Adaptive Penalty Research Articles

An Improved NSGA-III with a Comprehensive Adaptive Penalty Scheme for Many-Objective Optimization

Pareto dominance-based algorithms face a significant challenge in handling many-objective optimization problems. As the number of objectives increases, the sharp rise in non-dominated individuals makes it challenging for the algorithm to differentiate their quality, resulting in a loss of selection pressure. The application of the penalty-based boundary intersection (PBI) method can balance convergence and diversity in algorithms. The PBI method guides the evolution of individuals by integrating the parallel and perpendicular distances between individuals and reference vectors, where the penalty factor is crucial for balancing these two distances and significantly affects algorithm performance. Therefore, a comprehensive adaptive penalty scheme was proposed and applied to NSGA-III, named caps-NSGA-III, to achieve balance and symmetry between convergence and diversity. Initially, each reference vector’s penalty factor is computed based on its own characteristic. Then, during the iteration process, the penalty factor is adaptively adjusted according to the evolutionary state of the individuals associated with the corresponding reference vector. Finally, a monitoring strategy is designed to oversee the penalty factor, ensuring that adaptive adjustments align with the algorithm’s needs at different stages. Through a comparison involving benchmark experiments and two real-world problems, the competitiveness of caps-NSGA-III was demonstrated.

Trust-aware and improved density peaks clustering algorithm for fast and secure models in wireless sensor networks

Many trust-based models for wireless sensor networks do not account for trust attacks, which are destructive phenomena that undermine the security and reliability of these models. Therefore, a trust-based fast security model fused with an improved density peaks clustering algorithm (TFSM-DPC) is proposed to quickly identify trust attacks in this paper. First, when calculating direct trust values, TFSM-DPC designs the adaptive penalty factors based on the state of received and sent packets and behaviors, and introduces the volatilization factors to reduce the effect of historical trust values. Second, TFSM-DPC improved density peaks clustering (DPC) algorithm to evaluate the trustworthiness of each recommendation value, thus filtering malicious recommendations before calculating the indirect trust values. Moreover, to filter two types of recommendations, the improved DPC algorithm incorporates artificial benchmark data along with trust values recommended by neighbors as input data. Finally, based on the relationship between direct trust and indirect trust, a secure formula for calculate the comprehensive trust is designed. Therefore, the proposed TFSM-DPC can improve the accuracy of trust evaluation and speed up the identification of malicious nodes. Simulation results show that TFSM-DPC can effectively identify on-off, bad-mouth and collusion attacks, and improve the speed of excluding malicious nodes from the network, compared to other trust-based algorithms.

A Multiple Targets ISAR Imaging Method with Removal of Micro-Motion Connection Based on Joint Constraints

Combining multiple data sources, Digital Earth is an integrated observation platform based on air–space–ground–sea monitoring systems. Among these data sources, the Inverse Synthetic Aperture Radar (ISAR) is a crucial observation method. ISAR is typically utilized to monitor both military and civilian ships due to its all-day and all-weather superiority. However, in complex scenarios, multiple targets may exist within the same radar antenna beam, resulting in severe defocusing due to different motion conditions. Therefore, this paper proposes a multiple-target ISAR imaging method with the removal of micro-motion connections based on the integration of joint constraints. The fully motion-compensated targets exhibit low rank and local similarity in the high-resolution range profile (HRRP) domain, while the micro-motion components possess sparsity. Additionally, targets display sparsity in the image domain. Inspired by this, we formulate a novel optimization by promoting the low-rank, the Laplacian, and the sparsity constraints of targets and the sparsity constraints of the micro-motion components. This optimization problem is solved by the linearized alternative direction method with adaptive penalty (LADMAP). Furthermore, the different motions of various targets degrade their inherent characteristics. Therefore, we integrate motion compensation transformation into the optimization, accordingly achieving the separation of rigid bodies and the micro-motion components of different targets. Experiments based on simulated data demonstrate the effectiveness of the proposed method.

