Trained on large corpora of image-text pairs, vision-language models (VLMs) have proven broadly useful across many applications. However, they can still make errors that humans rarely do, particularly when exposed to adversarial inputs crafted to mislead them. Traditional approaches to uncovering such vulnerabilities typically optimize a single input, such as a text prompt, to induce incorrect predictions while remaining plausible to human readers. These methods tend to identify only one or a few high-impact adversarial examples, offering a narrow view of model weaknesses. In contrast, we argue that a Quality-Diversity (QD) perspective is more informative. Rather than searching for a single best attack, QD explicitly aims to generate many high-quality adversarial prompts spanning diverse behaviors and characteristics. This allows us not only to diagnose model weaknesses, but also to characterize which prompts are robust and which are especially fragile. Our experiments show that CVT-MAP-Elites, a QD method integrated into our pipeline, discovers a richer and more diverse set of meaningful adversarial samples than quality-only optimization. Consequently, our approach achieves broader search-space coverage and provides deeper insight into VLM failure modes on text-to-image retrieval tasks in both general and medical domains.

Training-free metrics, also known as Zero-Cost (ZC) proxies, enable efficient exploration in Neural Architecture Search (NAS) but are less effective than training-based metrics like validation accuracy in identifying high-performance networks. In this article, we investigate the effectiveness of ZC proxies by taking a deeper look into their fitness landscapes utilizing Local Optima Networks. We introduce MF-NAS, a two-stage NAS framework that first employs a ZC proxy-guided local search algorithm to explore the search space. Networks with the highest ZC scores are then fed into the Successive Halving (SH) algorithm to identify the top-performing architecture. However, we observe considerable performance gaps when different ZC metrics are employed. Analyzing those MF-NAS variants with Search Trajectory Networks, we find that high-performance networks could be encountered early or midway through the ZC proxy-guided local search process, making selection based solely on the highest ZC scores ineffective in certain cases. To address this issue, we propose the R-MF-NAS framework, where the selected networks for SH include not only those with the highest ZC scores but also promising solutions encountered during the local search stage. Experiments on diverse NAS benchmarks demonstrate the superiority of both MF-NAS and R-MF-NAS over state-of-the-art methods under a strict budget.

Transformer-based dialogue generation (DG) models are ubiquitous in modern conversational artificial intelligence platforms. These models, however, are susceptible to adversarial attacks, i.e., prompts that appear indiscernible from normal inputs but are maliciously crafted to make the models generate incoherent and irrelevant responses. Evaluating the adversarial robustness of DG models is crucial to their real-world deployment. Adversarial methods typically exploit gradient information to effectively modify key input tokens, thereby achieving excellent attack performance. Nevertheless, such white-box approaches are impractical in real-world scenarios since the models' internal parameters are inaccessible. While black-box methods, which exploit only input prompts and DG models' output responses, offer a wider applicability, they often suffer from poor performance. In a human-machine conversation, good responses are expected to be semantically coherent and textually succinct. We formulate adversarial attack on DG models as a bi-objective optimization problem, where input prompts are modified in order to minimize the response coherence and maximize the generation length. We propose a DG attack framework (DGAttack) that employs multi-objective optimization to consider both objectives simultaneously when perturbing user prompts to craft adversarial inputs. Experiments across four benchmark datasets and (large) language models demonstrate the excellent performance of DGAttack compared to existing state-of-the-art approaches.

The rapid increase of object detection's applications leads to a growing need for these models to be robust to adversarial examples. However, it has been shown that deep neural networks (DNNs) are vulnerable to adversarial examples. In this work, we explore the vulnerability of recent object detection models by generating sparse adversarial examples that differ from the original images by only a few pixels. Moreover, to be suitable for real-world scenarios, we consider the context in which we are ignorant of victim models and employ a gradient-free approach to generate imperceptible adversarial examples. Notably, there are two challenges that we have to address simultaneously: reducing the number of perturbed pixels and limiting the number of queries needed to successfully find an adversarial example. Existing methods usually try to solve only one of those challenges, regardless of the poor quality of the other, and result in high computational resources or perceptible adversarial examples. Our study aims to use only a small number of queries to generate imperceptible perturbations that make object detectors yield wrong predictions. Our experiments are conducted with the convolutional neural network-based YOLO family and the vision transformer-based models (i.e., DINO and DETR) on the PASCAL-VOC dataset.

