Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems

Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

Application of novel constrained friction processing method to produce fine grained biomedical Mg-Zn-Ca alloy

In order to obtain Mg alloys with fine microstructures and high mechanical performances,a novel friction-based processing method,name as“constrained friction processing(CFP)”,was investigated.Via CFP,defect-free Mg-Zn-Ca rods with greatly refined grains and high mechanical properties were produced.Compared to the previous as-cast microstructure,the grain size was reduced from more than 1 mm to around 4μm within 3 s by a single process cycle.The compressive yield strength was increased by 350%while the ultimate compressive strength by 53%.According to the established material flow behaviors by“tracer material”,the plastic material was transported by shear deformation.From the base material to the rod,the material experienced three stages,i.e.deformation by the tool,upward flow with additional tilt,followed by upward transportation.The microstructural evolution was revealed by“stop-action”technique.The microstructural development at regions adjacent to the rod is mainly controlled by twinning,dynamic recrystallization(DRX)as well as particle stimulated nucleation,while that within the rod is related to DRX combined with grain growth.

Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

Aseismic performances of constrained damping lining structures made of rubber-sand-concrete

Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using a rubber-sand-concrete(RSC)as the aseismic material,is proposed.The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests.The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis,composite loss factor and damping ratio of the transfer function analysis,and total vibration level of octave spectrum analysis were discussed.The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear,and that the hollow damping layer had a better aseismic performance than the flat damping layer one.The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated.The effects of the peak ground acceleration(PGA)and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain(PEEQ)were discussed.The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance,with PGA in the range(0.2-1.2)g and tunnel overburden depth in the range of 0-300 m.

Dynamic Event-Triggered Consensus Control for Input Constrained Multi-Agent Systems With a Designable Minimum Inter-Event Time

This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.

Numerical and experimental investigation into the evolution of the shock wave when a muzzle jet impacts a constrained moving body

The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.

Three-dimensional constrained gravity inversion of Moho depth and crustal structural characteristics at Mozambique continental margin

Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.

Constrained Multi-Objective Optimization With Deep Reinforcement Learning Assisted Operator Selection

Solving constrained multi-objective optimization problems with evolutionary algorithms has attracted considerable attention.Various constrained multi-objective optimization evolutionary algorithms(CMOEAs)have been developed with the use of different algorithmic strategies,evolutionary operators,and constraint-handling techniques.The performance of CMOEAs may be heavily dependent on the operators used,however,it is usually difficult to select suitable operators for the problem at hand.Hence,improving operator selection is promising and necessary for CMOEAs.This work proposes an online operator selection framework assisted by Deep Reinforcement Learning.The dynamics of the population,including convergence,diversity,and feasibility,are regarded as the state;the candidate operators are considered as actions;and the improvement of the population state is treated as the reward.By using a Q-network to learn a policy to estimate the Q-values of all actions,the proposed approach can adaptively select an operator that maximizes the improvement of the population according to the current state and thereby improve the algorithmic performance.The framework is embedded into four popular CMOEAs and assessed on 42 benchmark problems.The experimental results reveal that the proposed Deep Reinforcement Learning-assisted operator selection significantly improves the performance of these CMOEAs and the resulting algorithm obtains better versatility compared to nine state-of-the-art CMOEAs.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

GRU-integrated constrained soft actor-critic learning enabled fully distributed scheduling strategy for residential virtual power plant

In this study,a novel residential virtual power plant(RVPP)scheduling method that leverages a gate recurrent unit(GRU)-integrated deep reinforcement learning(DRL)algorithm is proposed.In the proposed scheme,the GRU-integrated DRL algorithm guides the RVPP to participate effectively in both the day-ahead and real-time markets,lowering the electricity purchase costs and consumption risks for end-users.The Lagrangian relaxation technique is introduced to transform the constrained Markov decision process(CMDP)into an unconstrained optimization problem,which guarantees that the constraints are strictly satisfied without determining the penalty coefficients.Furthermore,to enhance the scalability of the constrained soft actor-critic(CSAC)-based RVPP scheduling approach,a fully distributed scheduling architecture was designed to enable plug-and-play in the residential distributed energy resources(RDER).Case studies performed on the constructed RVPP scenario validated the performance of the proposed methodology in enhancing the responsiveness of the RDER to power tariffs,balancing the supply and demand of the power grid,and ensuring customer comfort.

