Elite Solutions Research Articles

Learnable self-supervised support vector machine based individual selection strategy for multimodal multi-objective optimization

Multimodal multi-objective optimization problem (MMOP) is a frontier research problem, which can provide decision makers with more choices without making trade-offs. Many multimodal multi-objective evolutionary algorithms (MMOEAs) have been proposed to solve MMOP. However, most MMOEAs tend to prioritize the objective dominance of individuals in the process of individual selection, and only individuals with the same objective dominance will be considered the diversity, which leads to the loss of many promising solutions. To solve the above problem, this paper proposes a learnable self-supervised support vector machine (SVM) based multimodal multi-objective optimization algorithm (SVMEA). Support vector machine can learn the knowledge about distinguishing the advantages and disadvantages of individuals from the data in the existing training set and select individuals, in which the objective dominance of individuals is as important as diversity. Moreover, a crowding distance calculation method based on Manhattan distance is designed. Compared with the traditional method using Euclidean distance to calculate crowding distance, it can better evaluate the diversity of individuals in the decision space and assist the selection of elite solutions. Experimental results show that the proposed SVMEA is competitive with seven other advanced MMOEAs on 34 benchmark problems and a practical application problem.

Design and Implementation of TDMA Scheduling Based on BRKGA

Abstract Messages in wireless Ad hoc networks may require intermediate multi-hop forwarding from the source to the target node. To find an optimum contend-free time slots scheduling solution in Ad hoc, a TDMA (Time Division Multiple Access) scheduling scheme based on BRKGA (Biased Random-key GA) is proposed. The algorithm divides the population of generation k into elite group and rest group. The elite solutions are copied directly to the next generation. One parent from the elite group and another parent from the rest population are randomly selected to crossover a new solution. The worst Pm solutions of the population of generation k are replaced by the mutants. The simulation results demonstrate that the TDMA based on BRKGA exhibits better performance in terms of lower frame length and higher channel utilization.

Two-stage particle swarm optimization with dual-indicator fusion ranking for multi-objective problems

Elite solutions guiding population evolution are often used as one of main ideas to improve the performance of multi-objective particle swarm optimization (MOPSO). However, in most research work, sole Pareto dominance criterion is often used to evaluate solutions. This sole criterion may easily cause some problems, such as the premature convergence. In this study, we propose an MOPSO variant with dual-indicator fusion ranking (TPSO-DF), to evaluate elite solutions and to guide search without sacrificing diversity. In TPSO-DF, two indicators are introduced by using the convergence and diversity information, respectively. Both indicators are then fusioned in a ranking measure to focus on valuable information and to filter out solutions with these valuable information. Meanwhile, an adaptive global leader selection strategy is introduced to take full advantage of valuable information and to guide population evolution toward the optimal direction. As another contribution of this study, a two-stage hybrid mutation strategy is designed by utilizing the valuable information differently in different evolutionary states of the algorithm to enhance performance. Compared to eight representative multi-objective evolutionary algorithms, the performance of TPSO-DF is validated by extensive experiments on ZDT and DTLZ test suites, as well as one practical problem. Experimental results show that TPSO-DF can achieve competitive performance on most of the test functions.

An adaptive evolutionary search-based method for efficiently tackling the set-union knapsack problem

This paper tackles the NP-hard set-union knapsack problem using a novel adaptive evolutionary algorithm. Such a problem has applications in database query optimization, network design, and project portfolio management. The method starts by creating an archive set with elite and diversified solutions, employing a customized procedure based on item scores and Hamming max-min distance for diversity. Various operators are added to enhance solution quality in the elite set and refine the search process. To counteract premature convergence, combination and subset reference update methods are used. The fusion strategy serves as an exploration mechanism, generating new solutions and preventing premature convergence. Finally, the effectiveness and performance of the proposed method is evaluated on a set of benchmark instances taken from existing literature and by conducting a thorough statistical analysis of all achieved results. All obtained results are systematically compared against those achieved by state-of-the-art methods, indicating a substantial improvement of 50% for the large-sized instances, outperforming those published in the literature.

