Multi-objective Search Research Articles

A UAV path planning method based on the framework of multi-objective jellyfish search algorithm.

Multi-constraint UAV path planning problems can be viewed as many-objective optimization problems that can be solved by meta-heuristic algorithms with good self-organizing optimization capabilities. However, such algorithms mostly use random initializing methods, resulting in low-quality initial paths that reduce the efficiency of subsequent algorithmic searches. Moreover, as the number of objective functions increases, meta-heuristic algorithms face inadequate selection pressure and convergence capability, which lead to poor solution. In order to address these issues, this paper proposes a UAV path planning method based on the framework of multi-objective jellyfish search algorithm (UMOJS). Firstly, an initializing strategy based on Rapidly-exploring Random Trees (RRT) is proposed to achieve higher quality initial paths. Secondly, a jellyfish updating strategy guided by the class-optimal individual is designed to enhance the convergence ability of the algorithm. Furthermore, a set of predefined reference points is imported to obtain Pareto optimal solutions with better convergence and distribution in many-objective optimization problems. To evaluate the superiority of the proposed UMOJS algorithm, three different difficulties of simulated flight environments are constructed to verify its performance. The experimental results show that UMOJS is not only able to gain more UAV paths with shorter length, but also more evenly distributed Pareto optimal solutions compared to five meta-heuristic algorithms when the constraint conditions are satisfied.

Multi-objective cooperation search algorithm based on decomposition for complex engineering optimization problems

This study introduces a novel multi-objective cooperation search algorithm based on decomposition (MOCSA/D) to address multi-objective competitive challenges in engineering problem. Inspired by the optimization strategy of single-objective Cooperation Search Algorithm (CSA) and the decomposition framework of MOEA/D, MOCSA/D algorithm randomly generates initial solutions in the optimization space, and then repeatedly executes four search strategies until the end of iteration: Cooperative updating strategy gathers high-quality information to update solutions with balanced distribution. Reflective adjustment strategy expands the exploration range of the population, enabling the acquisition of solutions with strong optimization capabilities. Internal competition strategy selects superior individuals with better performance for subsequent optimization. Density updating strategy improves the competitiveness of optimized individuals within the population, fostering a more diverse solution set. Three numerical experiments (including DTLZ, WFG unconstrained test problems, ZXH_CF constrained test problems and RWMOP real-world multi-objective optimization problems) are tested to further comprehensively evaluate the dominant performance of MOCSA/D. The test results in different problem scenarios show that compared with the existing excellent evolutionary algorithms, MOCSA/D can always obtain a better, stable and uniform distribution of non-dominated solutions, and has higher solving efficiency and optimization quality under different performance evaluation metrics with the increasing difficulty of solving problems. Finally, the proposed algorithm is applied to the multi-objective reservoir engineering optimization problem to verify the feasibility of the decision scheme and the comprehensive benefit optimization of MOCSA/D. Overall, MOCSA/D can simplify the problem optimization difficulty based on decomposition mechanism, and improve the global optimization of population, path diversity and individual competition through different search strategies, which provides an advantageous tool for addressing multi-objective competitive challenges.

Multi-objective optimization and multi-attribute decision-making support for optimal operation of multi stakeholder integrated energy systems

