Bi-level Multi-objective Evolutionary Learning: A Case Study on Multi-task Graph Neural Topology Search
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education（教育部智能感知与图像理解重点实验室）；International Research Center for Intelligent Perception（智能感知国际研究中心）
The construction of machine learning models involves many bi-level multi-objective optimization problems (BL-MOPs), where upper level (UL) candidate solutions must be evaluated via training weights of a model in the lower level (LL). Due to the Pareto optimality of sub-problems and the complex dependency across UL solutions and LL weights, an UL solution is feasible if and only if the LL weight is Pareto optimal. It is computationally expensive to determine which LL Pareto weight in the LL Pareto weight set is the most appropriate for each UL solution. This paper proposes a bi-level multi-objective learning framework (BLMOL), coupling the above decision-making process with the optimization process of the UL-MOP by introducing LL preference $r$. Specifically, the UL variable and $r$ are simultaneously searched to minimize multiple UL objectives by evolutionary multi-objective algorithms. The LL weight with respect to $r$ is trained to minimize multiple LL objectives via gradient-based preference multi-objective algorithms. In addition, the preference surrogate model is constructed to replace the expensive evaluation process of the UL-MOP. We consider a novel case study on multi-task graph neural topology search. It aims to find a set of Pareto topologies and their Pareto weights, representing different trade-offs across tasks at UL and LL, respectively. The found graph neural network is employed to solve multiple tasks simultaneously, including graph classification, node classification, and link prediction. Experimental results demonstrate that BLMOL can outperform some state-of-the-art algorithms and generate well-representative UL solutions and LL weights.
Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to its less-than-global view. We show that moving the investigation into topological space improves our understanding of why EAs work.
Federal University of Paraná（巴拉那联邦大学）；University of Orléans（奥尔良大学）
A variety of clustering criteria has been applied as an objective function in Evolutionary Multi-Objective Clustering approaches (EMOCs). However, most EMOCs do not provide detailed analysis regarding the choice and usage of the objective functions. Aiming to support a better choice and definition of the objectives in the EMOCs, this paper proposes an analysis of the admissibility of the clustering criteria in evolutionary optimization by examining the search direction and its potential in finding optimal results. As a result, we demonstrate how the admissibility of the objective functions can…
University of Trento（特伦托大学）；Fondazione Bruno Kessler (FBK)（布鲁诺·凯斯勒基金会）
Designing neural networks for object recognition requires considerable architecture engineering. As a remedy, neuro-evolutionary network architecture search, which automatically searches for optimal network architectures using evolutionary algorithms, has recently become very popular. Although very effective, evolutionary algorithms rely heavily on having a large population of individuals (i.e., network architectures) and is therefore memory expensive. In this work, we propose a Regularized Evolutionary Algorithm with low memory footprint to evolve a dynamic image classifier. In details, we in…
Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon（亥姆霍兹重离子研究中心材料系统建模研究所）；Institute for Continuum and Material Mechanics, Hamburg University of Technology（汉堡工业大学连续介质与材料力学研究所）
Evolutionary diversity optimization aims to compute a diverse set of solutions where all solutions meet a given quality criterion. With this paper, we bridge the areas of evolutionary diversity optimization and evolutionary multi-objective optimization. We show how popular indicators frequently used in the area of multi-objective optimization can be used for evolutionary diversity optimization. Our experimental investigations for evolving diverse sets of TSP instances and images according to various features show that two of the most prominent multi-objective indicators, namely the hypervolume…
The major difficulty in Multi-objective Optimization Evolutionary Algorithms (MOEAs) is how to find an appropriate solution that is able to converge towards the true Pareto Front with high diversity. Most existing methodologies, which have demonstrated their niche on various practical problems involving two and three objectives, face significant challenges in the dependency of the selection of the EA parameters. Moreover, the process of setting such parameters is considered time-consuming, and several research works have tried to deal with this problem. This paper proposed a new Multi-objectiv…
To handle different types of Many-Objective Optimization Problems (MaOPs), Many-Objective Evolutionary Algorithms (MaOEAs) need to simultaneously maintain convergence and population diversity in the high-dimensional objective space. In order to balance the relationship between diversity and convergence, we introduce a Kernel Matrix and probability model called Determinantal Point Processes (DPPs). Our Many-Objective Evolutionary Algorithm with Determinantal Point Processes (MaOEADPPs) is presented and compared with several state-of-the-art algorithms on various types of MaOPs \textcolor{blue}{…