Mixed-Integer Black-Box Optimization (MI-BBO) problems involve optimizing objective functions that have both continuous and integer decision variables without access to any problem-specific knowledge such as gradient or Hessian. Although recent studies have made notable progress in solving many MI-BBO problems, inherent challenges persist, particularly regarding the problem dimensionality and the expected runtime (ERT) required to reach the target values. In this paper, we propose an efficient MI-BBO method that uses evolution strategies with plateau handling techniques. To address problems with higher dimensions, we explore several high-dimensional algorithms, such as VD-CMA (a linear variant of CMA-ES for High Dimension Optimization) and CR-FM-NES (Cost-Reduction Fast Moving Natural Evolution Strategy), and appropriately adapt certain plateau handling techniques to enhance the optimization performance. Numerical experiments with standard benchmark functions against prominent recently-proposed MI-BBO algorithms demonstrate that our methods can solve problems with higher dimensions while maintaining the optimization efficiency. Moreover, the results also reveal the potential for scaling to more challenging problem classes with low computational costs. The source code can be found at: https://github.com/ELO-Lab/eMI-BBO.

Medical image retrieval is essential for clinical diagnosis and medical education, yet remains highly challenging in endoscopic imaging due to limited annotated data, the lack of domain-specific pretrained models, and subtle visual similarities across anatomical regions. In this work, we utilize self-supervised contrastive learning to pretrain a strong image encoder tailored for endoscopic data, which serves as the backbone for downstream retrieval tasks. For text-to-image retrieval, we adopt a multi-modal contrastive learning approach that aligns textual and visual representations based on this pretrained backbone. To further enhance retrieval performance, we propose a novel re-ranking module that leverages the reasoning capabilities of large vision-language models (LVLMs), such as GPT-4o and Gemini. We also provide a comparative analysis of various retrieval strategies, offering insights into their effectiveness in clinical scenarios. Our method achieves top-2 in text-to-image and top-5 in image-to-image retrieval at the ENTRep Challenge 2025, demonstrating its potential value for endoscopic image retrieval. Source code is available at https://github.com/ELO-Lab/ENTRep-LDSF.

Neural Architecture Search (NAS) aims to automate the process of architecture design to alleviate the burden of manual trial-and-error when seeking top-performing neural networks for certain tasks. Traditional NAS methods perform network evaluations with full network training, typically incurring hundreds of training epochs for each candidate architecture. Such expensive search costs are infeasible in real-world applications. Several zero-cost metrics, which are computed based on randomly initialized network weights, have been proposed for efficiently estimating architecture quality as a proxy for network accuracy performance. These metrics require much less computation time but may not exhibit sufficient correlation with the actual accuracy. Using a single proxy metric might mislead the search, especially in the region of good-performing architectures in the search space. In this paper, we propose a two-phase Evolutionary Neural Architecture Search with Zero-Cost Proxy-Based Hierarchical Initialization (eNAS-HI) framework. A tree search algorithm, guided by three training-free performance proxy metrics, is used to prune the search space and efficiently identify a diverse set of promising architectures in the initialization phase. These architectures then serve as the initial population for a genetic algorithm in the subsequent evolution phase. The diversity and quality of the initial population help eNAS-HI in finding top-performing architectures with reduced search costs.