A knowledge-guided Estimation of Distribution Algorithm for energy-efficient Joint Robotic Assembly Line Balancing and Feeding Problem

The assembly line serves as a fundamental system in discrete production. To address the challenges in balancing robotic assembly lines, timely part feeding, and the need for sustainable manufacturing, this paper studies an energy-efficient Joint Robotic Assembly Line Balancing and Feeding Problem (JRALB-FP) with the criteria of minimizing both cycle time and total fuel consumption cost. Considering the complexity of the multi-problem and multi-objective optimization, a knowledge-guided Estimation of Distribution Algorithm (KEDA) is proposed to solve energy-efficient JRALB-FP. First, a probability model of EDA for task-workstation allocation paired with a heuristic method-based sampling mechanism is created. Using this probability model, a specific encoding mechanism is designed for part-trailer allocation, and good initial solutions are produced. Second, several properties of the bi-objective problem are analyzed to guide the design of local search operators for both objectives optimization. Third, the updating mechanism of the probability model is designed to learn from the elite solutions. Fourth, two knowledge-guided local search operators are designed and implemented to exploit better non-dominated solutions sufficiently. A design of experiment is carried out to determine the parameters. Extensive computational tests and comparisons with the state-of-the-art multi-objective algorithms are carried out, which verify the effectiveness of the knowledge-guided local search operators, the problem-oriented heuristic-based sampling mechanism, and the special designs of the KEDA in solving the energy-efficient JRALB-FP.

Route recombination for deterministic and non-deterministic orienteering problems with time windows: A dynamic programming approach

In this paper, we consider the Orienteering Problem with Time Windows (OPTW) where the goal is to visit customers within available time windows while maximizing the total reward provided by successive customer visits. For this problem, we introduce a new route recombination procedure that takes a set of solutions as input and returns the best combination containing at most k subsequences of customer visits from these solutions. This route recombination procedure is based on a dynamic programming algorithm enhanced with pruning strategies that can significantly reduce the size of the search space. It is also able to deal with time-dependent transition times. The experiments show that the algorithm proposed can be used as a lightweight and efficient post-optimization procedure working on elite solutions provided by a standard incomplete OPTW solver. Moreover, it can be used in a non-deterministic context where the reward values are not precisely known in advance; in this case, OPTW solutions can be first generated for various reward scenarios during an offline phase, and then combined during an online phase to quickly get a high-quality solution given the last-known reward values.

Iterated local search with ejection chains for the space-free multi-row facility layout problem

This paper presents an iterated local search algorithm based on ejection chains to solve the space-free multi-row facility layout problem. The aim of this problem is to find a non-overlapping layout of facilities on a given number of rows such that there is no space between two adjacent facilities. In addition, the left-most facility of the arrangement must have zero abscissa. Our algorithm looks for a local optimal solution by continuously alternating ejection moves and trial moves to form an ejection chain. Since the ejection chain can compound simple moves to create more complex and powerful moves, it has a greater chance to discover better solutions. Additionally, we propose a directional perturbation strategy to produce a solution of both high quality and good diversity. The idea is to calculate the score of each facility based on the location concentration of facilities in the elite solution set and the historical perturbation times of facilities in the search process, and to select the facility with the highest score for perturbation. Experimental results on four benchmark sets containing a total of 290 instances reveal that the proposed algorithm performs better for 131 (45.2%) instances in terms of best solution values and for 196 (80.0%) instances in terms of average solution values than a recently reported state-of-the-art algorithm.

An incremental method-based machine learning approach for max–min knapsack with multiple scenarios

In this paper, the max–min knapsack problem with multiple scenarios is addressed using an incremental method-based machine learning approach. The method is structured around three key phases: a learning phase, an exploitation phase, and an exploration phase. During the learning phase, the algorithm initiates by generating a sequential set of initial elite solutions through a Q-table scoring procedure. Moving on to the exploitation phase, the goal is to improve the quality of the current solution through an intensification-based tabu search, emphasizing iterative solution optimization. The exploration phase introduces controlled randomness to diversify exploration, revealing promising sub-spaces and facilitating the discovery of new solutions. This iterative process results in a series of new elite solutions, some of which are combined to highlight the method’s efficiency. To maintain diversity, a new fusion operator is introduced, where couples related to elite solutions are combined, forming an incremental subset of elite solutions capable of exploring new solution subspaces. The proposed method is evaluated using benchmark instances from the literature, and its results are compared to those provided by recently published algorithms. The computational analysis underscores the algorithm’s competitiveness in producing high-quality solutions, often surpassing previously published methods with superior solution bounds.

