Constrained Optimization Problem Research Articles

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

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

Ensemble Clustering via Co-Association Matrix Self-Enhancement.

Ensemble clustering integrates a set of base clustering results to generate a stronger one. Existing methods usually rely on a co-association (CA) matrix that measures how many times two samples are grouped into the same cluster according to the base clusterings to achieve ensemble clustering. However, when the constructed CA matrix is of low quality, the performance will degrade. In this article, we propose a simple, yet effective CA matrix self-enhancement framework that can improve the CA matrix to achieve better clustering performance. Specifically, we first extract the high-confidence (HC) information from the base clusterings to form a sparse HC matrix. By propagating the highly reliable information of the HC matrix to the CA matrix and complementing the HC matrix according to the CA matrix simultaneously, the proposed method generates an enhanced CA matrix for better clustering. Technically, the proposed model is formulated as a symmetric constrained convex optimization problem, which is efficiently solved by an alternating iterative algorithm with convergence and global optimum theoretically guaranteed. Extensive experimental comparisons with 12 state-of-the-art methods on ten benchmark datasets substantiate the effectiveness, flexibility, and efficiency of the proposed model in ensemble clustering. The codes and datasets can be downloaded at https://github.com/Siritao/EC-CMS.

The Perturbation Method and Regularization of the Lagrange Multiplier Rule in Convex Constrained Optimization Problems

The Perturbation Method and Regularization of the Lagrange Multiplier Rule in Convex Constrained Optimization Problems

Reliability based optimisation of composite plates under aeroelastic constraints via adapted surrogate modelling and genetic algorithms

Composite materials are vital in aerospace for their exceptional strength-to-weight ratio. This study delves into reliability-based optimisation of composite plates within aeroelastic constraints, employing an efficient global optimisation method and genetic algorithms. Initial analysis focuses on aeroelastic responses such as limit flutter speed, gust response, and static loads, emphasising maximum strain assessment. To tackle optimisation challenges of composite stacking sequences, a homogenisation technique with lamination parameters is applied. We then formulate a constrained optimisation problem to minimise gust response while meeting flutter and maximum strain constraints. Surrogate models based on conditioned Gaussian Processes are developed for each aeroelastic response, facilitating optimisation within the composite design space. These models, with potential for local refinement, expedite optimal solution identification. Further, we integrate reliability-based optimisation into the framework to determine a robust stacking sequence using genetic algorithms, accounting for random fibre orientation variations. This holistic approach integrates aeroelastic analysis, constrained optimisation, surrogate modelling, and reliability-based optimisation, proving effective in designing reliable, efficient composite structures for aerospace, thus enhancing performance and safety.

A fixed-time stable forward–backward dynamical system for solving generalized monotone inclusions

AbstractWe propose a forward–backward splitting dynamical system for solving inclusion problems of the form $$0\in A(x)+B(x)$$ 0 ∈ A ( x ) + B ( x ) in Hilbert spaces, where A is a maximal operator and B is a single-valued operator. Involved operators are assumed to satisfy a generalized monotonicity condition, which is weaker than the standard monotone assumptions. Under mild conditions on parameters, we establish the fixed-time stability of the proposed dynamical system. In addition, we consider an explicit forward Euler discretization of the dynamical system leading to a new forward backward algorithm for which we present the convergence analysis. Applications to other optimization problems such as constrained optimization problems, mixed variational inequalities, and variational inequalities are presented and some numerical examples are given to illustrate the theoretical results.

AI Optimization-Based Heterogeneous Approach for Green Next-Generation Communication Systems.

Traditional heterogeneous networks (HetNets) are constrained by their hardware design and configuration. These HetNets have a limited ability to adapt to variations in network dynamics. Software-defined radio technology has the potential to address this adaptability issue. In this paper, we introduce a software-defined radio (SDR)-based long-term evolution licensed assisted access (LTE-LAA) architecture for next-generation communication networks. We show that with proper design and tuning of the proposed architecture, high-level adaptability in HetNets becomes feasible with a higher throughput and lower power consumption. Firstly, maximizing the throughput and minimizing power consumption are formulated as a constrained optimization problem. Then, the obtained solution, alongside a heuristic solution, is compared against the solutions to existing approaches, showing our proposed strategy is drastically superior in terms of both power efficiency and system throughput. This study is then concluded by employing artificial intelligence techniques in multi-objective optimization, namely random forest regression, particle swarm, and genetic algorithms, to balance out the trade-offs between maximizing the throughput and power efficiency and minimizing energy consumption. These investigations demonstrate the potential of employing the proposed LTE-LAA architecture in addressing the requirements of next-generation HetNets in terms of power, throughput, and green scalability.