CEM-RL is a state-of-the-art evolutionary rein-forcement learning (ERL) framework to perform policy search for control problems with continuous action spaces. CEM-RL employs a cross-entropy method (CEM) variant, in essence a Gaussian Estimation-of-Distribution Algorithm (EDA), to model the distribution of high-performing control policies, which are typically parameterized by (deep) neural networks. For each iteration, new policies are generated from the learned distribution and are further improved by an actor-critic policy gradient procedure, in particular, Deep Deterministic Policy Gradient (DDPG) or Twin-Delayed DDPG (TD3). In this paper, we employ the Adapted Maximum-Likelihood Gaussian Model Iterated Density-Estimation Evolutionary Algorithm (AMaLGaM), which offers a wider range of customization options than CEM. Beside DDPG and TD3, we consider the recently-introduced Double Actors Regularized Critics (DARC), that can address the overestimation bias of DDPG and the underestimation bias of TD3, for the integration with AMaLGaM. Benchmark results on MuJoCo continuous locomotion tasks demonstrate the excellent performance

Using zero-cost (ZC) metrics as proxies for network performance in Neural Architecture Search (NAS) allows search algorithms to thoroughly explore the architecture space due to their low computing costs. Nevertheless, recent studies indicate that relying exclusively on ZC proxies appears to be less effective than using traditional training-based metrics, such as validation accuracy, in seeking high-performance networks. In this study, we investigate the effectiveness of ZC proxies by taking a deeper look into fitness landscapes of ZC proxy-based local searches by utilizing Local Optima Networks (LONs). Our findings exhibit that ZC proxies having high correlation with network performance do not guarantee finding top-performing architectures, and ZC proxies with low correlations could still be better in certain situations. Our results further consolidate the suggestion of favoring training-based metrics over ZC proxies as the search objective. Although we could figure out architectures having the optimal ZC proxy scores, their true performance is often poor. We then propose the Multi-Fidelity Neural Architecture Search (MF-NAS) framework that makes use of the efficiency of ZC proxies and the efficacy of training-based metrics. Experimental results on a wide range of NAS benchmarks demonstrate the superiority of our MF-NAS to state-of-the-art methods under a strict budget.

Neural Architecture Search (NAS) is a promising approach to automate the design of neural network architectures, which can find architectures that perform better than manually designed ones. Hardware-aware NAS is a real-world application of NAS where the architectures found also need to satisfy certain requirements for the deployment of specific devices. Despite the practical importance, hardware-aware NAS still receives a lack of attention from the community. Existing research mostly focuses on the search space with a limited number of architectures, reducing the search process to finding the optimal hyperparameters. In addition, the performance evaluation of found networks is resources-intensive, which can severely hinder reproducibility. In this work, we propose a genetic algorithm approach to the hardware-aware NAS problem, incorporating a latency filtering selection to guarantee the latency validity of candidate solutions. We also introduce an extended search space that can cover various existing architectures from previous research. To speed up the search process, we also present a method to estimate the latency of candidate networks and a training-free performance estimation method to quickly evaluate candidate networks. Our experiments demonstrate that our method achieves competitive performance with state-of-the-art networks while maintaining lower latency with less computation requirements for searching.

Evolutionary algorithms (EAs) are often employed to tackle multimodal optimization (MMO), offering the possibility to obtain multiple distinct optimal solutions in one run of the algorithm. Nevertheless, it is challenging to analyze the behaviors of multimodal EAs (MEAs) due to the synergies between the global stage (typically a niching method) and the local stage (typically a core search algorithm) that exist in most MEAs. While Search Trajectory Networks (STNs) are a helpful visualization tool to characterize the behaviors of EAs in approaching a single global optimum, naively applying STNs in MMO yields unintelligible resulting graphs. We here propose an STN variant adapted specifically for depicting the progress of MEAs when locating the set of all global optima. Using this multimodal STN, we carry out investigations for four MEAs created from the combinations of two global-stage mechanisms (i.e., uniform random restart and hill-valley clustering) and two local-stage algorithms (i.e., an evolution strategy and a Gaussian estimation-of-distribution algorithm). Visualization results on 20 functions of the CEC 2013 niching benchmark suite exhibit intrinsic capabilities of these MEAs, yielding interesting explanations for their performance. Source code is available at: https://github.com/ELO-Lab/MDSTN.