Multi-modal multi-objective optimization aims to find all Pareto optimal solutions including overlapping solutions in the objective space. Multi-modal multi-objective optimization has been investigated in the evolutionary computation community since 2005. However, it is difficult to survey existing studies in this field because they have been independently conducted and do not explicitly use the term "multi-modal multi-objective optimization". To address this issue, this paper reviews existing studies of evolutionary multi-modal multi-objective optimization, including studies published under n…
Institute for Development and Research in Banking Technology（银行技术发展与研究院）；University of Hyderabad（海得拉巴大学）
In this paper, two multi-objective optimization frameworks in two variants (i.e., NSGA-III-ARM-V1, NSGA-III-ARM-V2; and MOEAD-ARM-V1, MOEAD-ARM-V2) are proposed to find association rules from transactional datasets. The first framework uses Non-dominated sorting genetic algorithm III (NSGA-III) and the second uses Decomposition based multi-objective evolutionary algorithm (MOEA/D) to find the association rules which are diverse, non-redundant and non-dominated (having high objective function values). In both these frameworks, there is no need to specify minimum support and minimum confidence. …
Most existing multiobjetive evolutionary algorithms (MOEAs) implicitly assume that each objective function can be evaluated within the same period of time. Typically. this is untenable in many real-world optimization scenarios where evaluation of different objectives involves different computer simulations or physical experiments with distinct time complexity. To address this issue, a transfer learning scheme based on surrogate-assisted evolutionary algorithms (SAEAs) is proposed, in which a co-surrogate is adopted to model the functional relationship between the fast and slow objective functi…
Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to build new MOEAs. Here a new model is proposed which includes two sub-models based on two classes of different schemas of MOEAs. According to the new model, some representatives algorithms are decomposed and some interesting issues are discussed.
In model-based evolutionary algorithms (EAs), the underlying search distribution is adapted to the problem at hand, for example based on dependencies between decision variables. Hill-valley clustering is an adaptive niching method in which a set of solutions is clustered such that each cluster corresponds to a single mode in the fitness landscape. This can be used to adapt the search distribution of an EA to the number of modes, exploring each mode separately. Especially in a black-box setting, where the number of modes is a priori unknown, an adaptive approach is essential for good performanc…
Computational drug design based on artificial intelligence is an emerging research area. At the time of writing this paper, the world suffers from an outbreak of the coronavirus SARS-CoV-2. A promising way to stop the virus replication is via protease inhibition. We propose an evolutionary multi-objective algorithm (EMOA) to design potential protease inhibitors for SARS-CoV-2's main protease. Based on the SELFIES representation the EMOA maximizes the binding of candidate ligands to the protein using the docking tool QuickVina 2, while at the same time taking into account further objectives lik…
Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most of existing run-time analyses for GSEMO assume a single cardinality constraint. In this work, we extend the theoretical results to partition matroid constraints which generalize cardinality constraints, and show that GSEMO can generally guarantee good approximation performance within polynomial expec…
A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann (2013). In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of the the optimal solution for the problem. Moreover, using a diversity mechanisms, we present a multi-objective evolutionary algorithm that finds a 2-approximation in expected polynomial time and introduce a population-based e…
Evolutionary Algorithms and Multi-Objective Minimum Spanning Trees with Limited Distinct Weight Values
Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL（里尔大学、法国国家科学研究中心、中央理工学院、CRIStAL联合研究实验室）；University of Minnesota Duluth（明尼苏达大学德卢斯分校）；Adelaide University（阿德莱德大学）
Constraint violation has been a building block to design evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, it is not uncommon that the constraint violation is hardly approachable in real-world black-box optimization scenarios. It is unclear that whether the existing constrained evolutionary multi-objective optimization algorithms, whose environmental selection mechanism are built upon the constraint violation, can still work or not when the formulations of the constraint functions are unknown. Bearing this consideration…
The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of $α$. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knap…
Eindhoven University of Technology（埃因霍温理工大学）；Nobleo Manufacturing（Nobleo制造公司）
Multi-objective evolutionary algorithms (MOEAs) are widely used to solve multi-objective optimization problems. The algorithms rely on setting appropriate parameters to find good solutions. However, this parameter tuning could be very computationally expensive in solving non-trial (combinatorial) optimization problems. This paper proposes a framework that integrates MOEAs with adaptive parameter control using Deep Reinforcement Learning (DRL). The DRL policy is trained to adaptively set the values that dictate the intensity and probability of mutation for solutions during optimization. We test…
TRUST-TAEA: A trustworthiness-guided two-archive evolutionary algorithm with variable-grouping sparse search for large-scale multi-objective optimization
Southwest Petroleum University（西南石油大学）；Jagiellonian University in Krakow（克拉科夫雅盖隆大学）
