Maximum mean discrepancy (MMD) has been widely employed to measure the distance between probability distributions. In this paper, we propose using MMD to solve continuous multi-objective optimization problems (MOPs). For solving MOPs, a common approach is to minimize the distance (e.g., Hausdorff) between a finite approximate set of the Pareto front and a reference set. Viewing these two sets as empirical measures, we propose using MMD to measure the distance between them. To minimize the MMD value, we provide the analytical expression of its gradient and Hessian matrix w.r.t. the search variables, and use them to devise a novel set-oriented, MMD-based Newton (MMDN) method. Also, we analyze the theoretical properties of MMD's gradient and Hessian, including the first-order stationary condition and the eigenspectrum of the Hessian, which are important for verifying the correctness of MMDN. To solve complicated problems, we propose hybridizing MMDN with multiobjective evolutionary algorithms (MOEAs), where we first execute an EA for several iterations to get close to the global Pareto front and then warm-start MMDN with the result of the MOEA to efficiently refine the approximation. We empirically test the hybrid algorithm on 11 widely used benchmark problems, and the results show the hybrid (MMDN + MOEA) can achieve a much better optimization accuracy than EA alone with the same computation budget.

In the domain of multi-objective optimization, evolutionary algorithms are distinguished by their capability to generate a diverse population of solutions that navigate the trade-offs inherent among competing objectives. This has catalyzed the ascension of evolutionary multi-objective optimization (EMO) as a prevalent approach. Despite the effectiveness of the EMO paradigm, the analysis of resultant solution sets presents considerable challenges. This is primarily attributed to the high-dimensional nature of the data and the constraints imposed by static visualization methods, which frequently culminate in visual clutter and impede interactive exploratory analysis. To address these challenges, this paper introduces ParetoLens, a visual analytics framework specifically tailored to enhance the inspection and exploration of solution sets derived from the multi-objective evolutionary algorithms. Utilizing a modularized, algorithm-agnostic design, ParetoLens enables a detailed inspection of solution distributions in both decision and objective spaces through a suite of interactive visual representations. This approach not only mitigates the issues associated with static visualizations but also supports a more nuanced and flexible analysis process. The usability of the framework is evaluated through case studies and expert interviews, demonstrating its potential to uncover complex patterns and facilitate a deeper understanding of multi-objective optimization solution sets. A demo website of ParetoLens is available at https://dva-lab.org/paretolens/.

Multi-objective evolutionary algorithms (MOEAs) are widely used for searching optimal solutions in complex multi-component applications. Traditional MOEAs for multi-component deep learning (MCDL) systems face challenges in enhancing the search efficiency while maintaining the diversity. To combat these, this paper proposes $\mu$MOEA, the first LLM-empowered adaptive evolutionary search algorithm to detect safety violations in MCDL systems. Inspired by the context-understanding ability of Large Language Models (LLMs), $\mu$MOEA promotes the LLM to comprehend the optimization problem and generate an initial population tailed to evolutionary objectives. Subsequently, it employs adaptive selection and variation to iteratively produce offspring, balancing the evolutionary efficiency and diversity. During the evolutionary process, to navigate away from the local optima, $\mu$MOEA integrates the evolutionary experience back into the LLM. This utilization harnesses the LLM's quantitative reasoning prowess to generate differential seeds, breaking away from current optimal solutions. We evaluate $\mu$MOEA in finding safety violations of MCDL systems, and compare its performance with state-of-the-art MOEA methods. Experimental results show that $\mu$MOEA can significantly improve the efficiency and diversity of the evolutionary search.

Network intrusion detection is one of the most important issues in the field of cyber security, and various machine learning techniques have been applied to build intrusion detection systems. However, since the number of features to describe the network connections is often large, where some features are redundant or noisy, feature selection is necessary in such scenarios, which can both improve the efficiency and accuracy. Recently, some researchers focus on using multi-objective evolutionary algorithms (MOEAs) to select features. But usually, they only consider the number of features and classification accuracy as the objectives, resulting in unsatisfactory performance on a critical metric, detection rate. This will lead to the missing of many real attacks and bring huge losses to the network system. In this paper, we propose DR-MOFS to model the feature selection problem in network intrusion detection as a three-objective optimization problem, where the number of features, accuracy and detection rate are optimized simultaneously, and use MOEAs to solve it. Experiments on two popular network intrusion detection datasets NSL-KDD and UNSW-NB15 show that in most cases the proposed method can outperform previous methods, i.e., lead to fewer features, higher accuracy and detection rate.

For autonomous crane lifting, optimal trajectories of the crane are required as reference inputs to the crane controller to facilitate feedforward control. Reducing the unactuated payload motion is a crucial issue for under-actuated tower cranes with spherical pendulum dynamics. The planned trajectory should be optimal in terms of both operating time and energy consumption, to facilitate optimum output spending optimum effort. This article proposes an anti-swing tower crane trajectory planner that can provide time-energy optimal solutions for the Computer-Aided Lift Planning (CALP) system developed at Nanyang Technological University, which facilitates collision-free lifting path planning of robotized tower cranes in autonomous construction sites. The current work introduces a trajectory planning module to the system that utilizes the geometric outputs from the path planning module and optimally scales them with time information. Firstly, analyzing the non-linear dynamics of the crane operations, the tower crane is established as differentially flat. Subsequently, the multi-objective trajectory optimization problems for all the crane operations are formulated in the flat output space through consideration of the mechanical and safety constraints. Two multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II) and Generalized Differential Evolution 3 (GDE3), are extensively compared via statistical measures based on the closeness of solutions to the Pareto front, distribution of solutions in the solution space and the runtime, to select the optimization engine of the planner. Finally, the crane operation trajectories are obtained via the corresponding planned flat output trajectories. Studies simulating real-world lifting scenarios are conducted to verify the effectiveness and reliability of the proposed module of the lift planning system.

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e.g., non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

Recent decades have witnessed great advancements in multiobjective evolutionary algorithms (MOEAs) for multiobjective optimization problems (MOPs). However, these progressively improved MOEAs have not necessarily been equipped with scalable and learnable problem-solving strategies for new and grand challenges brought by the scaling-up MOPs with continuously increasing complexity from diverse aspects, mainly including expensive cost of function evaluations, many objectives, large-scale search space, time-varying environments, and multi-task. Under different scenarios, divergent thinking is required in designing new powerful MOEAs for solving them effectively. In this context, research studies on learnable MOEAs with machine learning techniques have received extensive attention in the field of evolutionary computation. This paper begins with a general taxonomy of scaling-up MOPs and learnable MOEAs, followed by an analysis of the challenges that these MOPs pose to traditional MOEAs. Then, we synthetically overview recent advances of learnable MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive directions (i.e., learnable evolutionary discriminators for environmental selection, learnable evolutionary generators for reproduction, learnable evolutionary evaluators for function evaluations, and learnable evolutionary transfer modules for sharing or reusing optimization experience). The insight of learnable MOEAs is offered to readers as a reference to the general track of the efforts in this field.

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 the proposed approach with a simple benchmark problem and a real-world, complex warehouse design and control problem. The experimental results demonstrate the advantages of our method in terms of solution quality and computation time to reach good solutions. In addition, we show the learned policy is transferable, i.e., the policy trained on a simple benchmark problem can be directly applied to solve the complex warehouse optimization problem, effectively, without the need for retraining.

The performance of multiobjective algorithms varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from component parts. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still uncertain what are the most influential components leading to their performance improvement. This study introduces a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a well-performing Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) designed by the irace package on nine constrained problems. We then contrast the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the hypervolume. Our results indicate that the most influential components were the restart and update strategies, with higher increments in performance and more distinct metric values. Also, their relative influence depends on the problem difficulty: not using the restart strategy was more influential in problems where MOEA/D performs better; while the update strategy was more influential in problems where MOEA/D performs the worst.

Finding the most influential nodes in a network is a computationally hard problem with several possible applications in various kinds of network-based problems. While several methods have been proposed for tackling the influence maximisation (IM) problem, their runtime typically scales poorly when the network size increases. Here, we propose an original method, based on network downscaling, that allows a multi-objective evolutionary algorithm (MOEA) to solve the IM problem on a reduced scale network, while preserving the relevant properties of the original network. The downscaled solution is then upscaled to the original network, using a mechanism based on centrality metrics such as PageRank. Our results on eight large networks (including two with $\sim$50k nodes) demonstrate the effectiveness of the proposed method with a more than 10-fold runtime gain compared to the time needed on the original network, and an up to $82\%$ time reduction compared to CELF.