A many-objective evolutionary algorithm based on three states for solving many-objective optimization problem

In recent years, researchers have taken the many-objective optimization algorithm, which can optimize 5, 8, 10, 15, 20 objective functions simultaneously, as a new research topic. However, the current research on many-objective optimization technology also encounters some challenges. For example: Pareto resistance phenomenon, difficult diversity maintenance. Based on the above problems, this paper proposes a many-objective evolutionary algorithm based on three states (MOEA/TS). Firstly, a feature extraction operator is proposed. It can extract the features of the high-quality solution set, and then assist the evolution of the current individual. Secondly, based on Pareto front layer, the concept of "individual importance degree" is proposed. The importance degree of an individual can reflect the importance of the individual in the same Pareto front layer, so as to further distinguish the advantages and disadvantages of different individuals in the same front layer. Then, a repulsion field method is proposed. The diversity of the population in the objective space is maintained by the repulsion field, so that the population can be evenly distributed on the real Pareto front. Finally, a new concurrent algorithm framework is designed. In the algorithm framework, the algorithm is divided into three states, and each state focuses on a specific task. The population can switch freely among these three states according to its own evolution. The MOEA/TS algorithm is compared with 7 advanced many-objective optimization algorithms. The experimental results show that the MOEA/TS algorithm is more competitive in many-objective optimization problems.

A deep reinforcement learning algorithm framework for solving multi-objective traveling salesman problem based on feature transformation

As a special type of multi-objective combinatorial optimization problems (MOCOPs), the multi-objective traveling salesman problem (MOTSP) plays an important role in practical fields such as transportation and robot control. However, due to the complexity of its solution space and the conflicts between different objectives, it is difficult to obtain satisfactory solutions in a short time. This paper proposes an end-to-end algorithm framework for solving MOTSP based on deep reinforcement learning (DRL). By decomposing strategies, solving MOTSP is transformed into solving multiple single-objective optimization subproblems. Through linear transformation, the features of the MOTSP are combined with the weights of the objective function. Subsequently, a modified graph pointer network (GPN) model is used to solve the decomposed subproblems. Compared with the previous DRL model, the proposed algorithm can solve all the subproblems using only one model without adding weight information as input features. Furthermore, our algorithm can output a corresponding solution for each weight, which increases the diversity of solutions. In order to verify the performance of our proposed algorithm, it is compared with four classical evolutionary algorithms and two DRL algorithms on several MOTSP instances. The comparison shows that our proposed algorithm outperforms the compared algorithms both in terms of training time and the quality of the resulting solutions.

A dual-population Constrained Many-Objective Evolutionary Algorithm based on reference point and angle easing strategy

Constrained many-objective optimization problems (CMaOPs) have gradually emerged in various areas and are significant for this field. These problems often involve intricate Pareto frontiers (PFs) that are both refined and uneven, thereby making their resolution difficult and challenging. Traditional algorithms tend to over prioritize convergence, leading to premature convergence of the decision variables, which greatly reduces the possibility of finding the constrained Pareto frontiers (CPFs). This results in poor overall performance. To tackle this challenge, our solution involves a novel dual-population constrained many-objective evolutionary algorithm based on reference point and angle easing strategy (dCMaOEA-RAE). It relies on a relaxed selection strategy utilizing reference points and angles to facilitate cooperation between dual populations by retaining solutions that may currently perform poorly but contribute positively to the overall optimization process. We are able to guide the population to move to the optimal feasible solution region in a timely manner in order to obtain a series of superior solutions can be obtained. Our proposed algorithm's competitiveness across all three evaluation indicators was demonstrated through experimental results conducted on 77 test problems. Comparisons with ten other cutting-edge algorithms further validated its efficacy.

Evolutionary Multiobjective Molecule Optimization in an Implicit Chemical Space

Optimization techniques play a pivotal role in advancing drug development, serving as the foundation of numerous generative methods tailored to efficiently design optimized molecules derived from existing lead compounds. However, existing methods often encounter difficulties in generating diverse, novel, and high-property molecules that simultaneously optimize multiple drug properties. To overcome this bottleneck, we propose a multiobjective molecule optimization framework (MOMO). MOMO employs a specially designed Pareto-based multiproperty evaluation strategy at the molecular sequence level to guide the evolutionary search in an implicit chemical space. A comparative analysis of MOMO with five state-of-the-art methods across two benchmark multiproperty molecule optimization tasks reveals that MOMO markedly outperforms them in terms of diversity, novelty, and optimized properties. The practical applicability of MOMO in drug discovery has also been validated on four challenging tasks in the real-world discovery problem. These results suggest that MOMO can provide a useful tool to facilitate molecule optimization problems with multiple properties.