To efficiently tackle the optimal operation problem of multi-stakeholder integrated energy systems (IESs), this paper develops a multi-objective optimization and multi-attribute decision-making support method. Mathematically, The optimal operation of IESs interconnected with distributed district heating and cooling units (DHCs) via the power grid and gas network, can be formulated as a multi-objective optimization problem considering both economic, reliability and environment-friendly objectives with numerous constraints of each energy stakeholder. Firstly, a multi-objective group search optimizer with probabilistic operator and chaotic local search (MPGSO) is proposed to balance global and local optimality during the random search iteration. The MPGSO utilizes a crowding probabilistic operator to select producers to explore areas with higher potential but less crowding and reduce the number of fitness function calculations. Moreover, a new parameter selection strategy based on chaotic sequences with limited computational complexity is adopted to escape the local optimal solutions. Consequently, a set of superior Pareto-optimal fronts could be obtained by the MPGSO. Subsequently, a multi-attribute decision-making support method based on the interval evidential reasoning (IER) approach is used to determine a final optimal solution from the Pareto-optimal solutions, taking multiple attributes of each stakeholder into consideration. To verify the effectiveness of the MPGSO, the DTLZ suite of benchmark problems are tested compared with the original GSOMP, NSGA-II and SPEA2. Additionally, simulation studies are conducted on a modified IEEE 30-bus system connected with distributed DHCs and a 15-node gas network to verify the proposed approch. The quality of the obtained Pareto-optimal solutions is assessed using a set of criteria, including hypervolume (HV), generational distance (GD), and Spacing index, among others. Simulation results show that the number of Pareto-optimal solutions (NPS) of MPGSO are higher by about 32.6 %-62.1%, computation time (CT) are lower by about 2.94 %-46.1 % compared with other algorithms. Besides, to further evaluate the performance of the proposed approach in addressing larger-scale issues, the study employs the modified IEEE 118-bus system of greater magnitude. The proposed MPGSO algorithm effectively handles multi-objective and non-convex optimization problems with Pareto sets in terms of better convergence and distributivity.

Energy-economic analysis and optimization of a shell and tube heat exchanger using a multi-objective heat transfer search algorithm

This study presents the energy-economic analysis and optimization of a shell and tube heat exchanger. A water-water, segmental baffled shell and tube heat exchanger was designed using the Kern method and analysed by performing energy and economic modelling. The analysis is carried out considering the design variables on the shell side i.e. baffle cut, baffle spacing, shell diameter and tube side variables i.e. tube layout, tube outside diameter, number of tube passes and number of tubes. The multi-objective heat transfer search algorithm was used to optimize the heat exchanger for minimum total cost and maximum heat exchanger efficiency. Multiple optimal solutions were presented using the Pareto optimal curve. TOPSIS selection criteria was used to identify the optimum operating condition. Within the given bounds of the variables, the shell and tube heat exchanger can be operated at a minimum cost of 72,000 $/year resulting in 16.4 % efficiency, or, it can be operated at a maximum efficiency of 81.6 % with a total cost of 275,000 $/year. The scattered distribution of shell diameter, baffle spacing, number of tube passes and number of tubes between the lower and upper bound represent their substantial role in optimizing the heat exchanger performance. The number of tubes and tube passes showed the maximum variation in efficiency, while significantly less impact was observed when the tube layout was altered.

Optimal operation of CCHP system with duality operation strategy considering hydrogen trading and carbon capture

The combined cooling, heating, and power (CCHP) system, known for its outstanding compatibility performance, has been widely integrated with renewable energy sources such as hydrogen, wind, and photovoltaics, as well as decarbonization technologies in the energy field. However, the increased complexity of CCHP scheduling due to the high proportion of renewable energy sources and load fluctuations leads to negative returns if renewable energy sources are not scheduled reasonably and decarbonization technologies are not utilized. To address this challenge, this study introduced solid oxide electrolyzer cell (SOEC) and carbon capture system (CCS) into the CCHP system, and constructed a novel CCHP model considering hydrogen trading and decarbonization technologies. First, for the scheduling of SOEC and CCS, a game model was presented based on hydrogen sales and energy storage benefits. Second, a nudge and compel theory-based scheduling strategy and a duality operation strategy (DOS) considering sources-load fluctuation were proposed. Third, for the optimal energy scheduling problem of CCHP under new strategies and technologies, a novel multi-objective PID-based search algorithm with dynamic disturbance response was introduced. Finally, the proposed new strategies, methods, and models were verified through actual case studies on multiple typical days. The results revealed that, compared with the following electrical load strategy and following thermal load strategies, the DOS reduced costs by 3.03 % and 6.99 %, and emissions by 7.84 % and 1.39 %, respectively. The obtained outcomes contribute to the application and development of clean energy and decarbonization techniques.

Let decision-makers direct the search for robust solutions: An interactive framework for multiobjective robust optimization under deep uncertainty

The robust decision-making framework (RDM) has been extended to consider multiple objective functions and scenarios. However, the practical applications of these extensions are mostly limited to academic case studies. The main reasons are: (i) substantial cognitive load in tracking all the trade-offs across scenarios and the interplay between uncertainties and trade-offs, (ii) lack of decision-makers’ involvement in solution generation and confidence. To address these problems, this study proposes a novel interactive framework involving decision-makers in searching for the most preferred robust solutions utilizing interactive multiobjective optimization methods. The proposed interactive framework provides a learning phase for decision-makers to discover the problem characteristics, the feasibility of their preferences, and how uncertainty may affect the outcomes of a decision. This involvement and learning allow them to control and direct the multiobjective search during the solution generation process, boosting their confidence and assurance in implementing the identified robust solutions in practice.

Comprehensive performance analysis and optimization of an ORC-HDH system for power and freshwater production driven by marine exhaust gas

Freshwater serves as a vital energy source for ships, underscoring the paramount importance of research into desalination systems in facilitating diverse and reliable energy supply for maritime vessels. Aiming at numerous waste heat of marine engines and the shortage of freshwater resources on board, this paper designs an innovative waste heat recovery (WHR) system. It includes an organic Rankine cycle, a compression refrigeration cycle, and a humidification-dehumidification (HDH) desalination system to recover waste heat from exhaust gases in cascades, which can effectively produce power, cooling, and freshwater, respectively. A parametric study of the co-generation system in terms of the freshwater production, gained output ratio (GOR), cost per unit of freshwater production, net power output, and per unit of output power cost, are conducted to identify the key operating parameters. A set of operating parameters is determined for the HDH system with a temperature of the humidifier outlet of 358.15 K and a mass flow rate ratio (MR) of seawater to humid air of 4.5. The effect of the relative humidity and temperature of the humid air, as well as the salinity and temperature of the seawater, on the performance of the HDH subsystem are analyzed. And the optimal operating conditions of the co-generation system are obtained through multi-objective cuckoo search optimization. The results demonstrate that the co-generation system can produce an output-power of 1479.8 kW, 500 kW, and 0.49 kg/s for cooling and freshwater production by using the working-fluid R365mfc/Cyclopentane with a mixing ratio of 33:67 under optimal conditions. The GOR and cost per unit of HDH subsystem are 1.62 and 1.70 $/m3, with a capital payback period of 4.18 years. The equivalent output-power of the co-generation system is 9.5 % higher than that of an ORC system.

Short term road network Macroscopic Fundamental Diagram parameters and traffic state prediction based on LSTM

Macroscopic Fundamental Diagram (MFD) is widely used in traffic state evaluation due to its description of the macro level of urban road network. This study focuses on the discrimination and short-term prediction of macro traffic states in urban road networks, using MFD combined with FCM clustering for state partitioning to characterize different macro states of the road network. To predict the MFD state, this paper builds two LSTMs to perform short-term predictions on two important parameters in MFD: road network weighted flow qw and road network weighted density kw. The parameters of the first three statistical intervals and the predicted time period are used as inputs to output the MFD parameters for the predicted time period. To ensure that the two LSTM structures and hyper-parameters settings can achieve the best prediction performance for MFD, the parameter optimization process of both should be included in the same search framework for hyper-parameters search. Therefore, this paper uses GA algorithm combined with multi-objective particle swarm optimization algorithm as the solving algorithm, with the accuracy of solving two MFD parameters and the accuracy of MFD point positioning as the hyper-parameters solving objectives. The study was validated using actual road network data from Hong Kong, and the results showed that the method proposed in this paper has an MRE prediction error of less than 7.8% for the two parameters of MFD, and can predict the future temporal trend of the two parameters, demonstrating the feasibility of MFD related predictions. The model's prediction of the overall shape and change trajectory trend of MFD is consistent with reality, and some test sets in MFD state prediction show high accuracy, the overall accuracy is 81.45%. To verify the effectiveness of the multi-objective search algorithm, typical LSTM models and RNN models were used for comparison. The experiment proved that the model used in this study performed better in error control and state prediction. This study explores and practices a short-term prediction method for road network MFD parameters, MFD status, and their changing trends. Provided path reference for urban road network prediction, traffic control status, and MFD related research.