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.

A dual-population Constrained Many-Objective Evolutionary Algorithm based on reference point and angle easing strategy.

Constrained many-objective optimization problems (CMaOPs) have gradually emerged in various areas and are significant for this field. These problems often involve intricate Pareto frontiers (PFs) that are both refined and uneven, thereby making their resolution difficult and challenging. Traditional algorithms tend to over prioritize convergence, leading to premature convergence of the decision variables, which greatly reduces the possibility of finding the constrained Pareto frontiers (CPFs). This results in poor overall performance. To tackle this challenge, our solution involves a novel dual-population constrained many-objective evolutionary algorithm based on reference point and angle easing strategy (dCMaOEA-RAE). It relies on a relaxed selection strategy utilizing reference points and angles to facilitate cooperation between dual populations by retaining solutions that may currently perform poorly but contribute positively to the overall optimization process. We are able to guide the population to move to the optimal feasible solution region in a timely manner in order to obtain a series of superior solutions can be obtained. Our proposed algorithm's competitiveness across all three evaluation indicators was demonstrated through experimental results conducted on 77 test problems. Comparisons with ten other cutting-edge algorithms further validated its efficacy.

An online cooperative control strategy for enhancing microgrid participation into electricity market

This paper develops a cooperative control methodology for the online energy management of grid-connected microgrids. The main aim of this methodology is to actively manage the active power outputs of all dispatchable energy sources available within the microgrid as well as the power exchanged with the utility grid so as to match the total load demand at the minimum operating cost. This implies to solve a constrained multi-objective dynamic optimization problem aimed at minimizing the total microgrid operating costs and ensuring the real-time balance within the microgrid in compliance with its technical-operational constraints. Lyapunov's theorem using sensitivity theory is adopted to solve this optimization.To test the performances of the proposed control methodology, several computer simulations corresponding to different operating scenarios have been conducted on the PrInCE Lab experimental microgrid built at the Polytechnic University of Bari.

Optimal design of large-scale nonlinear Bayesian inverse problems under model uncertainty

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the inversion parameters, the governing PDEs include secondary uncertain parameters. We focus on problems with infinite-dimensional inversion and secondary parameters and present a scalable computational framework for optimal design of such problems. The proposed approach enables Bayesian inversion and OED under uncertainty within a unified framework. We build on the Bayesian approximation error (BAE) approach, to incorporate modeling uncertainties in the Bayesian inverse problem, and methods for A-optimal design of infinite-dimensional Bayesian nonlinear inverse problems. Specifically, a Gaussian approximation to the posterior at the maximum a posteriori probability point is used to define an uncertainty aware OED objective that is tractable to evaluate and optimize. In particular, the OED objective can be computed at a cost, in the number of PDE solves, that does not grow with the dimension of the discretized inversion and secondary parameters. The OED problem is formulated as a binary bilevel PDE constrained optimization problem and a greedy algorithm, which provides a pragmatic approach, is used to find optimal designs. We demonstrate the effectiveness of the proposed approach for a model inverse problem governed by an elliptic PDE on a three-dimensional domain. Our computational results also highlight the pitfalls of ignoring modeling uncertainties in the OED and/or inference stages.

Sparsity-driven loudspeaker gain optimization for sound field reconstruction with spherical microphone array

The paper presents a sparsity-driven method utilizing loudspeakers to reconstruct spatial sound fields using measurements obtained from a spherical microphone array (SMA). Employing spherical harmonics decomposition (SHD), the SMA recordings are characterized in the spherical harmonics domain. The gains for the loudspeakers are determined through an optimization problem, equating spherical harmonics pressure coefficients from primary and secondary sources. Furthermore, the sparsity within the loudspeaker feeds is redefined as a constrained sparse optimization problem, integrating linearity and orthogonality constraints. This method effectively reduces the required loudspeakers while maintaining sound field quality. The Bregman iteration method is applied to solve the constrained optimization problem. Rigorous evaluation based on reconstructed sound fields and objective measures highlights significant enhancements compared to least square and compressed sensing methods.