A Decomposition-Based Multi-Objective Flying Foxes Optimization Algorithm and Its Applications

The flying foxes optimization (FFO) algorithm stimulated by the strategy used by flying foxes for subsistence in heat wave environments has shown good performance in the single-objective domain. Aiming to explore the effectiveness and benefits of the subsistence strategy used by flying foxes in solving optimization challenges involving multiple objectives, this research proposes a decomposition-based multi-objective flying foxes optimization algorithm (MOEA/D-FFO). It exhibits a great population management strategy, which mainly includes the following features. (1) In order to improve the exploration effectiveness of the flying fox population, a new offspring generation mechanism is introduced to improve the efficiency of exploration of peripheral space by flying fox populations. (2) A new population updating approach is proposed to adjust the neighbor matrices to the corresponding flying fox individuals using the new offspring, with the aim of enhancing the rate of convergence in the population. Through comparison experiments with classical algorithms (MOEA/D, NSGA-II, IBEA) and cutting-edge algorithms (MOEA/D-DYTS, MOEA/D-UR), MOEA/D-FFO achieves more than 11 best results. In addition, the experimental results under different population sizes show that the proposed algorithm is highly adaptable and has good application prospects in optimization problems for engineering applications.

A multi-population multi-stage adaptive weighted large-scale multi-objective optimization algorithm framework

Weighted optimization framework (WOF) achieves variable dimensionality reduction by grouping variables and optimizing weights, playing an important role in large-scale multi-objective optimization problems. However, because of possible problems such as duplicate weight vectors in the selection process and loss of population diversity, the algorithm is susceptible to local optimization. Therefore, this paper develops an algorithm framework called multi-population multi-stage adaptive weighted optimization (MPSOF) to improve the performance of WOF in two aspects. First, the method of using multi-population is employed to address the issue of insufficient algorithmic diversity, while simultaneously reducing the likelihood of converging towards local optima. Secondly, a processing stage is incorporated into MPSOF, where a certain number of individuals are adaptively selected for updating based on the weight information and evolutionary status of different subpopulations, targeting different types of weights. This approach alleviates the impact of repetitive weights on the diversity of newly generated individuals, avoids the drawback of easily converging to local optima when using a single type of weight for updating, and effectively balances the diversity and convergence of subpopulations. Experiments of three types designed on several typical function sets demonstrate that MPSOF exceeds the comparison algorithms in the three metrics for Inverse Generation Distance, Hypervolume and Spacing.

Integrating transformers and many-objective optimization for drug design

BACKGROUND

Drug design is a challenging and important task that requires the generation of novel and effective molecules that can bind to specific protein targets. Artificial intelligence algorithms have recently showed promising potential to expedite the drug design process. However, existing methods adopt multi-objective approaches which limits the number of objectives.

RESULTS

In this paper, we expand this thread of research from the many-objective perspective, by proposing a novel framework that integrates a latent Transformer-based model for molecular generation, with a drug design system that incorporates absorption, distribution, metabolism, excretion, and toxicity prediction, molecular docking, and many-objective metaheuristics. We compared the performance of two latent Transformer models (ReLSO and FragNet) on a molecular generation task and show that ReLSO outperforms FragNet in terms of reconstruction and latent space organization. We then explored six different many-objective metaheuristics based on evolutionary algorithms and particle swarm optimization on a drug design task involving potential drug candidates to human lysophosphatidic acid receptor 1, a cancer-related protein target.

CONCLUSION

We show that multi-objective evolutionary algorithm based on dominance and decomposition performs the best in terms of finding molecules that satisfy many objectives, such as high binding affinity and low toxicity, and high drug-likeness. Our framework demonstrates the potential of combining Transformers and many-objective computational intelligence for drug design.

Neural Net-Enhanced Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization

The competitive swarm optimizer (CSO) classifies swarm particles into loser and winner particles and then uses the winner particles to efficiently guide the search of the loser particles. This approach has very promising performance in solving large-scale multiobjective optimization problems (LMOPs). However, most studies of CSOs ignore the evolution of the winner particles, although their quality is very important for the final optimization performance. Aiming to fill this research gap, this article proposes a new neural net-enhanced CSO for solving LMOPs, called NN-CSO, which not only guides the loser particles via the original CSO strategy, but also applies our trained neural network (NN) model to evolve winner particles. First, the swarm particles are classified into winner and loser particles by the pairwise competition. Then, the loser particles and winner particles are, respectively, treated as the input and desired output to train the NN model, which tries to learn promising evolutionary dynamics by driving the loser particles toward the winners. Finally, when model training is complete, the winner particles are evolved by the well-trained NN model, while the loser particles are still guided by the winner particles to maintain the search pattern of CSOs. To evaluate the performance of our designed NN-CSO, several LMOPs with up to ten objectives and 1000 decision variables are adopted, and the experimental results show that our designed NN model can significantly improve the performance of CSOs and shows some advantages over several state-of-the-art large-scale multiobjective evolutionary algorithms as well as over model-based evolutionary algorithms.

Optimizing grazing exclusion duration for carbon sequestration in grasslands: Incorporating temporal heterogeneity of aboveground biomass and soil organic carbon