An Automatic Software Defect Repair Method Based on Multi-Objective Genetic Programming

Due to the explosive growth of software quantity and the mixed ability of software developers, a large number of software defects emerge during the later stages of software maintenance. The search method based on genetic programming is one of the most popular in search algorithms, but it also has some issues. The single-objective approach to validate and select offspring patches without considering other constraints can affect the efficiency of patch generation. To address this issue, this paper proposes an automatic software repair method based on Multi-objective Genetic Programming (MGPRepair). Firstly, the method adopts a lightweight context analysis strategy to find suitable repair materials. Secondly, it decouples the replacement statements and insertion statements in the repair materials, using a lower-granularity patch representation method to encode the patches in the search space. Then, the automatic software defect repair is treated as a multi-objective search problem, and the NSGA-II multi-objective optimization algorithm is used to find simpler repair patches. Finally, the test case filtering technique is used to accelerate the patch validation process and generate correct patches. MGPRepair was experimentally evaluated on 395 real Java software defects from the Defects4J dataset. The experimental results show that MGPRepair can generate test case-passing patches for 51 defects, of which 35 defect patches are equivalent to manually generated patches. Its repair the efficiency and success rate are higher to other excellent automatic software defect repair methods such as jGenProg, RSRepair, ARJA, Nopol, Capgen, and SequenceR.

A hybrid method for fault diagnosis of rolling bearings

Abstract Traditional diagnostic methods often have insufficient accuracy and noise reduction, which leads to diagnostic errors. To address these issues, this paper proposes an advanced fault diagnosis model that combines the variational mode decomposition (VMD) improved by a Variable-Objective Search Whale Optimization Algorithm (VSWOA) with a Pelican Optimization (PO)-boosted Kernel Extreme Learning Machine (KELM) algorithm. The application of the method is shown here in the fault diagnosis of rolling bearings. The proposed VSWOA enhances the performance of VMD by incorporating a Sobol sequence, nonlinear time-varying factors, a multi-objective initial search strategy, and an elite Cauchy chaos mutation strategy, significantly improving noise reduction in vibration signals. Fault information is precisely extracted using waveform factors, sample entropy, and advanced composite multiscale fuzzy entropy, which enables effective feature screening and dimensionality reduction. The POA fine-tunes the KELM parameters, increasing the classification accuracy. The effectiveness of the model is verified through experimental evaluations using bearing data with injected Gaussian noise (from Case Western Reserve University) and the SpectraQuest datasets, where significant improvements in noise reduction and fault detection accuracy are achieved.

Designing a new sustainable healthcare network considering the COVID-19 pandemic: Artificial intelligence-based solutions

The COVID-19 pandemic, which is still spreading its new mutations all around the world, is considered a healthcare challenge around the world. The best approach to forestall this pandemic is to avoid exposure to the virus. Therefore, medical protective equipment is essential for fighting this pandemic. This underlines the chief role of having a sustainable supply chain network (SCN) for producing and distributing personal protective equipment to avoid shortage and augmenting costs. The reality, however, is that the COVID-19 pandemic leads to many developments in countries and this study is another step for these purposes. This research developsa multi-period, multi-objective, multi-echelon, and multi-product medical protective equipment sustainable SCN considering the production, distribution, allocation, and inventory with “risk pooling” strategy effect with the aim of filling the existing gaps in health SCN research during the COVID-19 pandemic. By applying the risk pooling strategy, lower inventory levels or higher service levels can be achieved without increasing inventory costs. This model explores the possibility of lateral transshipments between distribution centers, as a way to increase the reliability of SCN performance. We model a new production, inventory, distribution, location, and allocation problem and consider four objectives for our suggested model (i) minimizing total SCN costs, (ii) minimizing environmental effects, (iii) minimizing social impacts, and (iv) maximizing the reliability of demand delivery. The proposedmodel simultaneously examines all three dimensions of sustainability (economic, environmental, and social) as well as the reliability of demand delivery. Considering all of these decisions and assumptions brings the studied problem closer to reality. We employ various algorithms for solving our developed model with different sizes: the improved version of the augmented ε-constraint (AUGMECON2) algorithm for small and medium-sized problems and two meta-heuristic algorithms, i.e., Multi-Objective Whale Optimization Algorithm (MOWOA) and Multi-Objective Variable Neighborhood Search (MOVNS) algorithm, for large-sized ones. The Taguchi approach is used to tune the parameters of meta-heuristic algorithms, and a comparison is performed using four evaluation metrics: Mean Ideal Distance (MID), Number of Pareto Solutions (NPS), Maximum Spread (MS), and Spread of Non-Dominance Solution (SNS). Proposed solving methods for the studied problem and making comparisons between them are another innovation of this study. A couple of numerical examples are provided to illustrate the applicability of the presented solution methods. Finally, sensitivity analysis for problem parameters is performed to validate our suggested model. Our study reveals the superiority of the MOWOA over the other algorithms.

Multiobjective enterprise development algorithm for optimizing structural design by weight and displacement

This study presents a novel metaheuristic optimization algorithm for complex multiobjective engineering problems. By integrating advanced population and nondominated sorting techniques into the existing single-objective enterprise development algorithm, this new multiobjective approach effectively identifies Pareto-optimal solutions. The algorithm leverages these techniques to explore engineering solutions within multiobjective search spaces. We evaluated its performance using 29 multiobjective mathematical benchmark problems and conducted a comparative analysis against ten established metaheuristic optimization algorithms. The results demonstrate that the algorithm produces highly accurate approximations of Pareto-optimal fronts while maintaining a uniform distribution of solutions. Additionally, the algorithm was applied to real-world engineering challenges, including the optimization of structures such as the 942-bar tower, the 1536-bar double-layer barrel vault, and the 1410-bar double-layer dome truss, with the primary objectives of minimizing both structural weight and maximum nodal deflection. The findings highlight the algorithm's effectiveness in solving practical engineering problems and consistently achieving optimal Pareto fronts.

Fast Algorithms for Computing Fixed-Length Round Trips in Real-World Street Networks

This paper proposes and evaluates algorithms for calculating round trips of a prescribed length on directed street networks. This problem has several real-world applications, such as designing jogging routes and cycling tours. In this work, we focus specifically on methods that avoid the need to download, process, and store large map databases. At the same time, we aim for our methods to be fast, accurate, and capable of handling a wide range of prescribed distances, from just a few meters to many kilometres. To achieve this, our overall strategy involves using a small number of calls to a suitable online mapping service to collect relevant structural information for the problem at hand. All remaining computations are then performed locally on the client. Empirically, we demonstrate that our suggested techniques outperform existing open-source algorithms in terms of both accuracy and runtime requirements. Our most successful approach is based on multi-objective local search, utilizing specialized neighbourhood operators that exploit the underlying graph-theoretical properties of this problem, resulting in runtimes of around 2–3 s on a typical desktop computer.

Multi-objective evolutionary neural architecture search for network intrusion detection

Network Intrusion Detection (NID) becomes significantly important for protecting the security of information systems, as the frequency and complexity of network attacks are increasing with the rapid development of the Internet. Recent research studies have proposed various neural network models for NID, but they need to manually design the network architectures based on expert knowledge, which is very time-consuming. To solve this problem, this paper proposes a Multi-objective Evolutionary Neural Architecture Search (MENAS) method, which can automatically design neural network models for NID. First, a comprehensive search space is designed and then a weight-sharing mechanism is used to construct a supernet for NID, allowing each subnet to inherit weights from the supernet for direct performance evaluation. Subsequently, the subnets are encoded as chromosomes for multi-objective evolutionary search, which simultaneously optimizes two objectives: enhancing the model’s detection performance and reducing its complexity. To improve the search capability, a path-based crossover method is designed, which can iteratively refine the subnets’ architectures by simultaneously optimizing their accuracy and complexity for NID. At last, our MENAS method has been validated through extensive experiments on three well-known NID datasets: NSL-KDD, UNSW-NB15, and CICIDS2017. The experiments show that our MENAS method obtains an average 1.45% improvement on accuracy and an average 68.70% reduction on floating-point operations through multi-objective optimization process on six scenarios, which outperforms some state-of-the-art NID methods.