Intelligent learning-based cooperative and competitive multi-objective optimization for energy-aware distributed heterogeneous welding shop scheduling

This research is focused on addressing the energy-aware distributed heterogeneous welding shop scheduling (EADHWS) problem. Our primary objectives are to minimize the maximum finish time and total energy consumption. To accomplish this, we introduce a learning-based cooperative and competitive multi-objective optimization method, which we refer to as LCCMO. We begin by presenting a multi-rule cooperative initialization approach to create a population that combines strong convergence and diversity. This diverse population forms the foundation for our optimization process. Next, we develop a multi-level cooperative global search strategy that explores effective genes within solutions from different angles and sub-problems. This approach enhances our search for optimal solutions. Moreover, we design a competition and cooperation strategy for different populations to expedite convergence. This strategy encourages the exchange of information and ideas among diverse populations, thereby accelerating our progress. We also introduce a multi-operator cooperative local search technique, which investigates elite solutions from various directions, leading to improved convergence and diversity. In addition, we integrate Q-learning into our competitive swarm optimizer to explore different regions of the objective space, enhancing the diversity of the elite archive. Q-learning guides the selection of operators within the small-size population, contributing to more efficient optimization. To evaluate the effectiveness of LCCMO, we conduct numerical experiments on 20 instances. The experimental results unequivocally demonstrate that LCCMO outperforms six state-of-the-art algorithms. This underscores the potential of our learning and knowledge-driven evolutionary framework in enhancing performance and autonomy when it comes to solving EADHWS.

A Reinforcement-Learning-Based 3-D Estimation of Distribution Algorithm for Fuzzy Distributed Hybrid Flow-Shop Scheduling Considering On-Time-Delivery.

With the increasing level of mass-customization and globalization of competition, environmentally friendly production scheduling for distributed manufacturing considering customer satisfaction has received growing attention. Meanwhile, uncertain scheduling is becoming a force to be considered within intelligent manufacturing industries. However, little research has been found that surveyed the uncertain distributed scheduling considering both energy consumption and customer satisfaction. In this article, the fuzzy distributed hybrid flow-shop scheduling problem considering on-time delivery (FDHFSP-OTD) is addressed, and a 3-D estimation of distribution algorithm (EDA) with reinforcement learning (RL) is proposed to minimize the makespan and total energy consumption while maximizing delivery accuracy. First, two heuristics and a random method are designed and used cooperatively for initialization. Next, an EDA with a 3-D probability matrix is innovated to generate offspring. Then, a biased decoding method based on Q -learning is proposed to adjust the direction of evolution self-adaptively. Moreover, a local intensification strategy is employed for further enhancement of elite solutions. The effect of major parameters is analyzed and the best combination of values is determined through extensive experiments. The numerical results prove the effectiveness of each specially designed strategy and method, and the comparisons with existing algorithms demonstrate the high-potential of the 3D-EDA/RL in solving the FDHFSP-OTD.

An adaptive multitasking optimization algorithm based on population distribution.

Evolutionary multitasking optimization (EMTO) handles multiple tasks simultaneously by transferring and sharing valuable knowledge from other relevant tasks. How to effectively identify transferred knowledge and reduce negative knowledge transfer are two key issues in EMTO. Many existing EMTO algorithms treat the elite solutions in tasks as transferred knowledge between tasks. However, these algorithms may not be effective enough when the global optimums of the tasks are far apart. In this paper, we study an adaptive evolutionary multitasking optimization algorithm based on population distribution information to find valuable transferred knowledge and weaken the negative transfer between tasks. In this paper, we first divide each task population into K sub-populations based on the fitness values of the individuals, and then the maximum mean discrepancy (MMD) is utilized to calculate the distribution difference between each sub-population in the source task and the sub-population where the best solution of the target task is located. Among the sub-populations of the source task, the sub-population with the smallest MMD value is selected, and the individuals in it are used as transferred individuals. In this way, the solution chosen for the transfer may be an elite solution or some other solution. In addition, an improved randomized interaction probability is also included in the proposed algorithm to adjust the intensity of inter-task interactions. The experimental results on two multitasking test suites demonstrate that the proposed algorithm achieves high solution accuracy and fast convergence for most problems, especially for problems with low relevance.

Learning-based two-phase cooperative optimizer for distributed machine scheduling with heterogeneous factories and order priorities

In the realm of customized manufacturing, production cycles are often compressed to capture market opportunities swiftly. The blanking system stands as the inaugural and pivotal phase in the realm of large equipment customized manufacturing. This study abstracts a novel problem from real-world blanking systems, as the distributed unrelated parallel machine scheduling with heterogeneous factories and order priorities (DUPMS-HP). The presented work formulates the bi-objective DUPMS-HP, aiming to minimize both the total weighted tardiness and the workload gap of each machine. A learning-based two-phase cooperative optimizer (LCTPO) is introduced to address this NP-hard problem, featuring: i) a cooperative evolutionary algorithm during the first stage for global search to ensure diversity; ii) the incorporation of five problem-specific local search strategies in the first stage to balance priority and due date constraints. Additionally, reinforcement learning is applied to learn and select the best neighborhood search operator for each elite solution, further enhancing diversity. The effectiveness of the proposed algorithm is validated through a comparative analysis with five state-of-the-art algorithms on 20 instances. Experimental results affirm that LCTPO is more adept at solving DUPMS-HP compared to the alternative algorithms.

A Kriging-assisted Double Population Differential Evolution for Mixed-Integer Expensive Constrained Optimization Problems with Mixed Constraints

Many surrogate-assisted evolutionary algorithms (SAEA) with outstanding performance have been developed to handle Expensive Constrained Optimization Problems (ECOPs). But most of them are limited to solving ECOPs with continuous variables and inequality constraints. Therefore, a Kriging-assisted Double Population Differential Evolution (KDPDE) is proposed to deal with mixed-integer ECOPs with inequality and equality constraints. In particular, promising regions near the feasible region are created by Integer restriction Relaxation-based Double Population (IRDP) search framework, and then an Expected Improvement-based Classification local Search (EICS) is adopted to guide the infeasible solutions in the promising region into the feasible region. In order to improve the robustness of the algorithm, the widely distributed elite solutions are utilized by Elite solutions Retention-based Multi-directional Exploration (ERME) for diverse exploration, and the repetition rate information of individuals in the population is used by Population Diversity Maintenance Operation (PDMO) to adaptively avoid the population from falling into a local region. Therefore, KDPDE is capable of balancing the performance between convergence and robustness for mixed-integer ECOPS with mixed constraints. Experimental studies on several benchmark problems and a real-world application example demonstrate that KDPDE has excellent performance on solving such kind of problems under a limited computational budget.

Co-evolutionary and Elite learning-based bi-objective Poor and Rich Optimization algorithm for scheduling multiple workflows in the cloud

Cloud computing is a cost-effective environment for deploying large-scale scientific applications. However, multi-workflow scheduling has great challenge since users may request a series of applications with different Quality of Service (QoS) at the same time. In this paper, a Co-evolutionary and Elite learning-based bi-objective Poor and Rich Optimization algorithm (CE-PRO) is proposed for scheduling applications to minimize the makespan and cost of each workflow. First, an MPMO framework is combined with PRO to optimize two objectives by two populations, respectively for better balancing the search diversity and convergence speed, where each population is updated by an improved PRO, which adopts the middle-class sub-population and re-defines the update mechanism for rich individuals to enhance search diversity and reduce the possibility of falling into local optima. Second, to restrain each population focusing overly on its respective objective, a global information exchange pool is innovatively designed to save the non-dominated solutions ever found, which will be used back as the shared guiding solutions to foster inter-population communication and co-evolution during an evolutionary process. Third, a hybrid mutation-based Elite Enhancement Strategy (EES) is developed by introducing multiple scales of mutation operations into elite solutions alternatively and iteratively to exploit excellent individuals and explore more trade-off solutions. Extensive experiments are conducted on real world scientific workflows with different types and scales, and the experimental results demonstrate that in most cases, our proposed CE-PRO outperforms its peers in the number of obtained non-dominated solutions, and the solution diversity and quality as well. In particular, the dominance of CE-PRO is superior to its peers by at least 25.62%.

Cooperative coevolutionary surrogate ensemble-assisted differential evolution with efficient dual differential grouping for large-scale expensive optimization problems

This paper proposes a novel algorithm named surrogate ensemble assisted differential evolution with efficient dual differential grouping (SEADECC-EDDG) to deal with large-scale expensive optimization problems (LSEOPs) based on the CC framework. In the decomposition phase, our proposed EDDG inherits the framework of efficient recursive differential grouping (ERDG) and embeds the multiplicative interaction identification technique of Dual DG (DDG), which can detect the additive and multiplicative interactions simultaneously without extra fitness evaluation consumption. Inspired by RDG2 and RDG3, we design the adaptive determination threshold and further decompose relatively large-scale sub-components to alleviate the curse of dimensionality. In the optimization phase, the SEADE is adopted as the basic optimizer, where the global and the local surrogate model are constructed by generalized regression neural network (GRNN) with all historical samples and Gaussian process regression (GPR) with recent samples. Expected improvement (EI) infill sampling criterion cooperated with random search is employed to search elite solutions in the surrogate model. To evaluate the performance of our proposal, we implement comprehensive experiments on CEC2013 benchmark functions compared with state-of-the-art decomposition techniques. Experimental and statistical results show that our proposed EDDG is competitive with these advanced decomposition techniques, and the introduction of SEADE can accelerate the convergence of optimization significantly.

A two-stage preference driven multi-objective evolutionary algorithm for workflow scheduling in the Cloud

The workflow scheduling problem considered difficult in the Cloud becomes even more challenging when multiple scheduling criteria are used for optimization. It is much harder to maximize the conflicting interests of users, service providers and the environment, and to obtain “triple win” solutions. This paper presents a two-stage preference driven multi-objective evolutionary algorithm (tsp-MOEA) to address the workflow scheduling problem involving multiple roles. We formulate it as a multi-objective optimization problem with preferences for the first time by considering the special preferences of different participants in decision-making. In particular, a preference distance strategy is introduced in the first stage to speed up the arrival of solutions around the decision makers’ region of interest (ROI); and a special preference region ranking strategy is also designed to focus on searching in the ROI in the second stage. Moreover, the two-stage transition is completed adaptively, which can more fully find a variety of elite solutions. In addition, an elite learning strategy is adopted to guide the global evolution of the population to further enhance the quality of the solution. Extensive experiments demonstrate that the proposed tsp-MOEA approach outperforms recent state-of-the-art algorithms, and can provide significantly better solutions for scientific workflow scheduling in the Cloud.

Intelligent Path Planning of Mobile Robot Based on Genetic Algorithm

In this study, in order to deal with the path planning problems with genetic algorithm (GA) and improve its time efficiency, a new method combined with K-Nearest Neighbor (KNN) is proposed. GA is a well-known approach to figure out a path between two designated points while avoiding obstacles in the way. In traditional GA process, a set of solutions from the starting node to the destination are randomly generated in the beginning, which are called initial population. Although not every solution is feasible and the feasible ones may not be ideal, optimal path is likely to be obtained during the iterations. A new method is designed to reduce the number of iterations by constructing a dataset using traditional GA and selecting elite solutions as initial population when facing a new map. The selection criteria is the similarity between the distribution of obstacles and previous ones. Relevant experiments are organized to test the performance of the proposed method by comparing it with the traditional GA. According to the simulation results, the proposed method with elite initial population tends to converge more quickly.

