Knowledge transfer-based evolutionary optimization has garnered significant attention, such as in multi-task evolutionary optimization (MTEO), which aims to solve complex problems by simultaneously optimizing multiple tasks. While this emerging paradigm has been primarily focusing on task similarity, there remains a hugely untapped potential in harnessing the shared characteristics between different domains. For example, real-world complex systems usually share the same characteristics, such as the power-law rule, small-world property and community structure, thus making it possible to transfer solutions optimized in one system to another to facilitate the optimization. Drawing inspiration from this observation of shared characteristics within complex systems, we present a novel framework, multi-domain evolutionary optimization (MDEO). First, we propose a community-level measurement of graph similarity to manage the knowledge transfer among domains. Furthermore, we develop a graph learning-based network alignment model that serves as the conduit for effectively transferring solutions between different domains. Moreover, we devise a self-adaptive mechanism to determine the number of transferred solutions from different domains, and introduce a knowledge-guided mutation mechanism that adaptively redefines mutation candidates to facilitate the utilization of knowledge from other domains. To evaluate its performance, we use a challenging combinatorial problem known as adversarial link perturbation as the primary illustrative optimization task. Experiments on multiple real-world networks of different domains demonstrate the superiority of the proposed framework in efficacy compared to classical evolutionary optimization.
Evolutionary algorithms are popular heuristics for solving various combinatorial problems as they are easy to apply and often produce good results. Island models parallelize evolution by using different populations, called islands, which are connected by a graph structure as communication topology. Each island periodically communicates copies of good solutions to neighboring islands in a process called migration. We consider the speedup gained by island models in terms of the parallel running time for problems from combinatorial optimization: sorting (as maximization of sortedness), shortest p…
The network information system is a military information network system with evolution characteristics. Evolution is a process of replacement between disorder and order, chaos and equilibrium. Given that the concept of evolution originates from biological systems, in this article, the evolution of network information architecture is analyzed by genetic algorithms, and the network information architecture is represented by chromosomes. Besides, the genetic algorithm is also applied to find the optimal chromosome in the architecture space. The evolutionary simulation is used to predict the optim…
An important challenge in reinforcement learning, including evolutionary robotics, is to solve multimodal problems, where agents have to act in qualitatively different ways depending on the circumstances. Because multimodal problems are often too difficult to solve directly, it is helpful to take advantage of staging, where a difficult task is divided into simpler subtasks that can serve as stepping stones for solving the overall problem. Unfortunately, choosing an effective ordering for these subtasks is difficult, and a poor ordering can reduce the speed and performance of the learning proce…
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）
Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models
School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Dayalbagh Educational Institute (Deemed University)（达亚尔巴格教育学院（ deemed大学））；Amity University Uttar Pradesh（阿米蒂北方邦大学）；Amity School of Engineering and Technology（阿米蒂工程技术学院）
Quantum inspired Evolutionary Algorithms were proposed more than a decade ago and have been employed for solving a wide range of difficult search and optimization problems. A number of changes have been proposed to improve performance of canonical QEA. However, canonical QEA is one of the few evolutionary algorithms, which uses a search operator with relatively large number of parameters. It is well known that performance of evolutionary algorithms is dependent on specific value of parameters for a given problem. The advantage of having large number of parameters in an operator is that the sea…
The cryptanalysis of various cipher problems can be formulated as NP-Hard combinatorial problem. Solving such problems requires time and/or memory requirement which increases with the size of the problem. Techniques for solving combinatorial problems fall into two broad groups - exact algorithms and Evolutionary Computation algorithms. An exact algorithms guarantees that the optimal solution to the problem will be found. The exact algorithms like branch and bound, simplex method, brute force etc methodology is very inefficient for solving combinatorial problem because of their prohibitive comp…
The graph partitioning problem (GPP) is a representative combinatorial optimization problem which is NP-hard. Currently, various approaches to solve GPP have been introduced. Among these, the GPP solution using evolutionary computation (EC) is an effective approach. There has not been any survey on the research applying EC to GPP since 2011. In this survey, we introduce various attempts to apply EC to GPP made in the recent seven years.
Can Large Language Models Be Trusted as Evolutionary Optimizers for Network-Structured Combinatorial Problems?
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University（数学科学系，物理与数学科学学院，南洋理工大学）；School of Computer Science and Engineering, Nanyang Technological University（计算机科学与工程学院，南洋理工大学）
Evolutionary algorithms (EAs), such as the genetic algorithm (GA), offer an elegant way to handle combinatorial optimization problems (COPs). However, limited by expertise and resources, most users do not have enough capability to implement EAs to solve COPs. An intuitive and promising solution is to outsource evolutionary operations to a cloud server, whilst it suffers from privacy concerns. To this end, this paper proposes a novel computing paradigm, evolution as a service (EaaS), where a cloud server renders evolutionary computation services for users without sacrificing users' privacy. Ins…
Diversification in a set of solutions has become a hot research topic in the evolutionary computation community. It has been proven beneficial for optimisation problems in several ways, such as computing a diverse set of high-quality solutions and obtaining robustness against imperfect modeling. For the first time in the literature, we adapt the evolutionary diversity optimisation for a real-world combinatorial problem, namely patient admission scheduling. We introduce an evolutionary algorithm to achieve structural diversity in a set of solutions subjected to the quality of each solution. We …
This paper deals with the resolution of combinatorial optimization problems, particularly those concerning the maritime transport scheduling. We are interested in the management platforms in a river port and more specifically in container organisation operations with a view to minimizing the number of container rehandlings. Subsequently, we rmeet customers delivery deadlines and we reduce ship stoppage time In this paper, we propose a genetic algorithm to solve this problem and we present some experiments and results.
In this paper we systematically study the importance, i.e., the influence on performance, of the main design elements that differentiate scalarizing functions-based multiobjective evolutionary algorithms (MOEAs). This class of MOEAs includes Multiobjecitve Genetic Local Search (MOGLS) and Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) and proved to be very successful in multiple computational experiments and practical applications. The two algorithms share the same common structure and differ only in two main aspects. Using three different multiobjective combinatorial op…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while some others playing the role of random search, have become rather popular for tackling various NP-hard optimization problems. While empirical studies demonstrate that hybrid evolutionary algorithms are frequently successful at finding solutions having fitness sufficiently close to the optimal, many fewer articles address the computational complexity in a mathe…
Google（谷歌）；Columbia University（哥伦比亚大学）；Oxford University（牛津大学）；Waymo（Waymo公司）；UC Berkeley（加州大学伯克利分校）；University of Washington（华盛顿大学）
In this paper, we approach the problem of optimizing blackbox functions over large hybrid search spaces consisting of both combinatorial and continuous parameters. We demonstrate that previous evolutionary algorithms which rely on mutation-based approaches, while flexible over combinatorial spaces, suffer from a curse of dimensionality in high dimensional continuous spaces both theoretically and empirically, which thus limits their scope over hybrid search spaces as well. In order to combat this curse, we propose ES-ENAS, a simple and modular joint optimization procedure combining the class of…
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…
Evolutionary optimization is a generic population-based metaheuristic that can be adapted to solve a wide variety of optimization problems and has proven very effective for combinatorial optimization problems. However, the potential of this metaheuristic has not been utilized in Distributed Constraint Optimization Problems (DCOPs), a well-known class of combinatorial optimization problems prevalent in Multi-Agent Systems. In this paper, we present a novel population-based algorithm, Anytime Evolutionary DCOP (AED), that uses evolutionary optimization to solve DCOPs. In AED, the agents cooperat…
Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set of solutions has gained increasing attention in recent years. Diversity optimization in terms of features on the underlying problem allows to obtain a better understanding of possible solutions to the problem at hand and can be used for algorithm selection when dealing with combinatorial optimization problems such as the Traveling Salesperson Problem. We expl…
Photomosaic images are a type of images consisting of various tiny images. A complete form can be seen clearly by viewing it from a long distance. Small tiny images which replace blocks of the original image can be seen clearly by viewing it from a short distance. In the past, many algorithms have been proposed trying to automatically compose photomosaic images. Most of these algorithms are designed with greedy algorithms to match the blocks with the tiny images. To obtain a better visual sense and satisfy some commercial requirements, a constraint that a tiny image should not be repeatedly us…
Variable Search Stepsize for Randomized Local Search in Multi-Objective Combinatorial Optimization
School of Computer, China University of Geosciences（中国地质大学计算机学院）；Engineering Research Center of Natural Resource Information Management and Digital Twin Engineering Software, Ministry of Education（教育部自然资源信息管理与数字孪生工程软件工程研究中心）；Hubei Key Laboratory of Intelligent Geo-Information Processing（湖北省智能地理信息处理重点实验室）；School of Computer, Science and Informatics, De Montfort University（德蒙福特大学计算机、科学与信息学院）；School of Computer Science, University of Birmingham（伯明翰大学计算机科学学院）；School of Chemical Engineering, University of Birmingham（伯明翰大学化学工程学院）
Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究中心）；Leiden University Medical Center（莱顿大学医学中心）；TU Delft（代尔夫特理工大学）
We propose a novel surrogate-assisted Evolutionary Algorithm for solving expensive combinatorial optimization problems. We integrate a surrogate model, which is used for fitness value estimation, into a state-of-the-art P3-like variant of the Gene-Pool Optimal Mixing Algorithm (GOMEA) and adapt the resulting algorithm for solving non-binary combinatorial problems. We test the proposed algorithm on an ensemble learning problem. Ensembling several models is a common Machine Learning technique to achieve better performance. We consider ensembles of several models trained on disjoint subsets of a …
Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of evolutionary algorithms for a dynamic variant of a classical combinatorial optimization problem, namely makespan scheduling. We study the model of a strong adversary which is allowed to change one job at regular intervals. Furthermore, we investigate the setting of random changes. Our results show that randomized local search and a simple evolutionary algorithm are ve…
Evolutionary algorithms based on modeling the statistical dependencies (interactions) between the variables have been proposed to solve a wide range of complex problems. These algorithms learn and sample probabilistic graphical models able to encode and exploit the regularities of the problem. This paper investigates the effect of using probabilistic modeling techniques as a way to enhance the behavior of MOEA/D framework. MOEA/D is a decomposition based evolutionary algorithm that decomposes a multi-objective optimization problem (MOP) in a number of scalar single-objective subproblems and op…
The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization performance of evolutionary algorithms. Within the paper, we consider a constrained version of the problem named 2-Hop (1,2)-Minimum Spanning Tree problem (abbr. 2H-(1,2)-MSTP) in the context of evolutionary algorithms, which has been shown to be NP-hard. Following how evolutionary algorithms are applied to solve the MSTP, we first consider the evolutionary algorith…
For complex combinatorial optimization problems, models and algorithms are at the heart of the solution. The complexity of many types of satellite mission planning problems is NP-hard and places high demands on the solution. In this paper, two types of satellite scheduling problem models are introduced and a reinforcement learning based evolutionary algorithm framework based is proposed.
Nanjing University（南京大学）；Southern University of Science and Technology（南方科技大学）
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising results on the running time analysis (one essential theoretical aspect) of EAs have been obtained, while most of them focused on isolated combinatorial optimization problems, which do not reflect the general-purpose nature of EAs. To provide a general theoretical explanation of the behavior of EAs, it is desirable to study their performance on general classes of …
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…
This paper proposes a generalized Hybrid Real-coded Quantum Evolutionary Algorithm (HRCQEA) for optimizing complex functions as well as combinatorial optimization. The main idea of HRCQEA is to devise a new technique for mutation and crossover operators. Using the evolutionary equation of PSO a Single-Multiple gene Mutation (SMM) is designed and the concept of Arithmetic Crossover (AC) is used in the new Crossover operator. In HRCQEA, each triploid chromosome represents a particle and the position of the particle is updated using SMM and Quantum Rotation Gate (QRG), which can make the balance …
Evolutionary multi-objective algorithms have been widely shown to be successful when utilized for a variety of stochastic combinatorial optimization problems. Chance constrained optimization plays an important role in complex real-world scenarios, as it allows decision makers to take into account the uncertainty of the environment. We consider a version of the knapsack problem with stochastic profits to guarantee a certain level of confidence in the profit of the solutions. We introduce the multi-objective formulations of the profit chance constrained knapsack problem and design three bi-objec…
This paper describes the N-Tuple Bandit Evolutionary Algorithm (NTBEA), an optimisation algorithm developed for noisy and expensive discrete (combinatorial) optimisation problems. The algorithm is applied to two game-based hyper-parameter optimisation problems. The N-Tuple system directly models the statistics, approximating the fitness and number of evaluations of each modelled combination of parameters. The model is simple, efficient and informative. Results show that the NTBEA significantly outperforms grid search and an estimation of distribution algorithm.
Evolutionary computation (EC) algorithms, such as discrete and multi-objective versions of particle swarm optimization (PSO), have been applied to solve the Feature selection (FS) problem, tackling the combinatorial explosion of search spaces that are peppered with local minima. Furthermore, high-dimensional FS problems such as finding a small set of biomarkers to make a diagnostic call add an additional challenge as such methods ability to pick out the most important features must remain unchanged in decision spaces of increasing dimensions and presence of irrelevant features. We developed a …
Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem (GMST), and the generalised travelling salesman problem (GTSP) in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other …
Transfer Optimization is an incipient research area dedicated to solving multiple optimization tasks simultaneously. Among the different approaches that can address this problem effectively, Evolutionary Multitasking resorts to concepts from Evolutionary Computation to solve multiple problems within a single search process. In this paper we introduce a novel adaptive metaheuristic algorithm to deal with Evolutionary Multitasking environments coined as Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm (AT-MFCGA). AT-MFCGA relies on cellular automata to implement mechanisms in o…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming…
In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological features on the dynamics of an evolutionary algorithm, considering in particular the ability to find a large number of optima on multi-modal problems. We introduce a novel spatially-structured evolutionary algorithm and we apply it on two combinatorial problems: ONEMAX and the multi-modal NMAX. Considering three different network models we investigate the relat…
Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the structure of optimal solutions is given, which can be leveraged by means of biased search operators. We consider the Minimum Spanning Tree (MST) problem in a single- and multi-objective version, and introduce a biased mutation, which puts more emphasis on the selection of edges of low rank in terms of low domination number. We present example graphs where the b…
Recently, the discretization of decision and objective spaces has been discussed in the literature. In some studies, it is shown that the decision space discretization improves the performance of evolutionary multi-objective optimization (EMO) algorithms on continuous multi-objective test problems. In other studies, it is shown that the objective space discretization improves the performance on combinatorial multi-objective problems. However, the effect of the simultaneous discretization of both spaces has not been examined in the literature. In this paper, we examine the effects of the decisi…
Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these algorithms are not well understood and the field is lacking a solid theoretical foundation that explains when and why memetic algorithms are effective. We provide a rigorous runtime analysis of a simple memetic algorithm, the $(1+1)$ MA, on the Hurdle problem class, a landscape class of tuneable difficulty that shows a "big valley structure", a characteristic feat…
University of Southampton（南安普顿大学）；University of Birmingham（伯明翰大学）
Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully applied to classification, regression, decision and generative tasks and in this paper we extend its application to solving optimisation problems. Model Building Optimisation Algorithms (MBOAs), a branch of evolutionary algorithms, have been successful in combining machine learning methods and evolutionary search but, until now, they have not utilised DNNs. DO is …
Sun Yat-sen University（中山大学）；Guangdong University of Finance and Economics（广东财经大学）
Learning-based heuristics for solving combinatorial optimization problems has recently attracted much academic attention. While most of the existing works only consider the single objective problem with simple constraints, many real-world problems have the multiobjective perspective and contain a rich set of constraints. This paper proposes a multiobjective deep reinforcement learning with evolutionary learning algorithm for a typical complex problem called the multiobjective vehicle routing problem with time windows (MO-VRPTW). In the proposed algorithm, the decomposition strategy is applied …
The performance of base-line Evolutionary Algorithms (EAs) on combinatorial problems has been studied rigorously. From the theoretical viewpoint, the literature extensively investigates the linear problems, while the theoretical analysis of the non-linear problems is still far behind. In this paper, variations of the Packing While Travelling (PWT) -- also known as the non-linear knapsack problem -- are studied as an attempt to analyse the behaviour of EAs on non-linear problems from theoretical perspective. We investigate PWT for two cities and $n$ items with correlated weights and profits, us…
Filter pruning is a common method to achieve model compression and acceleration in deep neural networks (DNNs).Some research regarded filter pruning as a combinatorial optimization problem and thus used evolutionary algorithms (EA) to prune filters of DNNs. However, it is difficult to find a satisfactory compromise solution in a reasonable time due to the complexity of solution space searching. To solve this problem, we first formulate a multi-objective optimization problem based on a sub-network of the full model and propose a Sub-network Multiobjective Evolutionary Algorithm (SMOEA) for filt…