Grasslands account for approximately one-third of the global terrestrial carbon stocks. However, a limited understanding of the impact of grazing exclusion on carbon storage in grassland ecosystems hinders progress towards restoring overgrazed grasslands and promoting carbon sequestration. In this study, we conducted a comprehensive meta-analysis to investigate the effects of grazing exclusion on aboveground biomass (AGB) and soil organic carbon (SOC) in four grasslands: alpine grasslands (AP), tropical savannas (TS), temperate subhumid grasslands (TG), and a semi-desert steppe (SD). Our meta-analysis indicated that grazing exclusion significantly enhanced carbon sequestration in grassland ecosystems, and the benefits of carbon sequestration were most pronounced in the AP, followed by the TG, SD, and TS. Grazing exclusion duration (DUR) was a significant factor associated with the response of aboveground biomass (AGB) and soil organic carbon (SOC) to grazing exclusion. Moreover, the relationships between AGB and DUR were nonlinear, with existence thresholds of 18, 21, 12, 19, and 23 years in global grasslands (ALL), AP, TS, TG, and SD, respectively. However, the relationship between SOC and DUR was linear, with SOC continuing to increase as DUR increased (up to 40 years). The multi-objective optimization indicated that the optimal duration of grazing exclusion for grassland carbon sequestration was 18-20, 21-23, 12-14, 19-21, and 23-25 years for ALL, AP, TS, TG, and SD, respectively. Our study contributes to the enhancement of grazing management and offers better options for increasing carbon sequestration in grasslands.

MOBCA: Multi-Objective Besiege and Conquer Algorithm

The besiege and conquer algorithm has shown excellent performance in single-objective optimization problems. However, there is no literature on the research of the BCA algorithm on multi-objective optimization problems. Therefore, this paper proposes a new multi-objective besiege and conquer algorithm to solve multi-objective optimization problems. The grid mechanism, archiving mechanism, and leader selection mechanism are integrated into the BCA to estimate the Pareto optimal solution and approach the Pareto optimal frontier. The proposed algorithm is tested with MOPSO, MOEA/D, and NSGAIII on the benchmark function IMOP and ZDT. The experiment results show that the proposed algorithm can obtain competitive results in terms of the accuracy of the Pareto optimal solution.

Multi-objective and multi constrained task scheduling framework for computational grids

Grid computing emerged as a powerful computing domain for running large-scale parallel applications. Scheduling computationally intensive parallel applications such as scientific, commercial etc., computational grids is a NP-complete problem. Many researchers have proposed several task scheduling algorithms on grids based on formulating and solving it as an optimization problem with different objective functions such as makespan, cost, energy etc. Further to address the requirements/demands/needs of the users (lesser cost, lower latency etc.) and grid service providers (high utilization and high profitability), a task scheduler needs to be designed based on solving a multi-objective optimization problem due to several trade-offs among the objective functions. In this direction, we propose an efficient multi-objective task scheduling framework to schedule computationally intensive tasks on heterogeneous grid networks. This framework minimizes turnaround time, communication, and execution costs while maximizing grid utilization. We evaluated the performance of our proposed algorithm through experiments conducted on standard, random, and scientific task graphs using the GridSim simulator.

Multigranularity Surrogate Modeling for Evolutionary Multiobjective Optimization With Expensive Constraints

Multiobjective optimization problems (MOPs) with expensive constraints pose stiff challenges to existing surrogate-assisted evolutionary algorithms (SAEAs) in a very limited computational cost, due to the fact that the number of expensive constraints for an MOP is often large. For existing SAEAs, they always approximate constraint functions in a single granularity, namely, approximating the constraint violation (CV, coarse-grained) or each constraint (fine-grained). However, the landscape of CV is often too complex to be accurately approximated by a surrogate model. Although the modeling of each constraint function may be simpler than that of CV, approximating all the constraint functions independently may result in tremendous cumulative errors and high computational costs. To address this issue, in this article, we develop a multigranularity surrogate modeling framework for evolutionary algorithms (EAs), where the approximation granularity of constraint surrogates is adaptively determined by the position of the population in the fitness landscape. Moreover, a dedicated model management strategy is also developed to reduce the impact resulting from the errors introduced by constraint surrogates and prevent the population from trapping into local optima. To evaluate the performance of the proposed framework, an implementation called K-MGSAEA is proposed, and the experimental results on a large number of test problems show that the proposed framework is superior to seven state-of-the-art competitors.

A Multi-Objective Sine Cosine Algorithm Based on a Competitive Mechanism and Its Application in Engineering Design Problems

There are a lot of multi-objective optimization problems (MOPs) in the real world, and many multi-objective evolutionary algorithms (MOEAs) have been presented to solve MOPs. However, obtaining non-dominated solutions that trade off convergence and diversity remains a major challenge for a MOEA. To solve this problem, this paper designs an efficient multi-objective sine cosine algorithm based on a competitive mechanism (CMOSCA). In the CMOSCA, the ranking relies on non-dominated sorting, and the crowding distance rank is utilized to choose the outstanding agents, which are employed to guide the evolution of the SCA. Furthermore, a competitive mechanism stemming from the shift-based density estimation approach is adopted to devise a new position updating operator for creating offspring agents. In each competition, two agents are randomly selected from the outstanding agents, and the winner of the competition is integrated into the position update scheme of the SCA. The performance of our proposed CMOSCA was first verified on three benchmark suites (i.e., DTLZ, WFG, and ZDT) with diversity characteristics and compared with several MOEAs. The experimental results indicated that the CMOSCA can obtain a Pareto-optimal front with better convergence and diversity. Finally, the CMOSCA was applied to deal with several engineering design problems taken from the literature, and the statistical results demonstrated that the CMOSCA is an efficient and effective approach for engineering design problems.

Optimizing chemotherapy treatment outcomes using metaheuristic optimization algorithms: A case study

BACKGROUND

This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters.

OBJECTIVE

To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform.

METHODS

The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP.

RESULTS

Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis.

CONCLUSION

Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.

Benefiting From Single-Objective Feature Selection to Multiobjective Feature Selection: A Multiform Approach

Evolutionary multiobjective feature selection (FS) has gained increasing attention in recent years. However, it still faces some challenges, for example, the frequently appeared duplicated solutions in either the search space or the objective space lead to the diversity loss of the population, and the huge search space results in the low search efficiency of the algorithm. Minimizing the number of selected features and maximizing the classification performance are two major objectives in FS. Usually, the fitness function of a single-objective FS problem linearly aggregates these two objectives through a weighted sum method. Given a predefined direction (weight) vector, the single-objective FS task can explore the specified direction or area extensively. Different direction vectors result in different search directions in the objective space. Motivated by this, this article proposes a multiform framework, which solves a multiobjective FS task combined with its auxiliary single-objective FS tasks in a multitask environment. By setting different direction vectors, promising feature subsets from single-objective FS tasks can be utilized, to boost the evolutionary search of the multiobjective FS task. By comparing with five classical and state-of-the-art multiobjective evolutionary algorithms, as well as four well-performing FS algorithms, the effectiveness and efficiency of the proposed method are verified via extensive experiments on 18 classification datasets. Furthermore, the effectiveness of the proposed method is also investigated in a noisy environment.

Identification of optimal flow rate for culture media, cell density, and oxygen toward maximization of virus production in a fed-batch baculovirus-insect cell system

In recent times, it has been realized that novel vaccines are required to combat emerging disease outbreaks, and faster optimization is required to respond to global vaccine demands. Although, fed-batch operations offer better productivity, experiment-based optimization of a new fed-batch process remains expensive and time-consuming. In this context, we propose a novel computational framework that can be used for process optimization and control of a fed-batch baculovirus-insect cell system. Since the baculovirus expression vector system (BEVS) is known to be widely used platforms for recombinant protein/vaccine production, we chose this system to demonstrate the identification of optimal profile. Toward this, first, we constructed a mathematical model that captures the time course of cell and virus growth in a baculovirus-insect cell system. Second, the proposed model was used for numerical analysis to determine the optimal operating profiles of control variables such as culture media, cell density, and oxygen based on a multiobjective optimal control formulation. Third, a detailed comparison between batch and fed-batch culture was perfromed along with a comparison between various alternatives of fed-batch operation. Finally, we demonstrate that a model-based quantification of controlled feed addition in fed-batch culture is capable of providing better productivity as compared to a batch culture. The proposed framework can be utilized for the estimation of optimal operating regions of different control variables to achieve maximum infected cell density and virus yield while minimizing the substrate/media, uninfected cell, and oxygen consumption.

Competitive Decomposition-Based Multiobjective Architecture Search for the Dendritic Neural Model

The dendritic neural model (DNM) is computationally faster than other machine-learning techniques, because its architecture can be implemented by using logic circuits and its calculations can be performed entirely in binary form. To further improve the computational speed, a straightforward approach is to generate a more concise architecture for the DNM. Actually, the architecture search is a large-scale multiobjective optimization problem (LSMOP), where a large number of parameters need to be set with the aim of optimizing accuracy and structural complexity simultaneously. However, the issues of irregular Pareto front, objective discontinuity, and population degeneration strongly limit the performances of conventional multiobjective evolutionary algorithms (MOEAs) on the specific problem. Therefore, a novel competitive decomposition-based MOEA is proposed in this study, which decomposes the original problem into several constrained subproblems, with neighboring subproblems sharing overlapping regions in the objective space. The solutions in the overlapping regions participate in environmental selection for the neighboring subproblems and then propagate the selection pressure throughout the entire population. Experimental results demonstrate that the proposed algorithm can possess a more powerful optimization ability than the state-of-the-art MOEAs. Furthermore, both the DNM itself and its hardware implementation can achieve very competitive classification performances when trained by the proposed algorithm, compared with numerous widely used machine-learning approaches.

Use of Two Penalty Values in Multiobjective Evolutionary Algorithm Based on Decomposition

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) with the penalty-based boundary intersection (PBI) function (denoted as MOEA/D-PBI) has been frequently used in many studies in the literature. One essential issue in MOEA/D-PBI is its penalty parameter value specification. However, it is not easy to specify the penalty parameter value appropriately. This is because MOEA/D-PBI shows different search behavior when the penalty parameter values are different. The PBI function with a small penalty parameter value is good for convergence. However, the PBI function with a large value of penalty parameter is needed to preserve the diversity and uniformity of solutions. Although some methods for adapting the penalty parameter value for each weight vector have been proposed, they usually lead to slow convergence. In this article, we propose the idea of using two different values of penalty parameter simultaneously in MOEA/D-PBI. Although the idea is simple, the proposed algorithm is able to utilize both the convergence ability of a small penalty parameter value and the diversification ability of a large penalty parameter value of the PBI function. Experimental results demonstrate that the proposed algorithm works well on a wide range of test problems.

A Multi-Population Multi-Objective Evolutionary Algorithm Based on the Contribution of Decision Variables to Objectives for Large-Scale Multi/Many-Objective Optimization

Most existing multiobjective evolutionary algorithms treat all decision variables as a whole to perform genetic operations and optimize all objectives with one population at the same time. Considering different control attributes, different decision variables have different optimization effects on each objective, so decision variables can be divided into convergence- or diversity-related variables. In this article, we propose a new metric called the optimization degree of the convergence-related decision variable to each objective to calculate the contribution objective of each decision variable. All decision variables are grouped according to their contribution objectives. Then, a multiobjective evolutionary algorithm, namely, decision variable contributing to objectives evolutionary algorithm (DVCOEA), has been proposed. In order to balance the convergence and diversity of the population, the DVCOEA algorithm combines the multipopulation multiobjective framework, where two different optimization strategies are designed to optimize the subpopulation and individuals in the external archive, respectively. Finally, DVCOEA is compared with several state-of-the-art algorithms on a number of benchmark functions. Experimental results show that DVCOEA is a competitive approach for solving large-scale multi/many-objective problems.

Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by the weight decomposition of objectives. This article proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is then built accordingly. Compared with other learning-based methods, our method can greatly shorten the training time of multiple submodels. Due to the rapid and excellent adaptability of the meta-model, more submodels can be derived so as to increase the quality and diversity of the found solutions. The computational experiments on multiobjective traveling salesman problems and multiobjective vehicle routing problems with time windows demonstrate the superiority of our method over most of the learning-based and iteration-based approaches.

Latent space search based multimodal optimization with personalized edge-network biomarker for multi-purpose early disease prediction

Considering that cancer is resulting from the comutation of several essential genes of individual patients, researchers have begun to focus on identifying personalized edge-network biomarkers (PEBs) using personalized edge-network analysis for clinical practice. However, most of existing methods ignored the optimization of PEBs when multimodal biomarkers exist in multi-purpose early disease prediction (MPEDP). To solve this problem, this study proposes a novel model (MMPDENB-RBM) that combines personalized dynamic edge-network biomarkers (PDENB) theory, multimodal optimization strategy and latent space search scheme to identify biomarkers with different configurations of PDENB modules (i.e. to effectively identify multimodal PDENBs). The application to the three largest cancer omics datasets from The Cancer Genome Atlas database (i.e. breast invasive carcinoma, lung squamous cell carcinoma and lung adenocarcinoma) showed that the MMPDENB-RBM model could more effectively predict critical cancer state compared with other advanced methods. And, our model had better convergence, diversity and multimodal property as well as effective optimization ability compared with the other state-of-art methods. Particularly, multimodal PDENBs identified were more enriched with different functional biomarkers simultaneously, such as tissue-specific synthetic lethality edge-biomarkers including cancer driver genes and disease marker genes. Importantly, as our aim, these multimodal biomarkers can perform diverse biological and biomedical significances for drug target screen, survival risk assessment and novel biomedical sight as the expected multi-purpose of personalized early disease prediction. In summary, the present study provides multimodal property of PDENBs, especially the therapeutic biomarkers with more biological significances, which can help with MPEDP of individual cancer patients.

A double association-based evolutionary algorithm for many-objective optimization

In this paper, a double association-based evolutionary algorithm (denoted as DAEA) is proposed to solve many-objective optimization problems. In the proposed DAEA, a double association strategy is designed to associate solutions with each subspace. Different from the existing association methods, the double association strategy takes the empty subspace into account and associates it with a promising solution, which can facilitate the exploration of unknown areas. Besides, a new quality evaluation scheme is developed to evaluate the quality of each solution in subspace, where the convergence and diversity of each solution is first measured, and in order to evaluate the diversity of solutions more finely, the global diversity and local diversity is designed to measure the diversity of each solution. Then, a dynamic penalty coefficient is designed to balance the convergence and diversity by penalizing the global diversity distribution of solutions. The performance of DAEA is validated by comparing with five state-of-the-art many-objective evolutionary algorithms on a number of well-known benchmark problems with up to 20 objectives. Experimental results show that our DAEA has high competitiveness in solving many-objective optimizatiopn problems compared with the other compared algorithms.

Composite scanning mechanism based on an aperiodic optical phased array

A composite scanning mechanism is proposed based on an aperiodic optical phased array (OPA). The OPA of this scheme has a two-stage scanning mode of sub-aperture multi-beam and single-beam high-resolution scanning. The scanning mode can be adaptively switched according to different environmental conditions. While retaining the advantages of high-speed and multi-target detection of sub-aperture multi-beam steering, a high-resolution scanning of the region of interest is realized. Simultaneously, the array distribution of the phased array is optimized using the adaptive-reference-point-based multi-objective evolutionary algorithm to reduce the grating lobe. The research conducted provides ideas for OPAs in practical applications.

Handling multi-objective optimization problems with a comprehensive indicator and layered particle swarm optimizer

The multi-objective particle swarm optimization algorithm has several drawbacks, such as premature convergence, inadequate convergence, and inadequate diversity. This is particularly true for complex, high-dimensional, multi-objective problems, where it is easy to fall into a local optimum. To address these issues, this paper proposes a novel algorithm called IMOPSOCE. The innovations for the proposed algorithm mainly contain three crucial factors: 1) an external archive maintenance strategy based on the inflection point distance and distribution coefficient is designed, and the comprehensive indicator (CM) is used to remove the non-dominated solutions with poor comprehensive performance to improve the convergence of the algorithm and diversity of the swarm; 2) using the random inertia weight strategy to efficiently control the movement of particles, balance the exploration and exploitation capabilities of the swarm, and avoid excessive local and global searches; and 3) offering different flight modes for particles at different levels after each update to further enhance the optimization capacity. Finally, the algorithm is tested on 22 typical test functions and compared with 10 other algorithms, demonstrating its competitiveness and outperformance on the majority of test functions.

Seasonal catchment memory of high mountain rivers in the Tibetan Plateau

Rivers originating in the Tibetan Plateau are crucial to the population in Asia. However, research about quantifying seasonal catchment memory of these rivers is still limited. Here, we propose a model able to accurately estimate terrestrial water storage change (TWSC), and characterize catchment memory processes and durations using the memory curve and the influence/domination time, respectively. By investigating eight representative basins of the region, we find that the seasonal catchment memory in precipitation-dominated basins is mainly controlled by precipitation, and that in non-precipitation-dominated basins is strongly influenced by temperature. We further uncover that in precipitation-dominated basins, longer influence time corresponds to longer domination time, with the influence/domination time of approximately six/four months during monsoon season. In addition, the long-term catchment memory is observed in non-precipitation-dominated basins. Quantifying catchment memory can identify efficient lead times for seasonal streamflow forecasts and water resource management.

Normal vibration distribution search-based differential evolution algorithm for multimodal biomedical image registration

In linear registration, a floating image is spatially aligned with a reference image after performing a series of linear metric transformations. Additionally, linear registration is mainly considered a preprocessing version of nonrigid registration. To better accomplish the task of finding the optimal transformation in pairwise intensity-based medical image registration, in this work, we present an optimization algorithm called the normal vibration distribution search-based differential evolution algorithm (NVSA), which is modified from the Bernstein search-based differential evolution (BSD) algorithm. We redesign the search pattern of the BSD algorithm and import several control parameters as part of the fine-tuning process to reduce the difficulty of the algorithm. In this study, 23 classic optimization functions and 16 real-world patients (resulting in 41 multimodal registration scenarios) are used in experiments performed to statistically investigate the problem solving ability of the NVSA. Nine metaheuristic algorithms are used in the conducted experiments. When compared to the commonly utilized registration methods, such as ANTS, Elastix, and FSL, our method achieves better registration performance on the RIRE dataset. Moreover, we prove that our method can perform well with or without its initial spatial transformation in terms of different evaluation indicators, demonstrating its versatility and robustness for various clinical needs and applications. This study establishes the idea that metaheuristic-based methods can better accomplish linear registration tasks than the frequently used approaches; the proposed method demonstrates promise that it can solve real-world clinical and service problems encountered during nonrigid registration as a preprocessing approach.The source code of the NVSA is publicly available at https://github.com/PengGui-N/NVSA.

Multi-objective particle swarm optimization with reverse multi-leaders

Despite being easy to implement and having fast convergence speed, balancing the convergence and diversity of multi-objective particle swarm optimization (MOPSO) needs to be further improved. A multi-objective particle swarm optimization with reverse multi-leaders (RMMOPSO) is proposed as a solution to the aforementioned issue. First, the convergence strategy of global ranking and the diversity strategy of mean angular distance are proposed, which are used to update the convergence archive and the diversity archive, respectively, to improve the convergence and diversity of solutions in the archives. Second, a reverse selection method is proposed to select two global leaders for the particles in the population. This is conducive to selecting appropriate learning samples for each particle and leading the particles to quickly fly to the true Pareto front. Third, an information fusion strategy is proposed to update the personal best, to improve convergence of the algorithm. At the same time, in order to achieve a better balance between convergence and diversity, a new particle velocity updating method is proposed. With this, two global leaders cooperate to guide the flight of particles in the population, which is conducive to promoting the exchange of social information. Finally, RMMOPSO is simulated with several state-of-the-art MOPSOs and multi-objective evolutionary algorithms (MOEAs) on 22 benchmark problems. The experimental results show that RMMOPSO has better comprehensive performance.

An Evolutionary Algorithm With Constraint Relaxation Strategy for Highly Constrained Multiobjective Optimization

Highly constrained multiobjective optimization problems (HCMOPs) refer to constrained multiobjective optimization problems (CMOPs) with complex constraints and small feasible regions, which are commonly encountered in many real-world applications. Current constraint-handling techniques will face two difficulties when dealing with HCMOPs: 1) feasible solution is hard to be found and too much search effort is spent in locating the feasible region and 2) since the total feasible region of an HCMOP can consist of several disconnected subregions, the search process might be stuck in the comparatively larger feasible subregion, which does not contain the whole Pareto front (PF). To address these two issues, an evolutionary algorithm with constraint relaxation strategy based on differential evolution algorithm, that is, CRS-DE, is proposed in this article. In each generation, the CRS-DE relaxes the constraints by dividing the infeasible solutions into two subpopulations based on total constraint violation, that is, the "semifeasible" subpopulation (SF) and "infeasible" subpopulation (IF), respectively. The SF provides information on the promising regions of finding the feasible solution and is the driving force for convergence toward the PF, while the IF focuses on global exploration for new promising regions. Corresponding reproduction and selection strategies are devised for the SF, IF, and feasible subpopulations, which create a clear division of labor with cooperation to facilitate the search for feasible solutions. To leverage the influence of CRS and prevent the population from premature convergence, a mobility restriction mechanism is developed to restrict the individuals in the SF and IF from entering the feasible subpopulation and enhance the diversity of the whole population. Comprehensive experiments on a series of benchmark test problems and a real-world CMOP demonstrate the competitiveness of our method compared with other representative algorithms in terms of effectiveness and reliability in finding a set of well-distributed optimal solutions for HCMOPs.

Resource saving and carbon footprint reduction potential of urban symbiosis strategy in express packaging waste recycling network

The booming express delivery industry corresponds to the environmental challenges caused by massive express packaging waste (EPW). An efficient logistics network is necessary link to support EPW recycling. This study, therefore, designed a circular symbiosis network for EPW recycling based on urban symbiosis strategy. The treatment of EPW in this network includes reuse, recycling and replacing. An optimization model with multi-depot collaboration combining material flow analysis and optimization methods was developed and a hybrid non-dominated sorting genetic algorithm-II (NSGA-II) was designed as technical support for designing the circular symbiosis network while quantitatively assessing the economic and environmental benefits of the network. The results show that the designed circular symbiosis option has better resource saving and carbon footprint reduction potential than both the business as usual option and circular symbiosis option without service collaboration. In practice, the proposed circular symbiosis network can save EPW recycling costs and reduce carbon footprint. This study provides a practical guideline for the application of urban symbiosis strategies to help urban green governance and the sustainable development of express companies.

Solution Set Augmentation for Knee Identification in Multiobjective Decision Analysis

In multiobjective decision making, most knee identification algorithms implicitly assume that the given solutions are well distributed and can provide sufficient information for identifying knee solutions. However, this assumption may fail to hold when the number of objectives is large or when the shape of the Pareto front is complex. To address the above issues, we propose a knee-oriented solution augmentation (KSA) framework that converts the Pareto front into a multimodal auxiliary function whose basins correspond to the knee regions of the Pareto front. The auxiliary function is then approximated using a surrogate and its basins are identified by a peak detection method. Additional solutions are then generated in the detected basins in the objective space and mapped to the decision space with the help of an inverse model. These solutions are evaluated by the original objective functions and added to the given solution set. To assess the quality of the augmented solution set, a measurement is proposed for the verification of knee solutions when the true Pareto front is unknown. The effectiveness of KSA is verified on widely used benchmark problems and successfully applied to a hybrid electric vehicle controller design problem.

A Multiobjective Evolutionary Approach for Solving Large-Scale Network Reconstruction Problems via Logistic Principal Component Analysis

Currently, the problem of uncovering complex network structure and dynamics from time series is prominent in many fields. Despite the recent progress in this area, reconstructing large-scale networks from limited data remains a tough problem. Existing works treat connections of nodes as continuous values, leaving a challenge of setting a proper cut-off value to distinguish whether the connections exist or not. Besides, their performances on large-scale networks are far from satisfactory. Considering the reconstruction error and sparsity as two objectives, this article proposes a subspace learning-based evolutionary multiobjective network reconstruction algorithm, called SLEMO-NR, to solve the aforementioned problems. In the evolutionary process, we assume that binary-coded individuals obey the Bernoulli distribution and can use the probability and natural parameter as alternative representations. Moreover, our approach utilizes the logistic principal component analysis (LPCA) to learn a subspace containing the features of the network structure. The offspring solutions are generated in the learned subspace and then can be mapped back to the original space via LPCA. Benefitting from the alternative representations, a preference-based local search operator (PLSO) is proposed to concentrate on finding solutions approximate to the true sparsity. The experimental results on synthetic networks and six real-world networks demonstrate that, due to the well-learned network structure subspace and the preference-based strategy, our approach is effective in reconstructing large-scale networks compared to six existing methods.

A Surrogate-Assisted Differential Evolution Algorithm for High-Dimensional Expensive Optimization Problems

The radial basis function (RBF) model and the Kriging model have been widely used in the surrogate-assisted evolutionary algorithms (SAEAs). Based on their characteristics, a global and local surrogate-assisted differential evolution algorithm (GL-SADE) for high-dimensional expensive problems is proposed in this article, in which a global RBF model is trained with all samples to estimate a global trend, and then its optima is used to significantly accelerate the convergence process. A local Kriging model prefers to select points with good predicted fitness and great uncertainty, which can effectively prevent the search from getting trapped into local optima. When the local Kriging model finds the best solution so far, a reward search strategy is executed to further exploit the local Kriging model. The experiments on a set of benchmark functions with dimensions varying from 30 to 200 are conducted to evaluate the performance of the proposed algorithm. The experimental results of the proposed algorithm are compared to four state-of-the-art algorithms to show its effectiveness and efficiency in solving high-dimensional expensive problems. Besides, GL-SADE is applied to an airfoil optimization problem to show its effectiveness.

A Multi-Objective Carnivorous Plant Algorithm for Solving Constrained Multi-Objective Optimization Problems

Satisfying various constraints and multiple objectives simultaneously is a significant challenge in solving constrained multi-objective optimization problems. To address this issue, a new approach is proposed in this paper that combines multi-population and multi-stage methods with a Carnivorous Plant Algorithm. The algorithm employs the ϵ-constraint handling method, with the ϵ value adjusted according to different stages to meet the algorithm’s requirements. To improve the search efficiency, a cross-pollination is designed based on the trapping mechanism and pollination behavior of carnivorous plants, thus balancing the exploration and exploitation abilities and accelerating the convergence speed. Moreover, a quasi-reflection learning mechanism is introduced for the growth process of carnivorous plants, enhancing the optimization efficiency and improving its global convergence ability. Furthermore, the quadratic interpolation method is introduced for the reproduction process of carnivorous plants, which enables the algorithm to escape from local optima and enhances the optimization precision and convergence speed. The proposed algorithm’s performance is evaluated on several test suites, including DC-DTLZ, FCP, DASCMOP, ZDT, DTLZ, and RWMOPs. The experimental results indicate competitive performance of the proposed algorithm over the state-of-the-art constrained multi-objective optimization algorithms.

Research on high efficiency and high dynamic optimal matching of the electro-hydraulic servo pump control system based on NSGA-II

An electro-hydraulic servo pump control system (hereinafter referred to as EHSPCS) is a volume servo control unit that is highly integrated with servo motors, fixed-displacement pumps, hydraulic cylinders and functional valve groups. Because of its unique volume direct-drive control mode, the dynamic performance of the system is limited, and the thermal power loss is large, which seriously restricts the improvement of the working quality of the system. To improve the dynamic performance of the system and reduce the thermal power loss to the maximum extent, a multi-objective optimization design method for the EHSPCS is proposed by comprehensively considering the dynamic and efficient energy-saving characteristics of the system. The evaluation model of the dynamic period of the hydraulic cylinder and the thermal power loss of the servo motor are given. Parameters such as the electromagnetic torque of the servo motor, displacement of the hydraulic pump, and working area of the hydraulic cylinder are intelligently optimized by a non-dominated sorting genetic algorithm with elite strategy (NSGA-II). The Pareto front of multi-objective optimization and the corresponding Pareto solution set are obtained; thus, the optimal matching of the system characteristics is realized. Finally, the relevant theory of the multi-objective optimization algorithm is applied to optimize the performance parameters of the hydraulic servo motor, and the prototype is tested in engineering. The experimental results show that the dynamic period of the hydraulic servo motor is accelerated after optimization, and the thermal power loss is significantly reduced. The dynamic and efficient energy-saving characteristics of the system are improved, which further verifies the feasibility of the proposed theory.

Evolutionary multiobjective optimization via efficient sampling-based offspring generation

With the rising number of large-scale multiobjective optimization problems from academia and industries, some evolutionary algorithms (EAs) with different decision variable handling strategies have been proposed in recent years. They mainly emphasize the balance between convergence enhancement and diversity maintenance for multiobjective optimization but ignore the local search tailored for large-scale optimization. Consequently, most existing EAs can hardly obtain the global or local optima. To address this issue, we propose an efficient sampling-based offspring generation method for large-scale multiobjective optimization, where convergence enhancement and diversity maintenance, together with ad hoc local search, are considered. First, the decision variables are dynamically classified into two types for solving large-scale decision space in a divide-and-conquer manner. Then, a convergence-related sampling strategy is designed to handle those decision variables related to convergence enhancement. Two additional sampling strategies are proposed for diversity maintenance and local search, respectively. Experimental results on problems with up to 5000 decision variables have indicated the effectiveness of the algorithm in large-scale multiobjective optimization.

Bi-indicator driven surrogate-assisted multi-objective evolutionary algorithms for computationally expensive problems

This paper presents a bi-indicator-based surrogate-assisted evolutionary algorithm (BISAEA) for multi-objective optimization problems (MOPs) with computationally expensive objectives. In BISAEA, a Pareto-based bi-indictor strategy is proposed based on convergence and diversity indicators, where a nondominated sorting approach is adopted to carry out two-objective optimization (convergence and diversity indicators) problems. The radius-based function (RBF) models are used to approximate the objective values. In addition, the proposed algorithm adopts a one-by-one selection strategy to obtain promising samples from new samples for evaluating the true objectives by their angles and Pareto dominance relationship with real non-dominated solutions to improve the diversity. After the comparison with four state-of-the-art surrogate-assisted evolutionary algorithms and three evolutionary algorithms on 76 widely used benchmark problems, BISAEA shows high efficiency and a good balance between convergence and diversity. Finally, BISAEA is applied to the multidisciplinary optimization of blend-wing-body underwater gliders with 30 decision variables and three objectives, and the results demonstrate that BISAEA has superior performance on computationally expensive engineering problems.

Multi-Objective Collaborative Optimization of Distillation Column Group Based on System Identification

In this paper, a multi-objective collaborative optimization (MOCO) strategy is proposed for making decisions on a distillation column group. Firstly, based on data preprocessing, the operating modes of the tower group are determined by use of the fuzzy C-means clustering method. Secondly, based on the proposed concept of a collaborative variable, the discrete state-space model of the main towers are constructed by the subspace identification method. Then, a MOCO optimization model is designed for the ethylene plant. Finally, NSGA-III is used to solve the optimization problem. An analysis of a Pareto-optimal frontier and population is carried out. To illustrate the superiority of the proposed strategy, the results are compared with historical data and the appealing operation area is finally obtained.