An indicator-based multi-objective variable neighborhood search approach for query-focused summarization

Currently, automatic multi-document summarization is an interesting subject in numerous fields of study. As a part of it, query-focused summarization is becoming increasingly important in recent times. These methods can automatically produce a summary based on a query given by the user, including the most relevant information from the query at the same time as the redundancy among sentences is reduced. This can be achieved by developing and applying a multi-objective optimization approach. In this paper, an Indicator-based Multi-Objective Variable Neighborhood Search (IMOVNS) algorithm has been designed, implemented, and tested for the query-focused extractive multi-document summarization problem. Experiments have been carried out with datasets from Text Analysis Conference (TAC). The results were evaluated using the Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metrics. IMOVNS has greatly improved the results presented in the scientific literature, providing improvement percentages in ROUGE metric reaching up to 69.24% in ROUGE-1, up to 57.70% in ROUGE-2, and up to 77.37% in ROUGE-SU4 scores. Hence, the proposed IMOVNS offers a promising solution to the query-focused summarization problem, thus highlighting its efficacy and potential for enhancing automatic summarization techniques.

Semi-supervised accuracy predictor-based multi-objective neural architecture search

The rise of neural architecture search (NAS) demonstrates the deep exploration between the neural network architecture and its performance (e.g., accuracy). Many NAS methods are inefficient because they train all candidates from scratch to obtain their accuracies. Although predictor-based NAS algorithms have been vigorously developed to efficiently and accurately evaluate the performance of candidate architectures, the training of accuracy predictors still require hundreds of architectures with ground truth. To overcome this shortcoming, this paper investigates an evolutionary-based NAS method, which constructs a semi-supervised accuracy predictor to efficiently and accurately evaluate candidate architectures. A one-time extractor and strong regressors are implemented to further enhance the prediction performance of the semi-supervised accuracy predictor. Furthermore, a multi-objective approach is developed to find architectures with high ground truth in a tradeoff between high prediction accuracy and prediction confidence. Experimental results demonstrate the strong competitiveness of the proposed approach on NAS benchmarks. The code is available at https://github.com/outofstyle/SAPMNAS.

Resilient water infrastructure partnerships in institutionally complex systems face challenging supply and financial risk tradeoffs

As regions around the world invest billions in new infrastructure to overcome increasing water scarcity, better guidance is needed to facilitate cooperative planning and investment in institutionally complex and interconnected water supply systems. This work combines detailed water resource system ensemble modeling with multiobjective intelligent search to explore infrastructure investment partnership design in the context of ongoing canal rehabilitation and groundwater banking in California. Here we demonstrate that severe tradeoffs can emerge between conflicting goals related to water supply deliveries, partnership size, and the underlying financial risks associated with cooperative infrastructure investments. We show how hydroclimatic variability and institutional complexity can create significant uncertainty in realized water supply benefits and heterogeneity in partners’ financial risks that threaten infrastructure investment partnership viability. We demonstrate how multiobjective intelligent search can design partnerships with substantially higher water supply benefits and a fraction of the financial risk compared to status quo planning processes. This work has important implications globally for efforts to use cooperative infrastructure investments to enhance the climate resilience and financial stability of water supply systems.

Multi-Objective Real-Time Planning of Evacuation Routes for Underground Mine Fires