Neural Architecture Search (NAS) aims to automate the discovery of high-performing deep neural network architectures. Traditional objective-based NAS approaches typically optimize a certain performance metric (e.g., prediction accuracy), overlooking large parts of the architecture search space that potentially contain interesting network configurations. Furthermore, objective-driven population-based metaheuristics in complex search spaces often quickly exhaust population diversity and succumb to premature convergence to local optima. This issue becomes more complicated in NAS when performance objectives do not fully align with the actual performance of the candidate architectures, as is often the case with training-free metrics. While training-free metrics have gained popularity for their rapid performance estimation of candidate architectures without incurring computation-heavy network training, their effective incorporation into NAS remains a challenge. This paper presents the Pareto Dominance-based Novelty Search for multi-objective NAS with Multiple Training-Free metrics (MTF-PDNS). Unlike conventional NAS methods that optimize explicit objectives, MTF-PDNS promotes population diversity by utilizing a novelty score calculated based on multiple training-free performance and complexity metrics, thereby yielding a broader exploration of the search space. Experimental results on standard NAS benchmark suites demonstrate that MTF-PDNS outperforms conventional methods driven by explicit objectives in terms of convergence speed, diversity maintenance, architecture transferability, and computational costs.

Multi-Objective Evolutionary Neural Architecture Search (MOENAS) methods employ evolutionary algorithms to approximate a set of architectures representing optimal trade-offs between network performance and complexity. Directly estimating network performance via error rates or losses incurs long runtimes due to the computationally expensive network training procedure. Instead, low-cost metrics that require no network training have been proposed as a proxy for network performance. However, these metrics might exhibit inconsistent correlations with network performance across different search spaces . The influences of training-based and training-free metrics on the effectiveness and efficiency of MOENAS are still under-explored. We introduce the Enhanced Training-Free MOENAS (E-TF-MOENAS) that employs the widely-used NSGA-II as the search algorithm and optimizes multiple training-free performance metrics as separate objectives. Experiments on NAS-Bench-101 and NAS-Bench-201 show that E-TF-MOENAS outperforms training-free methods that use a single training-free performance metric and could obtain comparable results to training-based methods but with approximately 30 times less computation cost. E-TF-MOENAS obtains architectures in NAS-Bench-201 with state-of-the-art mean accuracies of 94.37%, 73.50%, and 46.62% for CIFAR-10, CIFAR-100, and ImageNet16-120, respectively, within less than 3 GPU hours. It is beneficial to utilize multiple training-free proxy metrics simultaneously and E-TF-MOENAS provides a convenient framework for building such an efficient NAS approach. The source code can be found at https://github.com/ELO-Lab/E-TF-MOENAS .

Evolutionary Reinforcement Learning arises from hybridizing the sample efficiency of policy gradient with the stability of evolutionary computation. Proximal Distilled Evolutionary Reinforcement Learning (PDERL) implements the hybridization by having information transferred between an RL agent operating alongside a population of candidate policies. PDERL employs two phenotype-based variation operators, behavior distillation crossover and proximal mutation, which exhibit better effectiveness compared to traditional genotype-based operators. We demonstrate that the proximal mutation is sensitive to its mutation magnitude hyperparameter, which yields damaging effects if its value is improperly set. Inspired from Differential Evolution, we propose a novel mutation procedure that operates on action vectors generated by candidate policies. The phenotypic differential mutation (PhDM) shows its stability in diversity maintenance with little disruption. A recently-introduced actor-critic policy gradient algorithm, Double Actors Regularized Critics (DARC), exhibits a superior sample efficiency. DARC alleviates both overestimation and underestimation bias via the usage of two actors for better exploration and a dedicated critic regularization technique. In this paper, we restructure PDERL to incorporate PhDM and the policy gradient mechanism of DARC. Experimental results show that our Phenotypic Evolutionary DARC (PhEDARC) outperforms both PDERL and DARC in four control tasks from OpenAI Gym. Ablation studies support our design choices.

Neural architecture search (NAS) involves automatically searching for promising deep neural network structures in certain architecture spaces. Depending on the number of criteria being concerned, NAS can be formulated as single-objective optimization problems (SONAS) or multi-objective optimization problems (MONAS). Evolutionary algorithms (EAs) are common approaches for NAS due to their effectiveness in solving challenging combinatorial problems. Recent studies, however, have analyzed SONAS landscapes and indicated that while NAS problems are multi-modal but local search algorithms with simple perturbation operators can escape local optima to reach global optima without much difficulty. Such investigations for MONAS remain under-explored. In this paper, we employ local optimal networks (LONs) for visually structuring the MONAS landscape with a simple local search procedure. Via detailed analyses, we then design LOMONAS, a dedicated Pareto local search algorithm for MONAS. The experimental results on four NAS benchmarks (MacroNAS, NAS-Bench-101, NAS-Bench-201, and NAS-Bench-ASR) exhibit the superior performance of LOMONAS compared to two widely-used multi-objective EAs (MOEAs), NSGA-II and MOEA/D. The findings indicate that Pareto local search algorithms are competitive with MOEAs in solving MONAS problems.

Real-world continuous control problems often require optimizing for multiple conflicting objectives. Various works in multi-objective reinforcement learning have been conducted to tackle such issues and obtained impressive performance. At the same time, evolutionary algorithms (EAs), which are extensively used in multi-objective optimization, have recently been demonstrated their competitiveness to RL algorithms, including multi-objective control for environments with discrete action spaces. However, using EAs for multi-objective continuous robot control is still an under-explored topic. For the single-objective setting, the Proximal Distilled Evolutionary Reinforcement Learning (PDERL) framework succeeds in combining the robustness of EA and the efficiency of RL methods. In this work, we bring the strengths of PDERL to the multiobjective realm to create the novel multi-objective PDERL framework called MOPDERL that consists of a warm-up stage and an evolution stage. In particular, MOPDERL collaboratively optimizes policies for each separate objective in the warm-up stage, and then exchanges that knowledge for further policy improvement during the multi-objective evolution stage. We benchmark MOPDERL on six MuJoCo robot locomotion environments, which have been modified for the multi-objective context. The results show that MOPDERL produces better-quality Pareto fronts and higher metric scores than the state-of-the-art PGMORL algorithm across five out of six environments.

In this paper, we propose CEM-SAC - a hybridization between the cross-entropy method (CEM), i.e., an estimation-of-distribution algorithm, and the soft-actor critic (SAC), i.e., a state-of-the-art policy gradient algorithm. Our work extends the evolutionary reinforcement learning (ERL) line of research on integrating the robustness of population-based stochastic black-box optimization, that typically assumes little to no problem-specific knowledge, into the training process of policy gradient algorithms, that exploits the sequential decision making nature for efficient gradient estimation. Our hybrid approach, CEM-SAC, exhibits both the stability of CEM and the efficiency of SAC in training policy neural networks of reinforcement learning agents for solving control problems. Experimental result comparisons with the three baselines CEM, SAC, and CEM-TD3, a recently-introduced ERL method that combines CEM and the twin-delayed deep deterministic policy gradient (TD3) algorithm, on a wide range of control tasks in the MuJoCo benchmarks confirm the enhanced performance of our proposed CEM-SAC. The source code is available at https://github.com/ELO-Lab/CEM-SAC.

Neural Architecture Search (NAS) has received much attraction from the research community in recent years. However, due to the massive amount of computational resources required, it is still infeasible to employ NAS into research and production in small labs and companies. Recent methods in NAS that aim to speed up the evaluation process are often limit themselves in other aspects, such as the search space that NAS operates on. In this work, we propose TF-GeneNAS, an evolution-based training-free NAS approach with a dynamic search space and search strategy based on Gene Expression Programming. We conduct experiments on three tasks in both Computer Vision and Natural Language Processing domains to demonstrates the effectiveness of our method. With only 3 CPU days of searching needed, TF-GeneNAS can find network architectures with better performance than previous evolution-based methods, which can require days of GPU resources, thus significantly lower the cost of searching. We also perform further studies to show the impact of our training-free estimation strategy on the NAS process. We hope that our promising results can encourage further research into more efficient evolution-based NAS methods.

The Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA) has been shown to exhibit excellent performance in solving various bi-objective benchmark and real-world problems. We assess the competence of MO-RV-GOMEA in tackling many-objective problems, which are normally defined as problems with at least four conflicting objectives. Most Pareto dominance-based Multi-Objective Evolutionary Algorithms (MOEAs) typically diminish in performance if the number of objectives is more than three because selection pressure toward the Pareto-optimal front is lost. This is potentially less of an issue for MO-RV-GOMEA because its variation operator creates each offspring solution by iteratively altering a currently existing solution in a few decision variables each time, and changes are only accepted if they result in a Pareto improvement. For most MOEAs, integrating scalarization methods is potentially beneficial in the many-objective context. Here, we investigate the possibility of improving the performance of MO-RV-GOMEA by further guiding improvement checks during solution variation in MO-RV-GOMEA with carefully constructed Tchebycheff scalarizations. Results obtained from experiments performed on a selection of well-known problems from the DTLZ and WFG test suites show that MO-RV-GOMEA is by design already well-suited for many-objective problems. Moreover, by enhancing it with Tchebycheff scalarizations, it outperforms M0EA/D-2TCHMFI, a state-of-the-art decomposition-based MOEA.

This article tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introduced to satisfy the future power demands. Because of many real-world details involved, the structure of the problem is not exploited easily using mathematical programming techniques, for which reason we consider solving this problem with evolutionary algorithms (EAs). We compare three types of EAs for optimizing expansion plans: the classic genetic algorithm (GA), the estimation-of-distribution algorithm (EDA), and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). Not fully knowing the structure of the problem, we study the effect of linkage learning through the use of three linkage models: univariate, marginal product, and linkage tree. We furthermore experiment with the impact of incorporating different levels of problem-specific knowledge in the variation operators. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions. In all EAs, the marginal product model and its linkage learning procedure have difficulty in capturing and exploiting the DNEP problem structure. GOMEA, especially when combined with the linkage tree structure, is found to have the most robust performance by far, even when an out-of-the-box variant is used that does not exploit problem-specific knowledge. Based on experiments, we suggest that when selecting optimization algorithms for power system expansion planning problems, EAs that have the ability to effectively model and efficiently exploit problem structures, such as GOMEA, should be given priority, especially in the case of black-box or grey-box optimization.

The recently introduced Multi-Objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) exhibits excellent scalability in solving a wide range of challenging discrete multi-objective optimization problems. In this paper, we address scalability issues in solving multi-objective optimization problems with continuous variables by introducing the Multi-Objective Real-Valued GOMEA (MO-RV-GOMEA), which combines MO-GOMEA with aspects of the multi-objective estimation-of-distribution algorithm known as MAMaLGaM. MO-RV-GOMEA exploits linkage structure in optimization problems by performing distribution estimation, adaptation, and sampling as well as solution mixing based on an explicitly-defined linkage model. Such a linkage model can be defined a priori when some problem-specific knowledge is available, or it can be learned from the population. The scalability of MO-RV-GOMEA using different linkage models is compared to the state-of-the-art multi-objective evolutionary algorithms NSGA-II and MAMaLGaM on a wide range of benchmark problems. MO-RV-GOMEA is found to retain the excellent scalability of MO-GOMEA through the successful exploitation of linkage structure, scaling substantially better than NSGA-II and MAMaLGaM. This scalability is even further improved when partial evaluations are possible, achieving strongly sub-linear scalability in terms of the number of evaluations.

Brachytherapy is a form of radiotherapy whereby a radiation source is guided near tumors, using devices such as catheter implants. In the present clinical workflow, catheters are first placed inside or close to the tumor based on clinical expertise. Subsequently, software is used to design a plan for the delivery of radiation. Treatment planning is essentially a multi-objective optimization problem, where conflicting objectives represent radiation delivered to tumor cells and healthy cells. However, current clinical software collapses this information into a single-objective, constrained optimization problem. Moreover, catheter positioning is typically not included. As a consequence, it is hard to obtain insight into the true nature of the trade-offs between key planning objectives and the placement of catheters. Such insights are however crucial in understanding how better treatment plans may be constructed. To obtain such insights, we interface with real-world clinical software and derive potential catheter positions for real-world patients. Selecting and configuring catheters requires mixed-integer optimization. For this reason, we extend the recently-proposed Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT) to tackle multi-objective optimization problems. Our results indicate that clinically acceptable plans of high quality may be achievable with less catheters than typically used in current clinical practice.

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which includes the Linkage Tree Genetic Algorithm (LTGA), has been shown to scale excellently on a variety of discrete, Cartesian-space, optimization problems. This paper shows that GOMEA can quite straightforwardly also be used to solve permutation optimization problems by employing the random keys encoding of permutations. As a test problem, we consider permutation flowshop scheduling, minimizing the total flow time on 120 different problem instances (Taillard benchmark). The performance of GOMEA is compared with the recently published generalized Mallows estimation of distribution algorithm (GM-EDA). Statistical tests show that results of GOMEA variants are almost always significantly better than results of GM-EDA. Moreover, even without using local search, the new GOMEA variants obtained the best-known solution for 30 instances in every run and even new upper bounds for several instances. Finally, the time complexity per solution for building a dependency model to drive variation is an order of complexity less for GOMEA than for GM-EDA, altogether suggesting that GOMEA also holds much promise for permutation optimization.

This paper tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introduced to satisfy the future power demands. We compare two evolutionary algorithms (EAs) for optimizing expansion plans: the classic genetic algorithm (GA) with uniform crossover and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) that learns and exploits linkage information between problem variables. We study the impact of incorporating different levels of problem-specific knowledge in the variation operators as well as two constraint-handling techniques: constraint domination and repair mechanisms. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions to the DNEP problem. GOMEA is found to have far more robust performance even when an out-of-box variant is used that doesn't exploit problem-specific knowledge. Based on experiments, we suggest that when selecting optimization algorithms for real-world applications like DNEP, EAs that have the ability to model and exploit problem structures, such as GOMEAs and estimation-of-distribution algorithms, should be given priority, especially when problem-specific knowledge is not straightforward to exploit, e.g. in the case of black-box optimization.

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), with a lean, but sufficient, linkage model and an efficient variation operator, has been shown to be a robust and efficient methodology for solving single objective (SO) optimization problems with superior performance compared to classic genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). In this paper, we bring the strengths of GOMEAs to the multi-objective (MO) optimization realm. To this end, we modify the linkage learning procedure and the variation operator of GOMEAs to better suit the need of finding the whole Pareto-optimal front rather than a single best solution. Based on state-of-the-art studies on MOEAs, we further pinpoint and incorporate two other essential components for a scalable MO optimizer. First, the use of an elitist archive is beneficial for keeping track of non-dominated solutions when the main population size is limited. Second, clustering can be crucial if different parts of the Pareto-optimal front need to be handled differently. By combining these elements, we construct a multi-objective GOMEA (MO-GOMEA). Experimental results on various MO optimization problems confirm the capability and scalability of our MO-GOMEA that compare favorably with those of the well-known GA NSGA-II and the more recently introduced EDA mohBOA.

A customary paradigm of designing a competent optimization algorithm is to combine an effective global searcher with an efficient local searcher. This paper presents and analyzes an entropy-based substructural local search method (eSLS) for the Bayesian Optimization Algorithm (BOA). The local searcher (the mutation operator) explores the substructural neighborhood areas defined by the probabilistic model encoded in the Bayesian network. The improvement of each local search step can be estimated by considering the variation this mutation causes to the entropy measurement of the population. Experiments show that incorporating BOA with eSLS results in a substantial reduction in the number of costly fitness evaluations until convergence. Moreover, this paper provides original insights into how the randomness of populations can be exploited to enhance the performance of optimization processes.

In evolutionary algorithms, the efficiency enhancement techniques are capable of solving difficult large scale problems in a scalable manner. This paper rigorously analyzes the Bayesian optimization algorithm (BOA) incorporated with an innovative evaluation relaxation method based on the entropy measurement theory (en-BOA). In particular, the concept of entropy is used to develop the evaluation relaxation strategy (ERS) and to determine the rate of convergence. Entropy measurement-based ERS is employed to recognize which candidate solution should be evaluated by the actual function or be estimated by the surrogate model. Experiments prove that en-BOA significantly reduces the number of actual evaluations and the scalability of BOA is not negatively affected. Moreover, the entropy measurement-based evaluation relaxation technique does not require any larger population sizes.