A Novel Path-Following Method for Time-Varying Optimizations with Optimal Parametric Functions

We address a broad category of nonlinear constrained optimization problems. We then reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system to track the respective optimal solution. We then re-parameterize the dynamical system according to a linear combination of parametric functions. By applying the calculus of variations, we optimize these parametric functions to minimize the optimality distance. Consequently, we develop an iterative dynamic algorithm, termed as OP-TVO, to achieve efficient convergence to the solution. We compare the performance of the proposed algorithm with the prediction correction method (PCM) in terms of optimality and computational complexity. The results demonstrate that OP-TVO effectively competes with PCM for the given class of optimization problems, suggesting a promising alternative to PCM. This work also introduces a novel paradigm for solving parametric dynamic systems.

Conformal structure-preserving SVM methods for the nonlinear Schrödinger equation with weakly linear damping term

In this paper, by applying the supplementary variable method (SVM), some high-order, conformal structure-preserving, linearized algorithms are developed for the damped nonlinear Schrödinger equation. We derive the well-determined SVM systems with the conformal properties and they are then equivalent to nonlinear equality constrained optimization problems for computation. The deduced optimization models are discretized by using the Gauss type Runge-Kutta method and the prediction-correction technique in time as well as the Fourier pseudo-spectral method in space. Numerical results and some comparisons between this method and other reported methods are given to favor the suggested method in the overall performance. It is worthwhile to emphasize that the numerical strategy in this work could be extended to other conservative or dissipative system for designing high-order structure-preserving algorithms.

A federated GAN network-based evolutionary constrained optimization approach to integrated coal mine energy system

The integrated coal mine energy system (ICMES) is a kind of system with multiple scenarios, variables and parameters, which belongs to dynamic constrained multi-objective optimization problem (DCMOP). One of the challenges in solving ICMES lies in searching for feasible solutions when the frequency of changes is quick. To solve the above mentioned issues, this paper proposes a federated GAN network-based evolutionary constrained optimization for ICMES (FGECO). Firstly, multiple GAN networks are utilized in the framework of federated learning (FL) to estimate the distribution of feasible regions that satisfy each constraint. Following that, they are fused to realize the intersection of all feasible regions, and generate one feasible region that can meet all constrained requirements. Subsequently, an initial population with guidance of evolution is generated based on the proposed shared GAN network model. Finally, FGECO is compared with four popular dynamic constrained multi-objective evolutionary algorithms (DCMOEAs) on ICMES. Experimental results indicate its superiority.

Hidden Convexity, Optimization, and Algorithms on Rotation Matrices

This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices [Formula: see text]. Such problems are nonconvex because of the constraint [Formula: see text]. Nonetheless, we show that certain linear images of [Formula: see text] are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of [Formula: see text] is convex and that the projection of [Formula: see text] onto its strict upper triangular entries is convex. These results allow us to construct exact convex reformulations for constrained optimization problems over [Formula: see text] with a single constraint or with constraints defined by low-rank matrices. Both of these results are maximal in a formal sense. Funding: A. Ramachandran was supported by the H2020 program of the European Research Council [Grant 805241-QIP]. A. L. Wang was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.GROOT.2019.015 (OPTIMAL)]. K. Shu was supported by the Georgia Institute of Technology (ACO-ARC fellowship).

CMGWO: Grey wolf optimizer for fusion cell-like P systems

The grey wolf optimizer is a widely used parametric optimization algorithm. It is affected by the structure and rank of grey wolves and is prone to falling into the local optimum. In this study, we propose a grey wolf optimizer for fusion cell-like P systems. Cell-like P systems can parallelize computation and communicate from cell membrane to cell membrane, which can help the grey wolf optimizer jump out of the local optimum. Design new convergence factors and use different convergence factors in other cell membranes to balance the overall exploration and utilization capabilities of the algorithm. At the same time, dynamic weights are introduced to accelerate the convergence speed of the algorithm. Experiments are performed on 24 test functions to verify their global optimization performance. Meanwhile, a support vector machine model optimized by the grey wolf optimizer for fusion cell-like P systems has been developed and tested on six benchmark datasets. Finally, the optimizing ability of grey wolf optimizer for fusion cell-like P systems on constrained optimization problems is verified on three real engineering design problems. Compared with other algorithms, grey wolf optimizer for fusion cell-like P systems obtains higher accuracy and faster convergence speed on the test function, and at the same time, it can find a better parameter set stably for the optimization of support vector machine parameters, in addition to being more competitive on constrained engineering design problems. The results show that grey wolf optimizer for fusion cell-like P systems improves the searching ability of the population, has a better ability to jump out of the local optimum, has a faster convergence speed, and has better stability.

