In this paper, we introduce a novel approach for addressing the multi-objective optimization problem in large language model merging via black-box multi-objective optimization algorithms. The goal of model merging is to combine multiple models, each excelling in different tasks, into a single model that outperforms any of the individual source models. However, the effectiveness of conventional model merging methods is constrained by human intuition or domain knowledge. While existing optimization-based model merging methods can automatically search for model merging parameter configurations, they often struggle to find a satisfactory configuration within a limited evaluation budget. To address this challenge, we propose a novel and sample-efficient automated model merging method, named MM-MO. This method leverages multi-objective Bayesian optimization algorithms to autonomously search for great merging configurations across various tasks. In MMMO, we proposed an enhanced acquisition strategy and an auxiliary optimization objective to improve the search process. Our enhanced acquisition strategy integrates a weak-to-strong method to refine the acquisition function, enabling previously evaluated superior configurations to guide the search for new ones. Meanwhile, Fisher information is utilized to further filter these configurations, increasing the possibility of finding high-quality merging configurations. Additionally, we design a sparsity metric as an auxiliary optimization objective, further enhance the models generalization performance across different tasks. We conducted comprehensive experiments with other mainstream model merging methods, demonstrating that the proposed MMMO algorithm is competitive and effective in achieving high-quality model merging.

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm (CDM-PSL) for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples efficiently. Besides, we introduce a weighting method based on information entropy to balance different objectives. This method is integrated with a guiding strategy to appropriately balancing different objectives during the optimization process. Experimental results on both synthetic and real-world problems demonstrates that CDM-PSL attains superior performance compared with state-of-the-art MOBO algorithms.

The nonidentifiability (NI) issue has been frequently reported in social simulation works, where different parameters of an agent-based simulation model yield indistinguishable simulated time series data under certain discrepancy metrics. This issue largely undermines the simulation fidelity yet lacks dedicated investigations. This article theoretically demonstrates that incorporating multiple time series data features during the model calibration phase can exponentially alleviate NI as the number of features increases. To implement this theoretical finding, a maximization-based aggregation function is proposed based on existing discrepancy metrics to form a new calibration objective function. For verification, the task of calibrating the financial market simulation (FMS), a typical yet complex social simulation, is considered. Empirical studies confirm the significant improvements in alleviating the NI of calibration tasks. Furthermore, as a model-agnostic method, it achieves much higher simulation fidelity of the chosen FMS model on both synthetic and real market data. Moreover, it is both theoretically and empirically analyzed that as long as the features are selected and not linearly correlated, they can contribute to alleviation, which demonstrates the robustness of the proposed objective. Hence, this article is expected to provide not only a rigorous understanding of NI in social simulation but also an off-the-shelf high-fidelity calibration objective function for FMS.

A series of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed for expensive multi-objective optimization problems (EMOPs), building cheap surrogate models to replace the expensive real function evaluations. However, the search efficiency of these SAEAs is not yet satisfactory. More efforts are needed to further exploit useful information from the real function evaluations in order to better guide the search process. Facing this challenge, this paper proposes a Hyperbolic Neural Network (HNN) based preselection operator to accelerate the optimization process based on limited evaluated solutions. First, the preselection task is modeled as a multi-label classification problem where solutions are classified into different layers (ordinal categories) through -relaxed objective aggregation. Second, in order to resemble the hierarchical structure of candidate solutions, a hyperbolic neural network is applied to tackle the multi-label classification problem. The reason for using HNN is that hyperbolic spaces more closely resemble hierarchical structures than Euclidean spaces. Moreover, to alleviate the data deficiency issue, a data augmentation strategy is employed for training the HNN. In order to evaluate its performance, the proposed HNN-based preselection operator is embedded into two surrogate-assisted evolutionary algorithms. Experimental results on two benchmark test suites and three real-world problems with up to 11 objectives and 150 decision variables involving seven state-of-the-art algorithms demonstrate the effectiveness of the proposed method.

Large-scale multiobjective optimization problems (LSMOPs), characterized by a substantial number of decision variables, pose significant challenges for many existing evolutionary algorithms. However, the search efficiency of these algorithms is not yet satisfactory. This is mainly because that the search efficiency of these algorithms may deteriorate dramatically since the search space increases exponentially with the number of decision variables. Having this in mind, we proposed a large-Scale multiobjective optimization framework named causal inference-based competitive swarm optimizer (CI-CSO). Specifically, a causal-information-(CI)-based operator is designed for competitive swarm optimizers. First, a causal inference technique named information geometric causal inference (IGCI) is introduced to adequately explore the CI between decision variables and fitness values. To further distinguish the positive or negative impacts of these critical variables on solution quality, a CI processing module is designed, facilitating targeted optimization. To enhance search efficiency, CI-based offspring generator are employed, leveraging the variance of causal effects to dynamically adjust the search step size and sampling range. To evaluate its performance, the proposed CI-based operator is embedded into two multiobjective evolutionary algorithms (MOEAs) (LSTPA and LMOCSO). To demonstrate the effectiveness of the proposed framework, experimental results are presented using the LSMOP test suite and five real-world problems, each involving up to 10 000 decision variables. In addition, six classic algorithms are included for comparison.

Multi-objective optimization problems (MOPs) containing a large number of decision variables, which are also known as large-scale multi-objective optimization problems (LSMOPs), pose great challenges to most existing evolutionary algorithms. This is mainly because that a high dimensional decision space degrades the effectiveness of search operators notably, and balancing convergence and diversity becomes a challenging task. In this paper, we propose a two-population based algorithm for large-scale multi-objective optimization named LSTPA. In the proposed algorithm, solutions are classified in to two subpopulations: a Convergence subPopulation (CP) and a Diversity subPopulation (DP), aiming at convergence and diversity respectively. In order to improve convergence speed, a fitness-aware variation operator (FAVO) is applied to drive DP solutions towards CP. Besides, an adaptive penalty based boundary intersection (APBI) strategy is adopted for environmental selection in order to balance convergence and diversity temporally during different stages of evolution process. Experimental results on benchmark test problems with 100-2000 decision variables demonstrate that the proposed algorithm can achieve the best overall performance compared with several state-of-the-art large-scale multi-objective evolutionary algorithms.

The agent-based financial market simulators serve as an important validation tool for trading strategies. For high-fidelity simulation, it is pivotal to calibrate the parameters of a simulator so that the generated simulation data resembles the observed real market data of interest. In traditional calibration methods, it is typical that the parameters of the simulator are set to be time-invariant. However, the dynamic nature of the real financial market introduces various variability into the behaviors of the market participants over different time intervals, posing in-herent limitations to the traditional methods. A more reasonable approach might involve employing a simulator with time-variant parameters. This suggests that the model parameters can be dynamically adjusted at different stages of the simulation to adapt to the evolving market. Consequently, the calibration problem of the financial market simulators can be treated as a dynamic optimization problem. To dynamically calibrate the simulators, we introduce an Evolutionary Dynamic Optimization (EDO) framework. By monitoring the changes of the best fitness, the whole simulation time interval is adaptively divided into multiple stages. Then the Negatively Correlated Search (NCS) algorithm is employed to effectively adjust the parameters at different simulation stages to better simulate the real financial market. Empirical results on both synthetic and real data verify that our dynamic calibration framework significantly outperforms traditional calibration methods that fixing a parameter for the whole simulation interval. The proposed strategy of detecting dynamic changes is also shown to be more reliable than the naive method of manually segmenting stages. In terms of calibration time, our proposed method significantly improves by nearly 93% compared to the fixed parameter setting, and approximately 61% compared to manual segmentation calibration.

Zero-shot coordination studies the training of well-generalizing human-AI coordination agents in the scenario where human data is unavailable. To obtain a coordination agent generalize to unseen humans, prevailing methods generate a population of partner agents as proxy models of human partners and then train a coordination agent with these partner agents. Constructed partner agents are expected to be as diverse as possible to cover a wide range of human behaviors, preventing a distribution shift between training and testing stages. Recent works concentrate on studying effective methods of creating a group of high-reward while diverse partner agents to model unseen human partners. However, the resulting high-reward partner agents do not accurately reflect real-world situations, considering that human decisions are not always optimal and may sometimes even hinder the progression of coordination. Therefore, these studies still struggle to capture the potential characteristics of human partners. In this work, reinforcement learning (RL) and supervised learning (SL) are integrated to train a reward-conditioned policy. By conditioned on different desired rewards, a reward-conditioned policy simulates both low-reward and high-reward partners. Additionally, a reward-bucketed replay buffer and curriculum learning are applied to enhance reward diversity and boost the training of coordination agents. Experiments demonstrate that the proposed reward-conditioned policy is capable of generating agents with different rewards. Moreover, the zero-shot coordination performance of agents trained with these partners surpasses previous methods in the majority of scenarios within the Overcooked human-AI coordination benchmark.

A recurrent neural network (RNN) has shown powerful performance in tackling various natural language processing (NLP) tasks, resulting in numerous powerful models containing both RNN neurons and feedforward neurons. On the other hand, the deep structure of RNN has heavily restricted its implementation on mobile devices, where quite a few applications involve NLP tasks. Magnitude-based pruning (MP) is a promising way to address such a challenge. However, the existing MP methods are mostly designed for feedforward neural networks that do not involve a recurrent structure, and, thus, have performed less satisfactorily on pruning models containing RNN layers. In this article, a novel stage-wise MP method is proposed by explicitly taking the featured recurrent structure of RNN into account, which can effectively prune feedforward layers and RNN layers, simultaneously. The connections of neural networks are first grouped into three types according to how they are intersected with recurrent neurons. Then, an optimization-based pruning method is applied to compress each group of connections, respectively. Empirical studies show that the proposed method performs significantly better than the commonly used RNN pruning methods; i.e., up to 96.84% connections are pruned with little or even no degradation of precision indicators on the testing datasets.

Due to computationally and/or financially costly evaluation, tackling expensive multi-objective optimization problems is quite challenging for evolutionary algorithms. One popular approach to these problems is building cheap surrogate models to replace the expensive real function evaluations. To this end, various kinds of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed, building surrogate models which predict the fitness values, classifications, or relation of the candidate solutions. However, off-spring generation, despite its important role in evolutionary optimization, has not received enough attention in these SAEAs. In this paper, a regularity model based framework, namely RM-SAEA, is proposed for better offspring generation in expensive multi-objective optimization. To be specific, RM-SAEA is featured with a heterogeneous offspring generation module, which is composed of a regularity model and a general genetic operator. Moreover, in order to alleviate the data deficiency issue in the expensive optimization scenario, a data augmentation strategy is employed while training the regularity model. Finally, two representative SAEAs are embedded into RM-SAEA in order to instantiate the proposed framework. Experimental results on benchmark multi-objective problems with up to 10 objectives demonstrate that RM-SAEA achieves the best overall performance compared with 6 state-of-the-art algorithms.

Multi-fidelity simulation is an effective approach to balancing speed and accuracy in expensive simulation, and its performance is affected by the quality of multi-fidelity simulation models. Building high-quality simulation models is non-trivial, especially for complex systems, because current manual modeling methods require sufficient domain knowledge and experience, increasing the labor and time costs. Motivated by the issues, this paper focuses on one of the most crucial simulation types, discrete event simulation, and develops a computer-aid multi-fidelity simulation modeling method called Optimization-based Multi-fidelity Simulation Modeling (OMFSM). OMFSM formulates multi-fidelity simulation modeling as a bi-objective simulation optimization problem to optimize speed and accuracy. An efficient optimization algorithm called Multi-objective Simulation Optimization based on Hypervolume (MOSO-HV) is tailored to select a set of high-quality models. Experimental results in a digital twin emergency department demonstrate that the computer-aid modeling method builds more and better multi-fidelity simulation models than manual modeling and reveal the effectiveness of MOSO-HV for OMFSM. The utility of OMFSM in multi-fidelity simulation is also justified by a real-world optimization problem. Note to Practitioners—Multi-fidelity simulation is an essential technique to fulfill the demand for accuracy analysis and quick decision-making in Industrial 4.0, such as digital twins and virtual reality. The quality of multi-fidelity simulation models significantly influences the performance of multi-fidelity simulation. Developers currently build multi-fidelity simulation models manually, and their experience determines the model’s quality. To reduce the labor and time costs in constructing high-quality multi-fidelity simulation models, we propose a computer-aid method named OMFSM from optimization for the first time. Experiments on a real case prove that OMFSM lightens the burden of manual modeling and provides more and better models for multi-fidelity simulation.

Deploying guardrails near elevator entrances is an effective way to alleviate congestion and improve the flow rate in subway stations. How to properly design the guardrail layout is a complex black-box optimization problem. Existing methods are mainly based on manual design, which are highly dependent on the empirical experience of the designers and may not get satisfactory results in complicated scenarios. To address the above issues, this article proposes an evolutionary framework to automatically optimize guardrail layouts in subway stations. In the proposed framework, a novel guardrail layout encoding method is proposed, which can facilitate the algorithm to generate regular guardrail layout design solutions. Furthermore, a new fitness evaluation function is proposed to effectively measure the quality of a given guardrail layout design strategy. To validate its effectiveness, the proposed framework is applied to two scenarios with different characteristics. Simulation results have demonstrated that the proposed framework can provide promising guardrail layout designs, which can alleviate the congestion of subway stations effectively.

Memetic algorithm (MA) is widely applied to optimize routing problems as it provides one way to combine local search with global search. However, the local search in MA needs to be carefully designed according to the problem’s characteristics. In this article, we consider a real-world large-scale waste collection problem with multiple depots, multiple disposal facilities, multiple trips, and working time constraints. Vehicles with a limited capacity and working time can start from different depots, collect waste at different sites, and make multiple trips to different disposal facilities to empty the waste and return to its origin. While the existing work considered problems with multiple trips and time constraints, none have tackled problems with multiple depots, multiple disposal facilities, multiple trips, as well as working time constraints. The change from “single-depot” to “multidepot” not only reflects better the situation in real life but also leads to a qualitative different and more complex problem. In this article, we first model this complex problem mathematically. Then, a novel region-focused MA is proposed to tackle this new challenge. Compared to classic MA, this region-focused one is enhanced by two major components: 1) a new heuristic-assisted solution initialization algorithm and 2) a region-focused local search with novel heuristics. Comprehensive computational studies show that our proposed approaches significantly outperform several state-of-the-arts on our real problem of thousands of tasks. The new local search procedure and solution initialization method significantly improve the search ability in combination with global search ability of MA.

Abstract Effective exploration is key to a successful search process. The recently proposed negatively correlated search (NCS) tries to achieve this by coordinated parallel exploration, where a set of search processes are driven to be negatively correlated so that different promising areas of the search space can be visited simultaneously. Despite successful applications of NCS, the negatively correlated search behaviors were mostly devised by intuition, while deeper (e.g., mathematical) understanding is missing. In this paper, a more principled NCS, namely NCNES, is presented, showing that the parallel exploration is equivalent to a process of seeking probabilistic models that both lead to solutions of high quality and are distant from previous obtained probabilistic models. Reinforcement learning, for which exploration is of particular importance, are considered for empirical assessment. The proposed NCNES is applied to directly train a deep convolution network with 1.7 million connection weights for playing Atari games. Empirical results show that the significant advantages of NCNES, especially on games with uncertain and delayed rewards, can be highly owed to the effective parallel exploration ability.

Generalization, i.e., the ability of solving problem instances that are not available during the system design and development phase, is a critical goal for intelligent systems. A typical way to achieve good generalization is to learn a model from vast data. In the context of heuristic search, such a paradigm could be implemented as configuring the parameters of a parallel algorithm portfolio (PAP) based on a set of “training” problem instances, which is often referred to as PAP construction. However, compared to the traditional machine learning, PAP construction often suffers from the lack of training instances, and the obtained PAPs may fail to generalize well. This article proposes a novel competitive co-evolution scheme, named co-evolution of parameterized search (CEPS), as a remedy to this challenge. By co-evolving a configuration population and an instance population, CEPS is capable of obtaining generalizable PAPs with few training instances. The advantage of CEPS in improving generalization is analytically shown in this article. Two concrete algorithms, namely, CEPS-TSP and CEPS-VRPSPDTW, are presented for the traveling salesman problem (TSP) and the vehicle routing problem with simultaneous pickup-delivery and time windows (VRPSPDTW), respectively. The experimental results show that CEPS has led to better generalization, and even managed to find new best-known solutions for some instances.

Network resource allocation is an important issue for designing energy-harvesting wireless sensor networks (EH-WSNs). This article considers the capacity assignment problem in EH-WSNs with the interference channel for fixed data and energy flow topologies. We focus on the optimal data rates, power allocations, and energy transfers, minimizing the total network delay for the network. We first consider a simplified model where the data flow is fixed on each data link and optimizes transmit power at each sensor node for a single energy harvest in a time slot. However, the optimization problem is nonconvex, making it difficult to find the optimal solution. Unlike the most traditional methods that approximate the original optimization problem as a convex optimization problem by considering the relatively high signal-to-interference-plus-noise ratio (SINR), this article aims to directly solve the original nonconvex formulation by employing a powerful evolutionary algorithm, i.e., negatively correlated search (NCS). Then, we investigate the joint optimization problem of capacity and flow for the entire EH-WSNs, and develop a novel multiobjective NCS algorithm (MOEA/D-NCS) to deal with the complicated nonlinear constraints and optimize the data rates, power allocations, and energy transfer simultaneously, so as to minimize the total network delay. The numerical results demonstrate that solving the nonconvex problem with approximated approach is a good alternative for solving the approximated convex problem with accurate optimization approaches; the joint optimization of capacity and flow is a good solution for EH-WSNs; and the scheme of partial transmission for data flow is an advantage in respect of decreasing the network delay. The solution of this article could also be beneficial to other complex optimization problems in the wireless network design.

The recently proposed Scalable Approach Based on Hierarchical Decomposition (SAHiD) has shown its superiority on large-scale capacitated arc routing problems (CARP) in terms of both computational efficiency and solution quality. The main idea of SAHiD is that the underlying Hierarchical decomposition (HD) scheme is able to efficiently obtain a good permutation of tasks for CARP in a hierarchical divide-and-conquer way, where both the number and size of subproblems can be kept in tractable for large-scale problems with thousands of tasks. Motivated by the frequent observations of the similarity between CARP and Capacitated Vehicle Routing Problem (CVRP), the HD scheme and SAHiD algorithm are expected to work well on CVRPs. This paper applies SAHiD to large-scale CVRPs and discovers that SAHiD does not work as well as expected on large-scale CVRP. Possible reasons for this are given after extensive experimental studies. Two directions for improving SAHiD on large-scale CVRP are pointed out.

Optimal energy-delay scheduling for capacity assignment problem in energy harvesting wireless sensor networks (EH-WSNs) with interference channel is addressed for fixed data flows and energy topologies. We formulate the optimization problem for a single time slot and multiple time slots, respectively. We focus on the optimal data rates, power allocations and energy transfers for the optimization problem. The objective is to minimize the total network delay. However, the optimization problem is non-convex, making it difficult to find the optimal solution. Unlike the most traditional methods that approximate the original optimization problem as a convex optimization problem by considering the relatively high Signal-to-Interference-plus-Noise Ratio (SINR), this paper aims to directly solve the original non-convex formulation by employing a powerful evolutionary algorithm, i.e., Negatively Correlated Search (NCS). The simulations under both no-energy-transfer scenario and energy-transfer scenario are carried out, demonstrating that solving the non-convex problem with approximated approach is a good alternative to solving the approximated convex problem with accurate optimization approaches. This idea could also be beneficial to other complex optimization problems in the wireless networks design.

Stochastic composite mirror descent (SCMD) is a simple and efficient method able to capture both geometric and composite structures of optimization problems in machine learning. Existing strategies require to take either an average or a random selection of iterates to achieve optimal convergence rates, which, however, can either destroy the sparsity of solutions or slow down the practical training speed. In this paper, we propose a theoretically sound strategy to select an individual iterate of the vanilla SCMD, which is able to achieve optimal rates for both convex and strongly convex problems in a non-smooth learning setting. This strategy of outputting an individual iterate can preserve the sparsity of solutions which is crucial for a proper interpretation in sparse learning problems. We report experimental comparisons with several baseline methods to show the effectiveness of our method in achieving a fast training speed as well as in outputting sparse solutions.

Divide-and-conquer (DC) is conceptually well suited to deal with high-dimensional optimization problems by decomposing the original problem into multiple low-dimensional subproblems, and tackling them separately. Nevertheless, the dimensionality mismatch between the original problem and subproblems makes it nontrivial to precisely assess the quality of a candidate solution to a subproblem, which has been a major hurdle for applying the idea of DC to nonseparable high-dimensional optimization problems. In this paper, we suggest that searching a good solution to a subproblem can be viewed as a computationally expensive problem and can be addressed with the aid of meta-models. As a result, a novel approach, namely self-evaluation evolution (SEE) is proposed. Empirical studies have shown the advantages of SEE over four representative compared algorithms increase with the problem size on the CEC2010 large scale global optimization benchmark. The weakness of SEE is also analyzed in the empirical studies.

In real-world applications, the oracle who can label all instances correctly may not exist or may be too expensive to acquire. Alternatively, crowdsourcing provides an easy way to get labels at a low cost from multiple non-expert annotators. During the past few years, much attention has been paid to learning from such crowdsourcing data, namelyLearning from Crowds(LFC). Despite their proper statistical foundations, the existing methods for LFC still suffer from several disadvantages, such as needing prior knowledge to select the expertise model to represent the behavior of annotators, involving non-convex optimization problems, or restricting the classifier type being used. This paper addresses LFC from a quality-sensitive perspective and presents a novel framework named QS-LFC. Through reformulating the original LFC problem as a quality-sensitive learning problem, the above-mentioned disadvantages of existing methods can be avoided. Further, a support vector machine (SVM) implementation of QS-LFC is proposed. Experimental results on both synthetic and real-world data sets demonstrate that QS-LFC can achieve better generalization performance and is more robust to the noisy labels, than the existing methods.

In the past few years, Evolutionary Algorithms (EAs) based UAV path planners have drawn increasing research interests. However, they are not scalable to large-scale problems, i.e., lots of waypoints. Recently, we have proposed a novel EA-based framework, named Separately Evolving Waypoints (SEW), that can deal with large-scale problems. However, the difficulty of UAV path planning depends not only on the number of waypoints, but on the number of constraints it has to satisfy, especially the number of obstacles. In particular, the number of waypoints required is also partly determined by the number of constraints. Hence, it is critical to further improve SEW with respect to large number of obstacles. Originally, a state-of-the-art global optimization approach is employed. In this work, we discuss how the increasing number of obstacles will deteriorate the performance of the global optimizer, then we propose multimodal optimization approaches that facilitates the performance of SEW against large number of obstacles.

Evolutionary algorithms (EAs) have been shown to be powerful tools for complex optimization problems, which are ubiquitous in both communication and big data analytics. This paper presents a new EA, namely negatively correlated search (NCS), which maintains multiple individual search processes in parallel and models the search behaviors of individual search processes as probability distributions. NCS explicitly promotes negatively correlated search behaviors by encouraging differences among the probability distributions (search behaviors). By this means, individual search processes share information and cooperate with each other to search diverse regions of a search space, which makes NCS a promising method for nonconvex optimization. The co-operation scheme of NCS could also be regarded as a novel diversity preservation scheme that, different from other existing schemes, directly promotes diversity at the level of search behaviors rather than merely trying to maintain diversity among candidate solutions. Empirical studies showed that NCS is competitive to well-established search methods in the sense that NCS achieved the best overall performance on 20 multimodal (nonconvex) continuous optimization problems. The advantages of NCS over state-of-the-art approaches are also demonstrated with a case study on the synthesis of unequally spaced linear antenna arrays.

Many real-world problems often have several, usually conflicting objectives. Traditional multi-objective optimization problems (MOPs) usually search for the Pareto-optimal solutions for this predicament. A special class of MOPs, the convex hull maximization problems which prefer solutions on the convex hull, has posed a new challenge for existing approaches for solving traditional MOPs, as a solution on the Pareto front is not necessarily a good solution for convex hull maximization. In this work, the difference between traditional MOPs and the convex hull maximization problems is discussed and a new Evolutionary Convex Hull Maximization Algorithm (ECHMA) is proposed to solve the convex hull maximization problems. Specifically, a Convex Hull-based sorting with Convex Hull of Individual Minima (CH-CHIM-sorting) is introduced, as well as a novel selection scheme, Extreme Area Extract-based selection (EAE-selection). Experimental results show that ECHMA significantly outperforms the existing approaches for convex hull maximization and evolutionary multi-objective optimization approaches in achieving a better approximation to the convex hull more stably and with a more uniformly distributed set of solutions.

In this paper, a novel multiple sub-models maintenance technique, named maintaining and processing sub-models (MAPS), is proposed. MAPS aims to enhance the ability of estimation of distribution algorithms (EDAs) on multimodal problems. The advantages of MAPS over the existing multiple sub-models based EDAs stem from the explicit detection of the promising areas, which can save many function evaluations for exploration and thus accelerate the optimization speed. MAPS can be combined with any EDA that adopts a single Gaussian model. The performance of MAPS has been assessed through empirical studies where MAPS is integrated with three different types of EDAs. The experimental results show that MAPS can lead to much faster convergence speed and obtain more stable solutions than the compared algorithms on 12 benchmark problems.

Evolutionary algorithm-based unmanned aerial vehicle (UAV) path planners have been extensively studied for their effectiveness and flexibility. However, they still suffer from a drawback that the high-quality waypoints in previous candidate paths can hardly be exploited for further evolution, since they regard all the waypoints of a path as an integrated individual. Due to this drawback, the previous planners usually fail when encountering lots of obstacles. In this paper, a new idea of separately evaluating and evolving waypoints is presented to solve this problem. Concretely, the original objective and constraint functions of UAVs path planning are decomposed into a set of new evaluation functions, with which waypoints on a path can be evaluated separately. The new evaluation functions allow waypoints on a path to be evolved separately and, thus, high-quality waypoints can be better exploited. On this basis, the waypoints are encoded in a rotated coordinate system with an external restriction and evolved with JADE, a state-of-the-art variant of the differential evolution algorithm. To test the capabilities of the new planner on planning obstacle-free paths, five scenarios with increasing numbers of obstacles are constructed. Three existing planners and four variants of the proposed planner are compared to assess the effectiveness and efficiency of the proposed planner. The results demonstrate the superiority of the proposed planner and the idea of separate evolution.

Path planning technique is vital to Unmanned Aerial Vehicle (UAV). Evolutionary Algorithms (EAs) have been widely used in planning path for UAV. In these EA-based path planners, Cartesian coordinate system and polar coordinate system are commonly used to codify the path. However, either of them has its drawback: Cartesian coordinate systems result in an enormous search space, whilst polar coordinate systems are unfit for local modifications resulting e.g., from mutation and/ or crossover. In order to overcome these two drawbacks, we solve the UAV path planning in a new coordinate system. As the new coordinate system is only a rotation of Cartesian coordinate system, it is inherently easy for local modification. Besides, this new coordinate system has successfully reduced the search space by explicitly dividing the mission space into several subspaces. Within this new coordinate system, an Estimation of Distribution Algorithms (EDAs) based path planner is proposed in this paper. Some experiments have been designed to test different aspects of the new path planner. The results show the effectiveness of this planner.