Robot error compensation strategy based on error sensitivity

Abstract Due to the errors in manufacturing and assembly, there are differences between the actual model and the theoretical model of the robot, which affects the positioning accuracy of the robot end-effector. In order to improve the accuracy of robot end-effector position, a robot error compensation strategy based on error sensitivity is proposed.Firstly, the robot kinematic model is established by Denavit-Hartenberg (D-H) method, and the sensitivity of end-effector position error is analyzed. According to the influence degree of different kinematic parameters on the robot end-effector position accuracy in the whole workspace, different weights are given to different kinematic parameters. {\color{red}Secondly, the kinematic error model is established, and the redundancy of the error parameter matrix is analyzed to obtain an independent error model. Thirdly, based on the error sensitivity analysis, a Weighted Levenberg-Marquard (WLM) algorithm with adaptive penalty factor is proposed, and the kinematic parameters are iteratively identified.} Finally, an error compensation experiment is carried out by using a universal serial six-degree-of-freedom robot. The experimental results show that the maximum error, mean absolute error and root mean square error of the position error on the test set are reduced by 90.75%, 89.86% and 95.64% respectively. The research in this paper provides a theoretical basis for robot end error compensation.

Generalized Nash Equilibrium Seeking for Noncooperative Game With Different Monotonicities by Adaptive Neurodynamic Algorithm.

This article proposes a novel adaptive neurodynamic algorithm (ANA) to seek generalized Nash equilibrium (GNE) of the noncooperative constrained game with different monotone conditions. In the ANA, the adaptive penalty term, which acts as trajectory-dependent penalty parameters, evolves based on the degree of constraints violation until the trajectory enters the action set of noncooperative game. It is shown that the trajectory of the ANA enters the action set in finite time benefited from the adaptive penalty term. Moreover, it is proven that the trajectory exponentially (or polynomially) converges to the unique GNE when the pseudo-gradient of cost function in noncooperative game satisfies strong (or "generalized" strong) monotonicity. To the best of our knowledge, this is the first time to study the polynomial convergence of GNE seeking algorithm. Furthermore, when the pseudo-gradient mentioned above satisfies monotonicity in general, based on Tikhonov regularization method, a new ANA for finding its ε -generalized Nash equilibrium ( ε -GNE) is proposed, and the related exponential convergence of the algorithm is established. Finally, the river basin pollution game and 5G base station location game are given as examples to showcase the algorithm's effectiveness.

Exploring interpretable evolutionary optimization via significance of each constraint and population diversity

Evolutionary algorithms (EAs) have been widely employed to solve complex constrained optimization problems (COPs). However, numerous EAs treat constraints as a collective black box, employing a uniform processing technique for all constraints. Generally, there exists variability in the significance of each constraint within COPs. To address this issue, this paper is the first attempt to investigate the significance of each constraint spontaneously during the evolution process, and then proposes a co-directed evolutionary algorithm (CdEA-SCPD) for exploring interpretable COPs. First, CdEA-SCPD develops an adaptive penalty function designed to assign different weights to constraints based on their violation severity, thereby varying the significance of each constraint to enhance interpretability and facilitate the algorithm to converge more rapidly toward the global optimum. In addition, a dynamic archiving strategy and a shared replacement mechanism are developed to improve the population diversity of CdEA-SCPD. Extensive experiments on benchmark functions from IEEE CEC2006, CEC2010, and CEC2017 and three engineering problems demonstrate the superiority of the proposed CdEA-SCPD compared to existing competitive EAs. Specifically, on the benchmark functions from IEEE CEC2010, the proposed method yields ρ values lower than 0.05 in the multiple-problem Wilcoxon's signed rank test and ranks first in the Friedman's test. Furthermore, ablation analysis and parameter analysis have demonstrated the beneficial effects of the proposed strategies.

CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

A smoothing approximation-based adaptive neurodynamic approach for nonsmooth resource allocation problem

In this paper, a smoothing approximation-based adaptive neurodynamic approach is proposed for a nonsmooth resource allocation problem (NRAP) with multiple constraints. The smoothing approximation method is combined with multi-agent systems to avoid the introduction of set-valued subgradient terms, thereby facilitating the practical implementation of the neurodynamic approach. In addition, using the adaptive penalty technique, private inequality constraints are processed, which eliminates the need for additional quantitative estimation of penalty parameters and significantly reduces the computational cost. Moreover, to reduce the impact of smoothing approximation on the convergence of the neurodynamic approach, time-varying control parameters are introduced. Due to the parallel computing characteristics of multi-agent systems, the neurodynamic approach proposed in this paper is completely distributed. Theoretical proof shows that the state solution of the neurodynamic approach converges to the optimal solution of NRAP. Finally, two application examples are used to validate the feasibility of the neurodynamic approach.