Resilient and robust management policy for multi‐stage supply chains with perishable goods and inaccurate forecast information: A distributed model predictive control approach

AbstractAn efficient supply chain (SC) management requires that decisions are taken to minimize the effects of parametric uncertainties and unpredictable external disturbances. In this article, we consider this problem with reference to a multi‐stage SC (MSSC) whose dynamics is characterized by the following elements of complexity: perishable goods with uncertain perishability rate, an uncertain future customer demand that is only known to fluctuate inside a given compact set. The problem we face is to define a resilient and robust Replenishment Policy (RP) such that at any stage the following requirements are satisfied: the fulfilled demand is maximized, overstocking is avoided, the bullwhip effect (BE) is mitigated. These objectives should be pursued despite the mentioned uncertainties and unexpected customer demand behaviors violating the bounds of the compact set. Robustness is here intended with respect to uncertainty on the perishability rate, and resiliency as the ability to quickly react to the mentioned unforeseen customer demands. We propose a method based on a distributed resilient robust model predictive control (DRRMPC) approach. Each local robust MPC (RMPC) involves solving a Min‐Max constrained optimization problem (MMCOP). To drastically reduce the numerical complexity of each MMCOP, we parametrize its solution by means of B‐spline functions.

Dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement

Dynamic constrained multi-objective optimization problems (DCMOPs) involve objectives, constraints, and parameters that change over time. This kind of problem presents a greater challenge for evolutionary algorithms because it requires the population to quickly track the changing pareto-optimal set (PS) under constrained conditions while maintaining the feasibility and good distribution of the population. To address these challenges, this paper proposes a dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement (CEDE), in which we have made improvements to both the static optimization and dynamic response parts, innovatively utilizing the valuable information latent in the optimization process to help the population evolve more comprehensively. The static optimization involves the co-evolution of three populations, through which their mutual synergy can more comprehensively identify potential true PS and provide more useful historical information for dynamic response. Additionally, to prevent the elimination of potentially valuable infeasible individuals (i.e., individuals that are not dominated by feasible individuals) due to pareto domination, we employ an archive set to store and update these individuals. When the environment changes, to effectively enhance population diversity under complex dynamic constraints and help the population to respond quickly to changes, we propose a diversity enhancement strategy, which includes a diversity maintenance strategy and a center point-based exploration strategy. This strategy effectively enhances population diversity in complex and changing environments, helping the population respond quickly to changes. The effectiveness of the algorithm is validated through two test sets. The experimental results show that CEDE can effectively use valuable information to cope with complex dynamic constraint environments. Compared with several of the most advanced algorithms, it is superior in 94% of the test problems, demonstrating strong competitiveness in handling DCMOPs.

A robust interpolated model predictive control based on recurrent neural networks for a nonholonomic differential-drive mobile robot with quasi-LPV representation: computational complexity and conservatism

This paper presents an improved Model Predictive Control (MPC) for path tracking of a nonholonomic mobile robot with a differential drive. Nonlinear dynamics and nonholonomic constraints make the optimisation problem of MPC for the robot challenging. Nonlinear dynamics of the robots are expressed by a Linear Parameter Varying (LPV), and a Recurrent Neural Network (RNN) solves the constrained optimisation problem, providing optimal velocities. Moreover, an interpolation-based approach has been introduced to augment the region of attraction. The algorithm ensures stability in the presence of bounded disturbances through the inclusion of free control moves in the control law. The controller efficiency has been evaluated in two scenarios in a hospital setting. The simulation results illustrate that the proposed method performs better than nonlinear MPC and standard LPV-based MPC in terms of computational cost, disturbance rejection, and region of attraction.

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms.