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

Multi-criteria Evolution of Neural Network Topologies: Balancing Experience and Performance in Autonomous Systems

Majority of Artificial Neural Network (ANN) implementations in autonomous systems use a fixed/user-prescribed network topology, leading to sub-optimal performance and low portability. The existing neuro-evolution of augmenting topology or NEAT paradigm offers a powerful alternative by allowing the network topology and the connection weights to be simultaneously optimized through an evolutionary process. However, most NEAT implementations allow the consideration of only a single objective. There also persists the question of how to tractably introduce topological diversification that mitigates overfitting to training scenarios. To address these gaps, this paper develops a multi-objective neuro-evolution algorithm. While adopting the basic elements of NEAT, important modifications are made to the selection, speciation, and mutation processes. With the backdrop of small-robot path-planning applications, an experience-gain criterion is derived to encapsulate the amount of diverse local environment encountered by the system. This criterion facilitates the evolution of genes that support exploration, thereby seeking to generalize from a smaller set of mission scenarios than possible with performance maximization alone. The effectiveness of the single-objective (optimizing performance) and the multi-objective (optimizing performance and experience-gain) neuro-evolution approaches are evaluated on two different small-robot cases, with ANNs obtained by the multi-objective optimization observed to provide superior performance in unseen scenarios

Parallel Multi-Objective Evolutionary Algorithms: A Comprehensive Survey

Multi-Objective Evolutionary Algorithms (MOEAs) are powerful search techniques that have been extensively used to solve difficult problems in a wide variety of disciplines. However, they can be very demanding in terms of computational resources. Parallel implementations of MOEAs (pMOEAs) provide considerable gains regarding performance and scalability and, therefore, their relevance in tackling computationally expensive applications. This paper presents a survey of pMOEAs, describing a refined taxonomy, an up-to-date review of methods and the key contributions to the field. Furthermore, some of the open questions that require further research are also briefly discussed

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field

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

Evolutionary Algorithms for Static and Dynamic Multiobjective Optimization

Many real-world optimization problems consist of a number of conflicting objectives that have to be optimized simultaneously. Due to the presence of multiple conflicting ob- jectives, there is no single solution that can optimize all the objectives. Therefore, the resulting multiobjective optimization problems (MOPs) resort to a set of trade-off op- timal solutions, called the Pareto set in the decision space and the Pareto front in the objective space. Traditional optimization methods can at best find one solution in a sin- gle run, thereby making them inefficient to solve MOPs. In contrast, evolutionary algo- rithms (EAs) are able to approximate multiple optimal solutions in a single run. This strength makes EAs good candidates for solving MOPs. Over the past several decades, there have been increasing research interests in developing EAs or improving their perfor- mance, resulting in a large number of contributions towards the applicability of EAs for MOPs. However, the performance of EAs depends largely on the properties of the MOPs in question, e.g., static/dynamic optimization environments, simple/complex Pareto front characteristics, and low/high dimensionality. Different problem properties may pose dis- tinct optimization difficulties to EAs. For example, dynamic (time-varying) MOPs are generally more challenging than static ones to EAs. Therefore, it is not trivial to further study EAs in order to make them widely applicable to MOPs with various optimization scenarios or problem properties. This thesis is devoted to exploring EAs’ ability to solve a variety of MOPs with dif- ferent problem characteristics, attempting to widen EAs’ applicability and enhance their general performance. To start with, decomposition-based EAs are enhanced by incorpo- rating two-phase search and niche-guided solution selection strategies so as to make them suitable for solving MOPs with complex Pareto fronts. Second, new scalarizing functions are proposed and their impacts on evolutionary multiobjective optimization are exten- sively studied. On the basis of the new scalarizing functions, an efficient decomposition- based EA is introduced to deal with a class of hard MOPs. Third, a diversity-first- and-convergence-second sorting method is suggested to handle possible drawbacks of convergence-first based sorting methods. The new sorting method is then combined with strength based fitness assignment, with the aid of reference directions, to optimize MOPs with an increase of objective dimensionality. After that, we study the field of dynamic multiobjective optimization where objective functions and constraints can change over time. A new set of test problems consisting of a wide range of dynamic characteristics is introduced at an attempt to standardize test environments in dynamic multiobjective optimization, thereby aiding fair algorithm comparison and deep performance analysis. Finally, a dynamic EA is developed to tackle dynamic MOPs by exploiting the advan- tages of both generational and steady-state algorithms. All the proposed approaches have been extensively examined against existing state-of-the-art methods, showing fairly good performance in a variety of test scenarios. The research work presented in the thesis is the output of initiative and novel attempts to tackle some challenging issues in evolutionary multiobjective optimization. This re- search has not only extended the applicability of some of the existing approaches, such as decomposition-based or Pareto-based algorithms, for complex or hard MOPs, but also contributed to moving forward research in the field of dynamic multiobjective optimiza- tion with novel ideas including new test suites and novel algorithm design

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

A Pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods

Handling Dynamic Multiobjective Optimization Environments via Layered Prediction and Subspace-Based Diversity Maintenance

Peer reviewedPostprin

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided