Multimodal Problems Research Articles

Wireless sensor networks-based adaptive differential evolution for multimodal optimization problems

In wireless sensor networks (WSN), we often detect the monitoring areas among different sensors so that the sensors can be switched on and off adaptively to save energy and extend their lifetime. Inspired by the principle of WSN, a WSN-based adaptive differential evolution (WSNADE) algorithm is proposed in this paper, together with a WSN-based adaptive niching technique (WANT) and two novel strategies called protection-based dual-scale mutation (PDM) strategy and multi-level reset (MLR) strategy, for solving multimodal optimization problems (MMOPs). In WANT, each individual is considered as a sensor with its monitoring area. If the monitoring areas of two individuals intersect, which means these two individuals monitor the similar area and should be partitioned into the same niche. In this way, WANT can adaptively form a niche for each individual, avoiding the sensitivity of niching parameters. Based on WANT, the PDM strategy is designed to select the appropriate mutation strategy for each individual. Besides, to save fitness evaluations (FEs) for exploring more promising areas, the MLR strategy is developed to store the promising individuals and reset the stagnant individuals. The experimental results on 20 multimodal benchmark test functions in CEC2015 multimodal competition show that the proposed WSNADE algorithm generally performs better than or at least comparable with other state-of-the-art multimodal algorithms, including the winner of the CEC2015 competition. Finally, WSNADE is applied to a real-world multimodal application in multiple competitive facilities location design (MCFLD) problem to illustrate its practical applicability.

Evolutionary Multimodal Multiobjective Optimization for Traveling Salesman Problems

Multimodal multiobjective optimization problems (MMOPs) are commonly seen in real-world applications. Many evolutionary algorithms have been proposed to solve continuous MMOPs. However, little effort has been made to solve combinatorial (or discrete) MMOPs. Searching for equivalent Pareto optimal solutions in the discrete decision space is challenging. Moreover, the true Pareto optimal solutions of a combinatorial MMOP are usually difficult to know, which has limited the development of its optimizer. In this paper, we first propose a test problem generator for multimodal multiobjective traveling salesman problems (MMTSPs). It can readily generate MMTSPs with known Pareto optimal solutions. Then we propose a novel evolutionary algorithm to solve MMTSPs. In our proposed algorithm, we develop two new edge assembly crossover operators, which are specialized in searching for superior solutions to MMTSPs. Moreover, the proposed algorithm uses a new environmental selection operator to maintain a good balance between the objective space diversity and decision space diversity. We compare our algorithm with five state-of-the-art designs. Experimental results convincingly show that our algorithm is powerful in solving MMTSPs.

A socio-economic and quality-oriented optimal fruit supply chain network design in a multi-market and multi-product environment: A real case study

This paper focuses on developing an optimal sustainable fruit Closed-Loop Supply Chain (CLSC). A novel multi-objective Mixed-Integer Linear Programming (MILP) model is suggested to formulate a multi-product, multi-market, multi-period, multi-level, multi-mode selling problem which aims to minimize cost and emissions and maximize the whole social segments’ responsiveness to fruit, vinegar, and compost. The model is solved by the LP-metric method and implemented in a real case in Iran. The findings indicate that achieving the highest level of responsiveness comes with a substantial cost for the network. However, this does not apply to environmental considerations. For decision-makers prioritizing sustainability, the proposed decision support system strongly advises against buying fruit from fruit cars. Due to the absence of positive impacts on the level of responsiveness, buying from fruit cars results in increased costs and emissions. For a cost- and environmentally-sensitive decision-maker, it is recommended to provide higher-quality fruits. Because the lower the quality of the fruit, leads to increased waste rates and emissions. Meeting increased vinegar demand, with its elevated costs and emissions, becomes justifiable only when the policymaker is actively seeking to achieve maximum responsiveness.

Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

An improved differential evolution algorithm for multi-modal multi-objective optimization.

Multi-modal multi-objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the Multi-modal multi-objective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non-dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain well-distributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.

Learning to disentangle and fuse for fine-grained multi-modality ship image retrieval

Multi-modality ship image retrieval aims to retrieve ship images from a large dataset, encompassing various modalities, when provided with a query ship image. One of the key challenges is addressing intra-modality variations and cross-modality discrepancies resulting from complex image content and different types of imaging systems. Current multi-modality retrieval methods primarily focus on extracting heterogeneous features from diverse modalities and mapping them into a shared feature space. However, these methods fail to determine the meaningfulness of the extracted features for retrieval tasks, as the features extracted across different modalities exhibit highly complex interactions. To overcome this limitation, we propose a novel framework, dubbed Disentangled Fusion Network (DFN), to decompose ship images into attribute and identity features, capturing modality-specific details and facilitating ship identification. This is achieved through an image disentanglement and fusion module, separating features across different modalities and converting the challenging multi-modality retrieval problem into a more manageable single-modality problem. To enable fine-grained retrieval, a region mining module identifies discriminative areas within ship images. The training process utilizes a bilevel optimization strategy to learn parameters, optimizing both image fusion and retrieval. Extensive experiments conducted on a publicly available multi-modality ship image dataset demonstrate the superior performance of the proposed DFN in image fusion and retrieval tasks.

Bayesian hybrid-kernel machine-learning-assisted sensitivity analysis and sensitivity-relevant inverse modeling for groundwater DNAPL contamination

Accurate source characterization and transport parameter estimation is important when seeking to predict the spatiotemporal distribution of dense non-aqueous phase liquid (DNAPL) contaminants in groundwater. However, this is a complex multimodal search problem prone to equifinality and premature convergence, which leads to considerable error. To address this, a sensitivity-relevant dynamic swarm intelligence (SRD-SI) algorithm embedded in a homotopy-variation mechanism is proposed in the present study to rationally balance the inversion processes of sensitivity-varied source characteristics and DNAPL transport parameters. In this approach, global optima are progressively approached in conjunction with the homotopy variation of the search space. Furthermore, to avoid computationally expensive numerical model repetition during the sensitivity analysis and inverse iterations, a Bayesian-based optimization framework that combines multiple kernel functions in a kernel extreme learning machine (KELM) model is designed considering the complex site conditions and statistical characteristics of the input variables, thus creating the Bayesian hybrid KELM (BHK-ELM) model for the reliable surrogate modeling of numerical DNAPL-transport simulations. The results show that the BHK-ELM model recognizes and effectively reconstructs the complex input − output mapping of the numerical model by increasing the determination coefficient R2 to 0.9988 while improving the computational efficiency approximately 4500-fold. Because source characteristics and boundary conditions are far more sensitive than transport parameters to the contaminant distribution, conventional inverse modeling methods struggle to accurately identify these transport parameters. In contrast, the proposed inverse modeling system combining sensitivity analysis, swarm intelligence, and homotopy variation is more stable and provides significantly more accurate estimations for all unknown variables. Compared with the traditional SI algorithm, the homotopy-variation SRD-SI reduced the maximum inversion relative error from 46.22 % to 9.53 %, while the mean inversion relative error was reduced from 11.09 % to 3.90 %.

Redesigning large-scale multimodal transit networks with shared autonomous mobility services

This study addresses a large-scale multimodal transit network design problem, with Shared Autonomous Mobility Services (SAMS) as both transit feeders and an origin-to-destination mode. The framework captures spatial demand and modal characteristics, considers intermodal transfers and express services, determines transit infrastructure investment and path flows, and generates transit routes. A system-optimal multimodal transit network is designed with minimum total door-to-door generalized costs of users and operators, satisfying transit origin–destination demand within a pre-set infrastructure budget. Firstly, the geography, demand, and modes in each zone are characterized with continuous approximation. The decisions of network link investment and multimodal path flows in zonal connection optimization are formulated as a minimum-cost multi-commodity network flow (MCNF) problem and solved efficiently with a mixed-integer linear programming (MILP) solver. Subsequently, the route generation problem is solved by expanding the MCNF formulation to minimize intramodal transfers. The model is illustrated through a set of experiments with the Chicago network comprised of 50 zones and seven modes, under three scenarios. The computational results present savings in traveler journey time and operator cost demonstrating the potential benefits of collaboration between multimodal transit systems and SAMS.

IMDE-UGAN: Improved Memetic Direction Exploitation Optimized U-Net Generative Adversarial Network for Classification of Diabetic Retinopathy

The most important human organ is the eye which is essential for the processing and absorbing of external visual information. Diabetic retinopathy (DR) is the primary factor contributing to the global increase in blindness. To maintain eye health, people have been paying lots of attention to the problem. However, there are still lots of people who have eye problems all around the world. Thus, we proposed the Improved Memetic Direction Exploitation Optimized U-Net Generative Adversarial Network (IMDE-optimized U-Net GAN) model for DR grading. Also, for Multimodal Optimization Problems (MMOPs), a Niching Competition-based Memetic Direction Exploitation (NC-MDE) method is proposed with adaptive local search operations. Additionally, SPatially-ADaptivE (SPADE)-based conditional GANs are used to segment DR. The U-Net GAN model is used to categorize DR images. In the discriminator design, the standard classification network is modified to create the decoder-encoder network known as U-Net. The complete network error of the U-Net GAN architecture is modeled using the IMDE archives. The various performance metrics are used in the method for testing the proposed including accuracy, specificity, sensitivity, and ROC curve. As a result, the proposed method achieves 98.89% of accuracy, 98.54% for sensitivity, and specificity, it achieves 98.67%.

Maximizing the Supply Chain Profit in Multimodal Transportation Problem with Transfer Part using Two-Echelon Genetic Algorithm

Multimodal transportation is a highly effective method for optimizing deadlines and reducing inventory costs, both of which are crucial in a supply chain environment. This study employs a mathematical programming model to optimize the supply chain profit for multimodal transportation distribution within a specified time window. The model considers five factors, such as production cost, transportation cost, transport time, penalty cost, and sales price. Additionally, a Two-Echelon Genetic Algorithm (TEGA) is proposed to solve the optimization problem, and a numerical example is provided to validate the model and algorithm. The study compares the performance of the proposed algorithm with the exact solution from a previous study, presents implementation details and numerical experiment results, and analyses the findings. The results demonstrate the efficiency and robustness of the algorithm, making it a significant contribution to transportation planning for freight transportation and supply chain management.

A Bi-Objective Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multimodal multi-objective optimization problems (MMOPs) possess multiple Pareto optimal sets corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple Pareto optimal sets. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of non-dominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problemsin real-world applications.

A Surrogate-Assisted Evolutionary Algorithm for Seeking Multiple Solutions of Expensive Multimodal Optimization Problems

A Surrogate-Assisted Evolutionary Algorithm for Seeking Multiple Solutions of Expensive Multimodal Optimization Problems

VL-Few: Vision Language Alignment for Multimodal Few-Shot Meta Learning

Complex tasks in the real world involve different modal models, such as visual question answering (VQA). However, traditional multimodal learning requires a large amount of aligned data, such as image text pairs, and constructing a large amount of training data is a challenge for multimodal learning. Therefore, we propose VL-Few, which is a simple and effective method to solve the multimodal few-shot problem. VL-Few (1) proposes the modal alignment, which aligns visual features into language space through a lightweight model network and improves the multimodal understanding ability of the model; (2) adopts few-shot meta learning in the multimodal problem, which constructs a few-shot meta task pool to improve the generalization ability of the model; (3) proposes semantic alignment to enhance the semantic understanding ability of the model for the task, context, and demonstration; (4) proposes task alignment that constructs training data into the target task form and improves the task understanding ability of the model; (5) proposes generation alignment, which adopts the token-level training and multitask fusion loss to improve the generation ability of the model. Our experimental results show the effectiveness of VL-Few for multimodal few-shot problems.

Multimodal network path optimization based on a two‐stage algorithm in the perspective of sustainable transport development

AbstractThe environmental issues brought on by carbon emissions from transport have risen to prominence in recent years. More and more academics are using the multi‐objective path optimization method to solve the multimodal optimization problem from the standpoint of sustainable development in order to address the environmental issues brought on by the transport process. The research proposes a two‐stage method to handle multi‐objective optimization convergence and simplify multimodal transport path optimization. In the first stage, a fuzzy C clustering model is established, and based on the clustering results, the multimodal transport network nodes are identified. In the second stage, a multimodal transport multi‐objective path optimization model is established, and the optimal path is solved using a genetic algorithm. The research method was applied in the Bohai Rim region. Results indicated that the fuzzy C‐clustering method and the genetic method were able to select the optimal node city, thus solving the actual site selection problem of multimodal transportation networks. Using the FCM model, the 86 city nodes were categorized into four types, leading to the establishment of the most proficient multimodal transportation network in the Bohai Rim region. Using a genetic algorithm for optimization, a stable state is reached after 25 iterations. In the validation experiment on path optimization, the cost was reduced by 47.12% compared to the minimum single objective time, and transportation carbon emissions saw a reduction of 28.23%. Similarly, compared to the lowest target for transportation carbon emissions, the cost was reduced by 39.48% and the time was reduced by 38.12%. Compared to the lowest target for transportation carbon emissions, the time was reduced by 32.02% and the carbon emissions were reduced by 19.23%. Notably, the transportation multi‐objective path optimization model showed significant improvement compared to the single‐target model. The research method has been proven to be superior, and can offer the most optimal transportation route guidance for participants in multimodal transportation. Furthermore, it can effectively tackle the issue of node selection convergence and multi‐objective optimization, while also serving as a valuable source of data to support the theoretical advancement of multimodal transportation network path optimization.

Two-stage evolutionary algorithm with fuzzy preference indicator for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are multi-objective optimization problems (MOPs) involving multiple equivalent global or local Pareto optimal solution sets (PSs). For decision-makers, not only the global optimal solution sets need to be found, but also the value of local optimal solution sets cannot be ignored. However, most multimodal multi-objective evolutionary algorithms (MMOEAs) tend to select solutions with better convergence, and it is difficult to obtain the global PSs and local PSs at the same time. Therefore, we propose a fuzzy preference indicator-based two-stage evolutionary algorithm (FPITSEA) in this paper. To evaluate more comprehensively the potential of each solution in the population for locating the global and local PS during the evolutionary process, a fuzzy preference indicator is designed in FPITSEA. The fuzzy preference indicator is used to guide the evolution of the population in the first stage to find the global and local Pareto optimal regions. Subsequently, an independent evolution strategy is implemented in the second stage to distinguish different PSs as accurately as possible while also ensuring the convergence quality of the solution set. In addition, an improved distance-based subset selection method is proposed, aiming to simultaneously improve the distribution of the solution set in the decision space and objective space. Experimental results on several test sets of MMOPs show the advantages of FPITSEA over several state-of-the-art MMOEAs.

Multimodal transportation routing optimization based on multi-objective Q-learning under time uncertainty

Multimodal transportation is a modern way of cargo transportation. With the increasing demand for cargo transportation, higher requirements are being placed on multimodal transportation multi-objective routing optimization. In multimodal transportation multi-objective routing optimization, in response to the limitations of classical algorithms in solving large-scale problems with multiple nodes and modes of transport, the limitations of directed transportation networks in the application, and the uncertainty of transport time, this paper proposes an optimization framework based on multi-objective weighted sum Q-learning, combined with the proposed undirected multiple-node network, and characterizes the uncertainty of time with a positively skewed distribution. The undirected multiple-node transportation network can better simulate cargo transportation and characterize transfer information, facilitate the modification of origin and destination, and avoid suboptimal solutions due to the manual setting of wrong route directions. The network is combined with weighted sum Q-learning to solve multimodal transportation multi-objective routing optimization problems faster and better. When modeling the uncertainty of transport time, a positively skewed distribution is used. The three objectives of transport cost, carbon emission cost, and transport time were studied and compared with PSO, GA, AFO, NSGA-II, and MOPSO. The experimental results show that compared with PSO, GA, and AFO using a directed transportation network, the proposed method has a significant improvement in optimization results and running time, and the running time is shortened by 26 times. The proposed method can better solve the boundary of the Pareto front and dominate the partial solutions of NSGA-II and MOPSO. The effect of time uncertainty on the performance of the algorithm is more significant in transport orders with high time weight. With the increase in uncertainty, the reliability of the route decreases. The effectiveness of the proposed method is verified.

A particle swarm optimization algorithm based on modified crowding distance for multimodal multi-objective problems

Multimodal multi-objective optimization problems (MMOPs) are commonly encountered in practice. The difficulty in solving MMOPs is obtaining all of the Pareto optimal sets without degrading the performance of the Pareto optimal front. To address this challenge, this study proposes a particle swarm optimization algorithm based on modified crowding distance (MOPSO_MCD). In MOPSO_MCD, a modified method for calculating the crowding distance (MCD) is devised, which allows for a more comprehensive assessment of the crowding relationship between individuals in the decision space and the objective space. Moreover, a cosine similarity-based elite selection mechanism is designed to identify the neighborhood optimal individuals of the individuals in the population and improve the decision space diversity. Additionally, an offspring competition mechanism is proposed to keep the population from trapping in the local optimum and enhance the global search ability of the MOPSO_MCD algorithm. Experimental results and statistical analysis show that MOPSO_MCD performs better than the other comparison algorithms on sixteen test functions and a map-based practical problem.

Enhancing differential evolution through a modified mutation strategy for unimodal and multimodal problem optimization

<p>Amid a lot of evolutionary methods (EMs), differential evolution (DE) is broadly used for various optimization issues. Though, it has rare shortcomings such as slow convergence, stagnation etc. Likewise, mutation and its control factor choice for DE is extremely inspiring for enhanced optimization. To increase the exploration competence of DE, a modified-DE (M-DE) is advised in this paper. It implemented a new mutation system, thru the perception of particle swarm optimization, to further trade off the population diversity. Meanwhile, centered on time-varying structure, new mutant control parameters incorporated with the suggested mutation scheme, to escaping local optima and keep evolving. Using the features of memory and robustly altered control parameters, exploitation and exploration ability of M-DE is well-adjusted. Also, admitted features of M-DE algorithm follows to speeding up convergence significantly. Finally, to verify the effectiveness of M-DE, groups of assessments have been piloted on six unimodal and seven multimodal benchmark suites. Performance of M-DE compared with different peer DE algorithms. According the investigational results, efficiency of the suggested M-DE technique has been confirmed.</p>

A reinforcement learning-based neighborhood search operator for multi-modal optimization and its applications

In this paper, a reinforcement learning-based neighborhood search operator (RLNS) is proposed for multi-modal optimization problems where the main novelties lie in the reinforcement learning-based neighborhood range selection strategy, the neighborhood subpopulation generation strategy and the local vector encirclement model. The reinforcement learning-based neighborhood range selection strategy is proposed to dynamically adjust the subpopulation size to address the issue of too many parameters to be adjusted in the multi-modal optimization algorithm based on the niching methods, while the neighborhood subpopulation generation strategy and the local vector encirclement model are designed with the hope of enhancing the individual’s ability to local exploitation to obtain more accurate solutions. To verify the effectiveness of the proposed RLNS, SSA-RLNS, PSO-RLNS and EO-RLNS are proposed by integrating the proposed RLNS with the existing sparrow search algorithm, particle swarm optimization and equilibrium optimizer. The performances of the proposed SSA-RLNS, PSO-RLNS, EO-RLNS and existing multi-modal optimization algorithms are tested in CEC2015 multi-niche benchmark functions. The experimental results show that the SSA-RLNS, PSO-RLNS and EO-RLNS could locate multiple global optimal solutions with satisfactory accuracy, which illustrate that the proposed RLNS could be successfully used to deal with multi-modal optimization problems by integrating with common population-based optimization algorithms. Finally, the SSA-RLNS is successfully applied in the inverse kinematics of robot manipulator.