Dynamic multi-objective optimization problems (DMOPs) remain a challenge to be settled, because of conflicting objective functions change over time. In recent years, transfer learning has been proven to be a kind of effective approach in solving DMOPs. In this paper, a novel transfer learning based dynamic multi-objective optimization algorithm (DMOA) is proposed called regression transfer learning prediction based DMOA (RTLP-DMOA). The algorithm aims to generate an excellent initial population to accelerate the evolutionary process and improve the evolutionary performance in solving DMOPs. Wh…
In evolutionary multiobjective optimization, effectiveness refers to how an evolutionary algorithm performs in terms of converging its solutions into the Pareto front and also diversifying them over the front. This is not an easy job, particularly for optimization problems with more than three objectives, dubbed many-objective optimization problems. In such problems, classic Pareto-based algorithms fail to provide sufficient selection pressure towards the Pareto front, whilst recently developed algorithms, such as decomposition-based ones, may struggle to maintain a set of well-distributed sol…
The aim of bi-objective optimization is to obtain an approximation set of (near) Pareto optimal solutions. A decision maker then navigates this set to select a final desired solution, often using a visualization of the approximation front. The front provides a navigational ordering of solutions to traverse, but this ordering does not necessarily map to a smooth trajectory through decision space. This forces the decision maker to inspect the decision variables of each solution individually, potentially making navigation of the approximation set unintuitive. In this work, we aim to improve appro…
Machine learning methods have been used to accelerate the molecule optimization process. However, efficient search for optimized molecules satisfying several properties with scarce labeled data remains a challenge for machine learning molecule optimization. In this study, we propose MOMO, a multi-objective molecule optimization framework to address the challenge by combining learning of chemical knowledge with Pareto-based multi-objective evolutionary search. To learn chemistry, it employs a self-supervised codec to construct an implicit chemical space and acquire the continues representation …
Evolutionary Soups: Evolving Mixture-of-Experts for Multi-Objective LLM Alignment
Fraunhofer Institute for Applied Information Technology FIT（弗劳恩霍夫应用信息技术研究所FIT）；University of Cologne（科隆大学）；University of Stuttgart（斯图加特大学）；University of Southampton（南安普顿大学）；Soochow University（苏州大学）；University Hospital of Cologne（科隆大学医院）
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multi-objective optimization, they are likely to perform poorly for multi-modal multi-objective optimization due to the lack of mechanisms to maintain the solution space diversity. To address this issue, this paper proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multi-modal multi-objective optimization. Our framework is based on three operations: assi…
Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize the total profit subject to the probability that total weight exceeds the capacity. We make use of prominent tail inequalities such as Chebyshev's inequality, and Chernoff bound to approximate the probabilistic constrai…
Since around 2000, it has been considered that elitist evolutionary multi-objective optimization algorithms (EMOAs) always outperform non-elitist EMOAs. This paper revisits the performance of non-elitist EMOAs for bi-objective continuous optimization when using an unbounded external archive. This paper examines the performance of EMOAs with two elitist and one non-elitist environmental selections. The performance of EMOAs is evaluated on the bi-objective BBOB problem suite provided by the COCO platform. In contrast to conventional wisdom, results show that non-elitist EMOAs with particular cro…
Constrained multi-objective optimization problems (CMOPs) are ubiquitous in real-world engineering optimization scenarios. A key issue in constrained multi-objective optimization is to strike a balance among convergence, diversity and feasibility. A recently proposed two-archive evolutionary algorithm for constrained multi-objective optimization (C-TAEA) has be shown as a latest algorithm. However, due to its simple implementation of the collaboration mechanism between its two co-evolving archives, C-TAEA is struggling when solving problems whose \textit{pseudo} Pareto-optimal front, which doe…
This paper examines the effect of mimicking discontinuous heredity caused by carrying more than one chromosome in some living organisms cells in Evolutionary Multi-Objective Optimization algorithms. In this representation, the phenotype may not fully reflect the genotype. By doing so we are mimicking living organisms inheritance mechanism, where traits may be silently carried for many generations to reappear later. Representations with different number of chromosomes in each solution vector are tested on different benchmark problems with high number of decision variables and objectives. A comp…
In this report, we suggest nine test problems for multi-task single-objective optimization (MTSOO), each of which consists of two single-objective optimization tasks that need to be solved simultaneously. The relationship between tasks varies between different test problems, which would be helpful to have a comprehensive evaluation of the MFO algorithms. It is expected that the proposed test problems will germinate progress the field of the MTSOO research.
