully chosen to avoid premature convergence to suboptimal designs. The relationship between genetic and calculus-based methods is explored. (3) A variable-complexity genetic algorithm is created to permit flexible parameterization, so that the level of description can change during optimization. This new optimizer automatically discovers novel designs in structural and aerodynamic tasks

An Evolutionary Approach to Multistage Portfolio Optimization

Portfolio optimization is an important problem in quantitative finance due to its application in asset management and corporate financial decision making. This involves quantitatively selecting the optimal portfolio for an investor given their asset return distribution assumptions, investment objectives and constraints. Analytical portfolio optimization methods suffer from limitations in terms of the problem specification and modelling assumptions that can be used. Therefore, a heuristic approach is taken where Monte Carlo simulations generate the investment scenarios and' a problem specific evolutionary algorithm is used to find the optimal portfolio asset allocations. Asset allocation is known to be the most important determinant of a portfolio's investment performance and also affects its risk/return characteristics. The inclusion of equity options in an equity portfolio should enable an investor to improve their efficient frontier due to options having a nonlinear payoff. Therefore, a research area of significant importance to equity investors, in which little research has been carried out, is the optimal asset allocation in equity options for an equity investor. A purpose of my thesis is to carry out an original analysis of the impact of allowing the purchase of put options and/or sale of call options for an equity investor. An investigation is also carried out into the effect ofchanging the investor's risk measure on the optimal asset allocation. A dynamic investment strategy obtained through multistage portfolio optimization has the potential to result in a superior investment strategy to that obtained from a single period portfolio optimization. Therefore, a novel analysis of the degree of the benefits of a dynamic investment strategy for an equity portfolio is performed. In particular, the ability of a dynamic investment strategy to mimic the effects ofthe inclusion ofequity options in an equity portfolio is investigated. The portfolio optimization problem is solved using evolutionary algorithms, due to their ability incorporate methods from a wide range of heuristic algorithms. Initially, it is shown how the problem specific parts ofmy evolutionary algorithm have been designed to solve my original portfolio optimization problem. Due to developments in evolutionary algorithms and the variety of design structures possible, a purpose of my thesis is to investigate the suitability of alternative algorithm design structures. A comparison is made of the performance of two existing algorithms, firstly the single objective stepping stone island model, where each island represents a different risk aversion parameter, and secondly the multi-objective Non-Dominated Sorting Genetic Algorithm2. Innovative hybrids of these algorithms which also incorporate features from multi-objective evolutionary algorithms, multiple population models and local search heuristics are then proposed. . A novel way is developed for solving the portfolio optimization by dividing my problem solution into two parts and then applying a multi-objective cooperative coevolution evolutionary algorithm. The first solution part consists of the asset allocation weights within the equity portfolio while the second solution part consists 'ofthe asset allocation weights within the equity options and the asset allocation weights between the different asset classes. An original portfolio optimization multiobjective evolutionary algorithm that uses an island model to represent different risk measures is also proposed.Imperial Users onl