When a fire occurs underground, pre-existing emergency escape routes may become ineffective. Such scenarios necessitate the real-time planning of escape routes that consider evolving conditions and prioritize safety. This paper proposes a multi-objective real-time search method for emergency escape routes using dynamic programming to address these challenges. Firstly, this paper discusses how the evacuation of an underground mine fire caused by external factors depends on the fire monitoring system, personnel positioning system, and emergency evacuation system, as well as the modeling and solution methods of evacuation route planning. Then, based on fire smoke, CO, and temperature sensor data from the mine ventilation network structure and monitoring system, the possible smoke spread in the event of an underground fire was calculated. The objectives are to optimize both the shortest equivalent length of the path and the shortest time to walk through the smoke flow while ensuring that temporary escape time does not exceed the rated protection time of the self-rescuer. A mathematical model for emergency escape route planning is established under these conditions. A labeling algorithm based on dynamic programming is employed to find the Pareto optimal solution set of emergency evacuation routes that meet emergency requirements. Finally, two path evaluation indicators, namely “escape target priority” and “personnel temporary escape time”, are introduced to re-rank the solutions in the Pareto optimal set, thereby obtaining disaster evacuation routes with different priorities. Example verification shows that the algorithm can quickly solve the disaster evacuation routes that meet the actual disaster evacuation needs in complex networks. Example verification shows that the algorithm can quickly solve the emergency escape routes in complex networks that meet actual emergency escape needs.

Multi-Objective Unsupervised Feature Selection and Cluster Based on Symbiotic Organism Search

Unsupervised learning is a type of machine learning that learns from data without human supervision. Unsupervised feature selection (UFS) is crucial in data analytics, which plays a vital role in enhancing the quality of results and reducing computational complexity in huge feature spaces. The UFS problem has been addressed in several research efforts. Recent studies have witnessed a surge in innovative techniques like nature-inspired algorithms for clustering and UFS problems. However, very few studies consider the UFS problem as a multi-objective problem to find the optimal trade-off between the number of selected features and model accuracy. This paper proposes a multi-objective symbiotic organism search algorithm for unsupervised feature selection (SOSUFS) and a symbiotic organism search-based clustering (SOSC) algorithm to generate the optimal feature subset for more accurate clustering. The efficiency and robustness of the proposed algorithm are investigated on benchmark datasets. The SOSUFS method, combined with SOSC, demonstrated the highest f-measure, whereas the KHCluster method resulted in the lowest f-measure. SOSFS effectively reduced the number of features by more than half. The proposed symbiotic organisms search-based optimal unsupervised feature-selection (SOSUFS) method, along with search-based optimal clustering (SOSC), was identified as the top-performing clustering approach. Following this, the SOSUFS method demonstrated strong performance. In summary, this empirical study indicates that the proposed algorithm significantly surpasses state-of-the-art algorithms in both efficiency and effectiveness. Unsupervised learning in artificial intelligence involves machine-learning techniques that learn from data without human supervision. Unlike supervised learning, unsupervised machine-learning models work with unlabeled data to uncover patterns and insights independently, without explicit guidance or instruction.

Multi-Task Multi-Objective Evolutionary Search Based on Deep Reinforcement Learning for Multi-Objective Vehicle Routing Problems with Time Windows

The vehicle routing problem with time windows (VRPTW) is a widely studied combinatorial optimization problem in supply chains and logistics within the last decade. Recent research has explored the potential of deep reinforcement learning (DRL) as a promising solution for the VRPTW. However, the challenge of addressing the VRPTW with many conflicting objectives (MOVRPTW) still remains for DRL. The MOVRPTW considers five conflicting objectives simultaneously: minimizing the number of vehicles required, the total travel distance, the travel time of the longest route, the total waiting time for early arrivals, and the total delay time for late arrivals. To tackle the MOVRPTW, this study introduces the MTMO/DRP-AT, a multi-task multi-objective evolutionary search algorithm, by making full use of both DRL and the multitasking mechanism. In the MTMO/DRL-AT, a two-objective MOVRPTW is constructed as an assisted task, with the objectives being to minimize the total travel distance and the travel time of the longest route. Both the main task and the assisted task are simultaneously solved in a multitasking scenario. Each task is decomposed into scalar optimization subproblems, which are then solved by an attention model trained using DRL. The outputs of these trained models serve as the initial solutions for the MTMO/DRL-AT. Subsequently, the proposed algorithm incorporates knowledge transfer and multiple local search operators to further enhance the quality of these promising solutions. The simulation results on real-world benchmarks highlight the superior performance of the MTMO/DRL-AT compared to several other algorithms in solving the MOVRPTW.