Decomposition has been the mainstream approach in the classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this article, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get o…
A preference based multi-objective evolutionary algorithm is proposed for generating solutions in an automatically detected knee point region. It is named Automatic Preference based DI-MOEA (AP-DI-MOEA) where DI-MOEA stands for Diversity-Indicator based Multi-Objective Evolutionary Algorithm). AP-DI-MOEA has two main characteristics: firstly, it generates the preference region automatically during the optimization; secondly, it concentrates the solution set in this preference region. Moreover, the real-world vehicle fleet maintenance scheduling optimization (VFMSO) problem is formulated, and a…
In this paper, we proposed a multi-objective approach for the EEG Inverse Problem. This formulation does not need unknown parameters that involve empirical procedures. Due to the combinatorial characteristics of the problem, this alternative included evolutionary strategies to resolve it. The result is a Multi-objective Evolutionary Algorithm based on Anatomical Restrictions (MOEAAR) to estimate distributed solutions. The comparative tests were between this approach and 3 classic methods of regularization: LASSO, Ridge-L and ENET-L. In the experimental phase, regression models were selected to…
In this paper we consider the problem of finding Pulse Repetition Intervals allowing the best compromises mitigating range and Doppler ambiguities in a Pulsed-Doppler radar system. We revisit a problem that was proposed to the Evolutionary Computation community as a real-world case to test Many-objective Optimization algorithms. We use it as a baseline to compare several Evolutionary Algorithms for black-box optimization with different metrics. Resulting data is aggregated to build a reference set of Pareto optimal points and is the starting point for further analysis and operational use by th…
Evolutionary many-objective optimization has been gaining increasing attention from the evolutionary computation research community. Much effort has been devoted to addressing this issue by improving the scalability of multiobjective evolutionary algorithms, such as Pareto-based, decomposition-based, and indicator-based approaches. Different from current work, we propose a novel algorithm in this paper called AnD, which consists of an angle-based selection strategy and a shift-based density estimation strategy. These two strategies are employed in the environmental selection to delete the poor…
Dynamic Detection of Relevant Objectives and Adaptation to Preference Drifts in Interactive Evolutionary Multi-Objective Optimization
Centre for Logistics & Sustainability Analytics, Kent Business School, University of Kent（肯特大学肯特商学院物流与可持续性分析中心）；Université de Haute-Alsace（上阿尔萨斯大学）；Alliance Manchester Business School, University of Manchester（曼彻斯特大学联盟曼彻斯特商学院）
East China University of Science and Technology（华东理工大学）；University of Surrey（萨里大学）
Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization is always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and is subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogat…
In this paper, we design a set of multi-objective constrained optimization problems (MCOPs) and propose a new repair operator to address them. The proposed repair operator is used to fix the solutions that violate the box constraints. More specifically, it employs a reversed correction strategy that can effectively avoid the population falling into local optimum. In addition, we integrate the proposed repair operator into two classical multi-objective evolutionary algorithms MOEA/D and NSGA-II. The proposed repair operator is compared with other two kinds of commonly used repair operators on b…
Multi-objective optimization problems whose objectives have different evaluation costs are commonly seen in the real world. Such problems are now known as multi-objective optimization problems with heterogeneous objectives (HE-MOPs). So far, however, only a few studies have been reported to address HE-MOPs, and most of them focus on bi-objective problems with one fast objective and one slow objective. In this work, we aim to deal with HE-MOPs having more than two black-box and heterogeneous objectives. To this end, we develop a multi-objective Bayesian evolutionary optimization approach to HE-…