Adaptive Constraint Penalty-Based Multiobjective Operation Optimization of an Industrial Dynamic System With Complex Multiconstraint.

Aiming at the operation optimization of the wastewater treatment process (WWTP) with nonstationary time-varying dynamics and complex multiconstraint, this article proposes a novel adaptive constraint penalty decomposed multiobjective evolutionary algorithm with synthetical distance (SD)-based cross-generation crossover. First, the concept of spatial SD is presented to comprehensively evaluate the similarity of individual solutions from two aspects of distance and angle, and the individual information between two adjacent generations is used to enhance the diversity of individuals and accelerate the convergence of the algorithm. Second, aiming at the complex multiconstraint during the operation optimization of WWTP, an adaptive penalty algorithm is further adopted to punish the individual solutions that violate the constraints, so as to improve the handling efficiency and success rate of constraints. Furthermore, in view of the time-varying dynamics of actual WWTP, a recursive bilinear subspace identification method based on sliding window is adopted to establish the optimization models as well as the constraint models with self-learning parameter, which provides accurate model guarantee for high-performance multiobjective operation optimization. Finally, the effectiveness, superiority, and practicability of the proposed method are verified through test function experiments as well as operation optimization control experiments of WWTP.

A co-evolutionary algorithm with adaptive penalty function for constrained optimization

Several constrained optimization problems have been adequately solved over the years thanks to the advances in the area of metaheuristics. Nevertheless, the question as to which search logic performs better on constrained optimization often arises. In this paper, we present Dual Search Optimization (DSO), a co-evolutionary algorithm that includes an adaptive penalty function to handle constrained problems. Compared to other self-adaptive metaheuristics, one of the main advantages of DSO is that it is able auto-construct its own perturbation logics, i.e., the ways solutions are modified to create new ones during the optimization process. This is accomplished by co-evolving the solutions (encoded as vectors of integer/real values) and perturbation strategies (encoded as Genetic Programming trees), in order to adapt the search to the problem. In addition to that, the adaptive penalty function allows the algorithm to handle constraints very effectively, yet with a minor additional algorithmic overhead. We compare DSO with several algorithms from the state-of-the-art on two sets of problems, namely: (1) seven well-known constrained engineering design problems and (2) the CEC 2017 benchmark for constrained optimization. Our results show that DSO can achieve state-of-the-art performances, being capable to automatically adjust its behavior to the problem at hand.

Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees

The growing time-series data make it possible to glimpse the hidden dynamics in various fields. However, developing a computational toolbox with high interpretability to unveil the interaction dynamics from data remains a crucial challenge. Here, we propose a new computational approach called automated dynamical model inference based on expression trees (ADMIET), in which the machine learning algorithm, the numerical integration of ordinary differential equations and the interpretability from prior knowledge are embedded into the symbolic learning scheme to establish a general framework for revealing the hidden dynamics in time-series data. ADMIET takes full advantage of both machine learning algorithm and expression tree. Firstly, we translate the prior knowledge into constraints on the structure of expression tree, reducing the search space and enhancing the interpretability. Secondly, we utilize the proposed adaptive penalty function to ensure the convergence of gradient descent algorithm and the selection of the symbols. Compared to gene expression programming, ADMIET exhibits its remarkable capability in function fitting with higher accuracy and broader applicability. Moreover, ADMIET can better fit parameters in nonlinear forms compared to regression methods. Furthermore, we apply ADMIET to two typical biological systems and one real data with different prior knowledge to infer the dynamical equations. The results indicate that ADMIET can not only discover the interaction relationships but also provide accurate estimates of the parameters in the equations. These results demonstrate ADMIET’s superiority in revealing interpretable dynamics from time-series biological data.