DETDO: An adaptive hybrid dandelion optimizer for engineering optimization

Dandelion Optimizer (DO) is a recently proposed swarm intelligence algorithm that coincides with the process of finding the best reproduction site for dandelion seeds. Compared with the classical Meta-heuristic algorithms, DO exhibits strong competitiveness, but it also has some drawbacks. In this paper, we proposed an adaptive hybrid dandelion optimizer called DETDO by combining three strategies of adaptive tent chaotic mapping, differential evolution (DE) strategy, and adaptive t-distribution perturbation to address the shortcomings of weak DO development, easy to fall into local optimum and slow convergence speed. Firstly, the adaptive tent chaos mapping is used in the initialization phase to obtain a uniformly distributed high-quality initial population, which helps the algorithm to enter the correct search region quickly. Secondly, the DE strategy is introduced to increase the diversity of dandelion populations to avoid algorithm stagnation, which improves the exploitation capability and the accuracy of the optimal solution. Finally, adaptive t-distribution perturbation around the elite solution successfully balances the exploration and exploitation phases while improving the convergence speed through a reasonable conversion from Cauchy to Gaussian distribution. The proposed DETDO is compared with classical or advanced optimization algorithms on CEC2017 and CEC2019 test sets, and the experimental results and statistical analysis demonstrate that the algorithm has better optimization accuracy and speed. In addition, DETDO has obtained the best results in solving six real-world engineering design problems. Finally, DETDO is applied to two bar topology optimization cases. Under a series of complex constraints, DETDO produces a lighter bar structure than the current scheme. It further illustrates the effectiveness and applicability of DETDO in practical problems. The above results mean that DETDO with strong competitiveness will become a preferred swarm intelligence algorithm to cope with optimization problems.

Enhanced bare-bones particle swarm optimization based evolving deep neural networks

In this research, we propose a variant of the Bare-Bones Particle Swarm Optimization (BBPSO) algorithm for hyper-parameter selection and deep architecture generation for image, audio and video classification tasks. Since the search process of the original BBPSO model is guided by a single leader and the particles’ personal best experiences, there is a lack of interactions pertaining to the neighbouring elite solutions. To overcome this limitation, we propose a versatile search process for a modified BBPSO model that incorporates a number of effective components and operations. These include the neighbouring and global best signals, search actions with Cauchy/Levy scale factors, sub-dimension operations guided by the local and global elite solutions, and a Levy-driven local search mechanism. Moreover, root-finding algorithms are employed which use informative mathematical principles to estimate new root offspring for leader/particle enhancement. A reinforcement learning algorithm is subsequently used to identify the optimal sequential deployment of these numerical analysis methods to increase robustness. Several medical imaging data sets, i.e., ISIC 2017, PH2 and Dermofit skin lesion databases, the ALL-IDB2 microscopic blood image data set, the MURA musculoskeletal radiographic database, the CK + facial expression data set, as well as the Coswara respiratory audio data set and UCF101 video action data set, are employed for evaluation. The proposed BBPSO-optimized Convolutional Neural Network (CNN), bidirectional Long Short-Term Memory (BiLSTM) with attention mechanism, and CNN-BiLSTM models outperform those devised by other PSO and BBPSO variants, as well as state-of-the-art existing studies, significantly, for image, audio respiratory abnormality and realistic video action recognition.

Bi-preference linkage-driven artificial bee colony algorithm with multi-operator fusion

The artificial bee colony algorithm (ABC) struggles in handling complex optimization problems with high dimensions in light of its search operators’ strong exploration and weak exploitation properties. To tackle this situation, in this study, we propose a bi-preference linkage-driven ABC algorithm with multi-operator fusion, named BPLABC. BPLABC couples a preference-free stochastic search operator with a global best-guided search operator in the employed bee phase to maintain the population diversity while enhancing the population quality. During the onlooker bee phase, a tailored bi-type elite-guided exploitation mechanism is employed to regulate the exploitation intensity of the promising elite nectar sources selected via a new roulette selection probability calculation paradigm. To discourage the onlooker bees from slipping into local traps, after the scout bee phase, an auxiliary adversarial search operator is assembled to tug certain promising elite solutions away from the present pseudo-global best solution. To illustrate the effectiveness and efficiency of BPLABC, two sets of test suits consisting of 23 benchmark problems, 30 complex CEC2014 functions, and two real-world problems are picked for testing. Experimental results showed that BPLABC can achieve superior or equivalent performance to several representative ABC variants on the majority of the tested problems.