Effect of thermo-mechanical conditions during constrained friction processing on the particle refinement of AM50 Mg-alloy phases

Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In this study,the effect of CFP on the microstructural refinement of AM50 rods is investigated in terms of particle size and morphology of the eutectic and secondary phases originally present in the base material,in particular the eutecticβ-Mg_(17)Al_(12)and Al-Mn phases.For that purpose,as-cast and solution heat-treated base material and processed samples were analyzed.The Al_(8)Mn_(5) intermetallic phase was identified as the main secondary phase present in all samples before and after the processing.A notorious refinement of these particles was observed,starting from particles with an average equivalent length of a few micrometers to around 560 nm after the processing.The refinement of the secondary phase refinement is attributed to a mechanism analogous to the attrition comminution,where the combination of temperature increase and shearing of the material enables the continuous breaking of the brittle intermetallic particles into smaller pieces.As for the eutectic phase,the results indicate the presence of the partially divorcedβ-Mg_(17)Al_(12)particles exclusively in the as-cast base material,indicating that no further phase transformations regarding the eutectic phase,such as dynamic precipitation,occurred after the CFP.In the case of the processed as-cast material analyzed after the CFP,the thermal energy generated during the processing led to temperature values above the solvus limit of the eutectic phase,which associated with the mechanical breakage of the particles,enabled the complete dissolution of this phase.Therefore,CFP was successfully demonstrated to promote an extensive microstructure refinement in multiple aspects,in terms of grain sizes of theα-Mg phase and presence and morphology of the Al-Mn and eutecticβ-Mg_(17)Al_(12).

Avoiding the Use of Lagrange Multipliers. II. Constrained Extrema of Functionals and the Evaluation of Constrained Derivatives

A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.

Evolutionary Multitasking With Global and Local Auxiliary Tasks for Constrained Multi-Objective Optimization

Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.

An Enhanced Adaptive Differential Evolution Approach for Constrained Optimization Problems

Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest selection mechanism is proposed to integrate the current mutation strategy in constrained optimization problems.Based on the improved pbest selection method,an adaptive differential evolution approach is proposed,which helps the population jump out of the infeasible region.If all the individuals are infeasible,the top 5%of infeasible individuals are selected.In addition,a modified truncatedε-level method is proposed to avoid trapping in infeasible regions.The proposed adaptive differential evolution approach with an improvedεconstraint processmechanism(IεJADE)is examined on CEC 2006 and CEC 2010 constrained benchmark function series.Besides,a standard IEEE-30 bus test system is studied on the efficiency of the IεJADE.The numerical analysis verifies the IεJADE algorithm is effective in comparisonwith other effective algorithms.

Position Optimization for Mobile Relay Communications with Constrained Energy over a Whole Horizontal Plane

This paper concerns the position optimization problem of a mobile relay over a whole horizontal plane.This problem is important because the position of a mobile relay directly affects the end-to-end performance,e.g.,reliability,connectivity,and data rate.In this paper,we propose a new position optimization scheme of a mobile relay over a whole horizontal plane based on the one-bit feedback information from the destination node,which improves the performance over the prior scheme whose position of the mobile relay is optimized over a fixed orbit.In the proposed scheme,the mobile relay is equipped with merely one single onboard antenna.Moreover,no prior information about the positions of both the source node and the destination node is required.Thus,the proposed scheme can work at low network resources scenario,which is particularly suitable for mobile relay communication with constrained energy,e.g.,the communications in a disaster area where the infrastructure is heavily damaged,volcano monitoring,and wireless powered communication networking.According to the characteristics of the proposed scheme,we further design two heuristic implementations to calculate the optimal position of a mobile relay over a whole horizontal plane.The first implementation has better steady performance whereas the second implementation has better convergence speed.We implement the proposed scheme and conduct an extensive performance comparison between the proposed scheme and prior schemes to verify the advantages of the proposed scheme.