A CFD-DEM investigation into hydraulic transport and retardation response characteristics of drainage pipeline siltation using intelligent model

Siltation of drainage pipelines is a major disaster-causing factor in urban flooding. Owing to critical bed shear stress and the possibility of settlement at the bottom of pipes, there are significant nonlinear differences in the hydraulic transport and retardation response characteristics of siltation particles under different initial flow velocities, siltation degrees, and siltation lengths. Studies on siltation in drainage pipelines lack a comprehensive understanding of the intricate coupling dynamics between siltation particles and water flow, and the regularity governing the siltation transport behaviour under varying water flow conditions remains unclear. To solve these problems, this study constructs computational fluid dynamics and discrete element (CFD-DEM) coupling method and adaptive penalty model for pipeline deposition based on probabilistic settlement function, adaptive genetic algorithm, and bidirectional long short-term memory neural network (PSF-AGA-BLSTM). A three-dimensional transient hydraulic model of pipeline siltation was adopted to clarify the critical bed shear stress of the silt particles, after which an adaptive genetic algorithm with a probability settlement function as fitness was constructed to generate a numerous silt particle sample sets with settlement result labels. Adaptive genetic algorithms were combined with bidirectional long short-term memory neural networks to establish a spatiotemporal adaptive penalisation mechanism for pipeline silt particle transport. The simulation model based on PSF-AGA-BLSTM and CFD-DEM was analysed using simulation and scale tests and was found to have strong robustness and reliability. The results showed that the effects of siltation degree, flow rate, and siltation length on the transport of silt particles were all non-negligible; when the siltation degree exceeded 0.2, the siltation degree had a more significant effect on particle transport than siltation length and flow rate. The transport of silt particles occurred in two phases, rapid growth and steady growth under erosion by water flow. The rate of change in silt length accounted for up to 45% of the reason for silt nudging and silt spreading. The study clarified the hydraulic transport law of silt particles and analyzed the effect of different influencing factors. These efforts provide technical support for subsequent pipe cleaning and maintenance as well as flood prevention and mitigation.

A Semi-Supervised Adaptive Matrix Machine Approach for Fault Diagnosis in Railway Switch Machine.

The switch machine, an essential element of railway infrastructure, is crucial in maintaining the safety of railway operations. Traditional methods for fault diagnosis are constrained by their dependence on extensive labeled datasets. Semi-supervised learning (SSL), although a promising solution to the scarcity of samples, faces challenges such as the imbalance of pseudo-labels and inadequate data representation. In response, this paper presents the Semi-Supervised Adaptive Matrix Machine (SAMM) model, designed for the fault diagnosis of switch machine. SAMM amalgamates semi-supervised learning with adaptive technologies, leveraging adaptive low-rank regularizer to discern the fundamental links between the rows and columns of matrix data and applying adaptive penalty items to correct imbalances across sample categories. This model methodically enlarges its labeled dataset using probabilistic outputs and semi-supervised, automatically adjusting parameters to accommodate diverse data distributions and structural nuances. The SAMM model's optimization process employs the alternating direction method of multipliers (ADMM) to identify solutions efficiently. Experimental evidence from a dataset containing current signals from switch machines indicates that SAMM outperforms existing baseline models, demonstrating its exceptional status diagnostic capabilities in situations where labeled samples are scarce. Consequently, SAMM offers an innovative and effective approach to semi-supervised classification tasks involving matrix data.

Optimization and scheduling scheme of park-integrated energy system based on multi-objective Beluga Whale Algorithm

To improve the consumption rate of renewable energy and ensure the stability of power and heat supply within the industrial park, a park-integrated energy system (PIES), which incorporates electric heating equipment, energy storage devices, and multiple micro sources, is established. Based on the established PIES, a price-based demand response (PDR) mechanism is introduced to establish a multi-objective optimization and scheduling model with two time scales: day-ahead scheduling and intra-day scheduling, aiming to minimize the impact on the main grid and ensure the flexibility of system operation and real-time scheduling. With the objectives of minimizing operating costs and maximizing environmental benefits for PIES, a hybrid algorithm named Non-Dominated Sorting Beluga Whale Optimization (NSBWO), which combines the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and the Beluga Whale Optimization (BWO) algorithm is proposed to solve the optimization problem of the model. Simultaneously, an adaptive penalty function is introduced in the algorithm to handle constraint problems in optimization and additional penalty term for wind and solar curtailment is included within the constraints to improve the consumption rate of sustainable energy. The proposed NSBWO algorithm exhibits more robust search capabilities and faster convergence speed than the NSGA-II and MOPSO algorithm. Simulation results show that the proposed NSBWO algorithm can achieve low-carbon economic scheduling of the system in both long-term and short-term time scales and improve renewable energy consumption. Due to its flexibility, intra-day scheduling has lower operating costs than day-ahead scheduling.

Adaptive knowledge transfer-based particle swarm optimization for constrained multitask optimization

Constrained multitask optimization (CMTO) problems are frequently encountered in practical applications. However, since the feasible regions of different tasks are difficult to match under constraints, it is hard to obtain and transfer effective knowledge among different tasks, resulting in poor convergence performance. To address this issue, a constrained multitask particle swarm optimization algorithm with knowledge transfer-based adaptive penalty function (CMTPSO-APF) is proposed to improve the convergence performance. The main contributions of CMTPSO-APF are three-fold. First, a dynamic particle topology is designed to improve the neighborhood similarity for different tasks with constrained conditions. Then, the particles with similar spatial structures can facilitate the knowledge transfer between different tasks. Second, a covariance matrix learning mechanism is proposed to obtain valid knowledge with constrained conditions. Then, the proposed method can promote the population to move in the direction of the optimal solution. Third, a knowledge transfer-based adaptive penalty function for constrained multitask optimization is designed to achieve the dynamical change of penalty factor according to the evolution state. Then, the adaptive penalty function can promote the transfer of effective knowledge and improve the convergence. Finally, some simulation experiments are carried out on the CMTO benchmark test suites and the practical application of the wastewater treatment process. The results indicate that CMTPSO-APF can improve the convergence performance.

Risk-averse distributed optimization for integrated electricity-gas systems considering uncertainties of Wind-PV and power-to-gas

The uncertainties of wind power and photovoltaic (Wind-PV) systems pose a threat to the steady functioning of integrated electricity-gas systems and restrict their effective consumption. In this case, an optimal operation model considering the cost risk of Wind-PV uncertainties is proposed. Firstly, the cost risk of uncertainties in typical scenarios is measured by conditional value at risk (CVaR). Secondly, considering that the power system and the natural gas system as different stakeholders have barriers in information exchange, a distributed optimization operation model is established, and the uncertainty of the conversion efficiency of the coupling unit from Power-to-Gas (P2G) is considered. Then, the integrated electricity-gas systems are decoupled through consistency constraints, and the model is solved by an algorithm framework based on adaptive penalty ADMM. This work analyzed the impact of uncertainty and CVaR parameters on optimized operation, and discussed the performance of related distributed algorithms. The following conclusions were drawn: 1) the proposed model reduces costs by 1.72% and can measure the operation risk caused by uncertainty factors, which provide guidance for decision makers; 2) the total cost will increase by 3.9% when the uncertainty factor reaches the preset maximum value, which demonstrates that the uncertainty of conversion efficiency should be controlled to reduce the operation cost of P2G; 3) As the convergence accuracy gradually improves, the proposed method is easier to converge and converges faster.

P2BPO: Permeable Penalty Barrier-Based Policy Optimization for Safe RL

Safe Reinforcement Learning (SRL) algorithms aim to learn a policy that maximizes the reward while satisfying the safety constraints. One of the challenges in SRL is that it is often difficult to balance the two objectives of reward maximization and safety constraint satisfaction. Existing algorithms utilize constraint optimization techniques like penalty-based, barrier penalty-based, and Lagrangian-based dual or primal policy optimizations methods. However, they suffer from training oscillations and approximation errors, which impact the overall learning objectives. This paper proposes the Permeable Penalty Barrier-based Policy Optimization (P2BPO) algorithm that addresses this issue by allowing a small fraction of penalty beyond the penalty barrier, and a parameter is used to control this permeability. In addition, an adaptive penalty parameter is used instead of a constant one, which is initialized with a low value and increased gradually as the agent violates the safety constraints. We have also provided a theoretical proof of the proposed method's performance guarantee bound, which ensures that P2BPO can learn a policy satisfying the safety constraints with high probability while achieving a higher expected reward. Furthermore, we compare P2BPO with other SRL algorithms on various SRL tasks and demonstrate that it achieves better rewards while adhering to the constraints.

Distributed Voltage Reactive Power Control of Distribution Network Considering the Coordination Between DPV and SVC

With the increasing permeability rate of DPV in the distribution network, the safe and economic operation of the distribution network is faced with many challenges, among which the problem of voltage exceeding the limit must be solved urgently. A method for distributed voltage reactive power control, which involves coordinating DPV and SVC, is suggested to enhance the voltage regulation capacity in high-permeability distribution networks. Firstly, considering the limited reactive power regulation capacity of DPV, a coordinated control strategy is proposed to enable SVC when the reactive power capacity of DPV is insufficient. Secondly, a voltage-reactive power control model for distribution networks is established, with a focus on minimizing node voltage deviations and network losses. An adaptive penalty factor adjustment strategy, based on the alternating direction multiplier method, is introduced to achieve a comprehensive solution for this model. Finally, the enhanced IEEE 33-node system is utilized for verification and analysis. The outcomes demonstrate that the suggested coordination strategy involving DPV and SVC, alongside the distributed optimization control method, offers economic advantages and effectively achieves the safe and cost-effective operation of the distribution network.

Waveform design through the trade-off relationship between the MI criterion and the SINR criterion

Aiming at the diversity requirements of cognitive radar monitoring tasks, a joint optimization design criterion that comprehensively considers the mutual information (MI) and signal-to-interference-to-noise ratio (SINR) between the target and the echo is proposed. In view of the challenges brought by the traditional water-filling algorithm, this paper further studies how to effectively solve the new optimization criteria to improve the overall performance of the system. Specifically, this paper proposes a PCMA-ES algorithm that combines an adaptive penalty function with the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) algorithm. The penalty function aims to prioritize feasible solutions by assigning them the highest fitness. For infeasible solutions with lower constraint violations, the fitness is slightly lower, allowing for better utilization of information from infeasible solutions. The simulation results show that the PCMA-ES algorithm has lower time complexity or better performance than the traditional water-filling algorithm, and can solve more complex transmission waveforms. In addition, the waveform designed with a joint optimization criterion outperforms that based on a single optimization criterion. The radar detection focus can be adjusted to meet the specific requirements of diverse detection tasks.

Preference-based multi-objective evolutionary algorithm with linear combination scalarizing function and reference point adjustment

In practice, the decision-maker (DM) may be only interested in a particular part of Pareto optimal front (PF). For this reason, many preference-based multi-objective evolutionary algorithms (MOEA) have been proposed to find a solution set that approximates the region of the interest (ROI). Most existing preference-based methods focus on selecting solutions in the ROI. Nevertheless, the enhancement of convergence in preference-based MOEAs has been neglected. Most decomposition-based approaches often employ the achievement scalarizing function (ASF) as their scalarizing function. However, it holds a weaker search ability than the weighted sum function (WSF) despite its capability to tackle problems with arbitrary PF geometries. In order to strengthen the selective pressure toward the PF, this paper proposes a new scalarizing function, LSF, which is a linear combination of the WSF and the ASF. Then, a simple adaptive penalty scheme is employed in LSF to balance the search ability and robustness. To focus the search on the ROI, we develop a reference point adjustment method that dynamically adjusts the position of the reference point according to the distance from the approximated target point. We apply the above two innovations to the MOEA/D framework and propose a new preference-based MOEA, namely RAMOEAD. Experimental results show that RAMOEAD is highly competitive when compared with five state-of-the-art preference-based MOEAs. Finally, the proposed algorithm is extended to double reference points for solving the problems in which the ROIs are defined by the reservation and aspiration points.