Cementless Semi-Constrained Rotating Platform Total Knee Replacement: A Concise Follow-Up of a Previous Report at a Minimum of Twenty Years

Background: A previous report evaluated the initial 310 cementless, Buechel-Pappas (B-P), Semi-Constrained Rotating Platform total knee replacements in 257 patients followed for an average of 7.6 years, range 2 - 18 years. Diagnoses were osteoarthritis in 233 patients, post traumatic arthritis in 4 patients and rheumatoid arthritis in 22 patients. Knee Scores, using a strict knee scoring scale were 86.4% excellent, 12.3% good, 0.3% fair and 1.0% poor results. Survivorship, using an end point of revision for any mechanical reason (including component loosening, bearing wear and bearing dislocation) was 99.4%. Survivorship for a poor knee score (including persistent pain, loosening, instability and infection was 97.6%. The purpose of the present study is to report the updated results of this same patient cohort at a minimum follow-up of twenty years. Methods: The average age of patients at the time of surgery was 67 years, range 34 to 91 years. A total of 20 patients (22 knees) were still living, with a follow-up of 20 - 30 years (mean 23.47 years). The same strict knee scoring scale and survivorship analysis were used to evaluate patient outcomes at the 20 to 30 years interval. Results: Survivorship, in the current study, using the same end points as in the previous study, was 96.5% at the 20 and 30-year intervals. Late mechanical failure and osteolysis were not identified. Conclusion: This cementless, semi-constrained rotating platform total knee replacement has stood the test of time for more than 20 years and can be considered acceptable for long-term use, in properly selected patients.

Projected Runge-Kutta methods for constrained Hamiltonian systems

Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

Feasibility-Guided Constraint-Handling Techniques for Engineering Optimization Problems

The particle swarm optimization(PSO)algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and sh.PSO is essentially an unconstrained algorithm and requires constraint handling techniques(CHTs)to solve constrained optimization problems(COPs).For this purpose,we integrate two CHTs,the superiority of feasibility(SF)and the violation constraint-handling(VCH),with a PSO.These CHTs distinguish feasible solutions from infeasible ones.Moreover,in SF,the selection of infeasible solutions is based on their degree of constraint violations,whereas in VCH,the number of constraint violations by an infeasible solution is of more importance.Therefore,a PSO is adapted for constrained optimization,yielding two constrained variants,denoted SF-PSO and VCH-PSO.Both SF-PSO and VCH-PSO are evaluated with respect to ve engineering problems:the Himmelblau’s nonlinear optimization,the welded beam design,the spring design,the pressure vessel design,and the three-bar truss design.The simulation results show that both algorithms are consistent in terms of their solutions to these problems,including their different available versions.Comparison of the SF-PSO and the VCHPSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used.We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.

Active Vibration Control of Beam Using Electro-magnetic Constrained Layer Damping

This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coil of the electromagnet is electrified with proper control strategy, the electromagnet can exert magnetic force opposite to the direction of structural deformation so that the structural vibration is attenuated. A mathematical model is developed based on the equivalent current method to calculate the electromagnetic control force produced by EMCLD. The governing equations of the system are obtained using Hamilton＇s Principle and then reduced with the assumed-mode method. A simulation on vibration control of a cantilever beam is conducted under the velocity proportional feedback to demonstrate the energy dissipation capability of EMCLD, and the beam system with the same parameter is experimented. The results of experiment and simulation are compared and the results show that the EMCLD is an effective means for suppressing modal vibration. The results also indicate that the beam system has better control performance for larger control current. The EMCLD method presented in this paper provides an applicable and efficient tool for the vibration control of structures.