Constraint Optimization Research Articles

The improved local cost simulation algorithms based on coalition structure generation for solving distributed constraint optimization problems

The improved local cost simulation algorithms based on coalition structure generation for solving distributed constraint optimization problems

Scalable log-ratio lasso regression for enhanced microbial feature selection with FLORAL.

Identifying predictive biomarkers of patient outcomes from high-throughput microbiome data is of high interest, while existing computational methods do not satisfactorily account for complex survival endpoints, longitudinal samples, and taxa-specific sequencing biases. We present FLORAL, an open-source tool to perform scalable log-ratio lasso regression and microbial feature selection for continuous, binary, time-to-event, and competing risk outcomes, with compatibility for longitudinal microbiome data as time-dependent covariates. The proposed method adapts the augmented Lagrangian algorithm for a zero-sum constraint optimization problem while enabling a two-stage screening process for enhanced false-positive control. In extensive simulation and real-data analyses, FLORAL achieved consistently better false-positive control compared to other lasso-based approaches and better sensitivity over popular differential abundance testing methods for datasets with smaller sample sizes. In a survival analysis of allogeneic hematopoietic cell transplant recipients, FLORAL demonstrated considerable improvement in microbial feature selection by utilizing longitudinal microbiome data over solely using baseline microbiome data.

Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results.

Scheduling of Earth observing satellites using distributed constraint optimization

Earth observation satellites (EOS) are satellites equipped with optical sensors that orbit the Earth to take photographs of particular areas at the request of users. With the development of space technology, the number of satellites has increased continuously. Yet still, the number of satellites cannot meet the explosive growth of applications. Thus, scheduling solutions are required to satisfy requests and obtain high observation efficiency. While the literature on multi-satellite scheduling is rich, most solutions are centralized algorithms. However, due to their cost, EOS systems are often co-funded by several agents (e.g., countries, companies, or research institutes). Central solutions require that these agents share their requests for observations with others. To date, there has yet to be a solution for EOS scheduling that protects the private information of the interested parties. In this study, we model the EOS scheduling problem as a distributed constraint optimization problem (DCOP). This modeling enables the generation of timetables for the satellites in a distributed manner without a priori sharing users’ private information with some central authority. For solving the resulting DCOP, we use and compare the results of two different local search algorithms—Distributed Stochastic Algorithm and Maximum Gain Message—which are known to produce efficient solutions in a timely manner. The modeling and solving of the resulting DCOP constitute our new solution method, which we term Distributed Satellite Timetable Solver (DSTS). Experimental evaluation reveals that the DSTS method provides solutions of higher quality than a commonly used centralized greedy algorithm and is comparable to an additional centralized algorithm that we propose.

Constraint Qualifications and Optimality Conditions for Multiobjective Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds

In this paper, we investigate constraint qualifications and optimality conditions for multiobjective mathematical programming problems with vanishing constraints (MOMPVC) on Hadamard manifolds. The MOMPVC-tailored generalized Guignard constraint qualification (MOMPVC-GGCQ) for MOMPVC is introduced in the setting of Hadamard manifolds. By employing MOMPVC-GGCQ and the intrinsic properties of Hadamard manifolds, we establish Karush–Kuhn–Tucker (KKT)-type necessary Pareto efficiency criteria for MOMPVC. Moreover, we introduce several MOMPVC-tailored constraint qualifications and develop interrelations among them. In particular, we establish that the MOMPVC-tailored constraint qualifications introduced in this paper turn out to be sufficient conditions for MOMPVC-GGCQ. Suitable illustrative examples are furnished in the framework of well-known Hadamard manifolds to validate and demonstrate the importance and significance of the derived results. To the best of our knowledge, this is the first time that constraint qualifications, their interrelations, and optimality criteria for MOMPVC have been explored in the framework of Hadamard manifolds.

Constraint qualifications and optimality conditions for nonsmooth multiobjective mathematical programming problems with vanishing constraints on Hadamard manifolds via convexificators

In this paper, we introduce the notion of convexificators in the framework of Hadamard manifolds. We derive some calculus rules for convexificators on Hadamard manifolds and employ them to investigate nonsmooth multiobjective programming problems with vanishing constraints on Hadamard manifolds (abbreviated as, (NMPVC)). The Abadie constraint qualification (abbreviated as, (ACQ)), as well as the generalized (ACQ) (abbreviated as, (GACQ)), are introduced for (NMPVC) in terms of convexificators. Further, (GACQ) is employed to establish the well-known Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary Pareto efficiency criteria for (NMPVC). Moreover, we introduce several other constraint qualifications for (NMPVC) in the Hadamard manifold setting using convexificators and establish interrelations among them. We have furnished non-trivial examples in the framework of some well-known Hadamard manifolds to illustrate the significance of our results. As far as the best of our knowledge is concerned, constraint qualifications and optimality conditions for (NMPVC) have not yet been studied in the framework of Hadamard manifolds via convexificators.

Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization Algorithm

One of the most prominent application areas for quantum computers is solving hard constraint satisfaction and optimization problems. However, detailed analyses of the complexity of standard quantum algorithms have suggested that outperforming classical methods for these problems would require extremely large and powerful quantum computers. The quantum approximate optimization algorithm (QAOA) is designed for near-term quantum computers, yet previous work has shown strong limitations on the ability of QAOA to outperform classical algorithms for optimization problems. Here we instead apply QAOA to hard constraint satisfaction problems, where both classical and quantum algorithms are expected to require exponential time. We analytically characterize the average success probability of QAOA on a constraint satisfaction problem commonly studied using statistical physics methods: random k-SAT at the threshold for satisfiability, as the number of variables n goes to infinity. We complement these theoretical results with numerical experiments on the performance of QAOA for small n, which match the limiting theoretical bounds closely. We then compare QAOA with leading classical solvers. For random 8-SAT, we find that for more than 14 quantum circuit layers, QAOA achieves more efficient scaling than the highest-performance classical solver we tested, WalkSATlm. Our results suggest that near-term quantum algorithms for solving constraint satisfaction problems may outperform their classical counterparts. Published by the American Physical Society 2024

Coevolutionary multitasking for constrained multiobjective optimization

Addressing the challenges of constrained multiobjective optimization problems (CMOPs) with evolutionary algorithms requires balancing constraint satisfaction and optimization objectives. Coevolutionary multitasking (CEMT) offers a promising strategy by leveraging synergies from distinct, complementary tasks. The primary challenge in CEMT frameworks is constructing suitable auxiliary tasks that effectively complement the main CMOP task. In this paper, we propose an adaptive CEMT framework (ACEMT), which customizes two adaptive auxiliary tasks to enhance CMOP-solving efficiency. The first auxiliary task dynamically narrows constraint boundaries, facilitating exploration in regions with smaller feasible spaces. The second task focuses specifically on individual constraints, continuously adapting to expedite convergence and uncover optimal regions. In solving the main CMOP task, this dual-auxiliary-task strategy not only improves search thoroughness but also clarifies the balance between constraints and objectives. Concretely, ACEMT incorporates an adaptive constraint relaxation technique for the first auxiliary task and a specialized constraint selection strategy for the second. These innovations foster effective knowledge transfer and task synergy, addressing the key challenge of auxiliary task construction in CEMT frameworks. Extensive experiments on three benchmark suites and real-world applications demonstrate ACEMT’s superior performance compared to state-of-the-art constrained evolutionary algorithms. ACEMT sets a new standard in CMOP-solving by strategically constructing and adapting auxiliary tasks, representing a significant advancement in this research direction.

Event‐triggered optimal control based on prescribed performance for a two‐link robotic manipulator

SummaryIn this article, an event‐triggered optimal control method based on prescribed performance is investigated for a constrained two‐link robotic manipulator system. To satisfy the performance constraints of the system, an equated error model of the dynamics model is established by means of two auxiliary functions and the prescribed performance technique. A predictive controller based on an adaptive event triggering mechanism is obtained by solving a constraint optimization problem for this transformed error model, and the triggering threshold can be adjusted based on real‐time changes of the system. This controller realizes the tracking of the joint angle with the desired angle and meets the prescribed performance conditions. Finally, the control algorithm is shown to be an effective method for improving control performance through numerical simulations and comparison with other prescribed performance functions.

Multi-algorithm based evolutionary strategy with Adaptive Mutation Mechanism for Constraint Engineering Design Problems

This paper proposes a new multi-algorithm based evolution strategy with the addition of adaptive mutation operators for global optimization. The new algorithm namely Kepler meerkat naked (KMN) algorithm is based on Kepler’s optimization algorithm (KOA), meerkat optimization algorithm (MOA), and naked mole-rat algorithm (NMRA), as the core algorithms and, grey wolf optimizer (GWO) and cuckoo search (CS) inspired equations for enhanced exploration and exploitation. The proposed algorithm uses six new mutation operators for parametric enhancements, and follows an iterative division mechanism for a balanced operation. A comparative analysis is done with respect to classical benchmarks, CEC 2014, CEC 2017, CEC 2019 and CEC 2022 benchmark datasets for performance evaluation. Six engineering design problems are also used to test the performance of the proposed KMN algorithm for constraint optimization. Apart from that, a binary version of KMN namely bKMN is also proposed, and ten feature selection datasets are used for performance evaluation. Performance testing of the KMN and bKMN algorithm is done with success history-based DE (SHADE), LSHADE-SPACMA, self-adaptive DE (SaDE), fast opposition-based learning golden jackal optimization (FROBL-GJO), LSHADE-EpSin, jSO, EBOwithCMAR, among others. Experimental and statistical results are performed using Wilcoxon’s and Friedman’s tests, and it has been found that the proposed algorithms are highly competitive in contrast to other algorithms under study.

Optimizing Room Temperature Control: A Comparative Analysis of Deep Reinforcement Learning and Contextual Bayesian Optimization Methods

Building temperature control presents significant modeling challenges due to the complexity of internal systems and varied usage patterns. Consequently, black box modeling has become a prevalent approach in this domain. This technique broadly encompasses deep learning and Bayesian optimization methods, each offering unique mechanisms for deriving optimal control parameters. Deep learning methods iteratively refine control parameters using extensive datasets, whereas Bayesian optimization employs Gaussian process regression and acquisition functions to pinpoint optimal solutions. This paper conducts a comparative analysis of two innovative methods within these branches: the application of Deep Reinforcement Learning (DRL) for integrated control of household temperature and electric vehicle charging, and the Primal-Dual Contextual Bayesian Optimization (PDCBO) method for adaptive thermal control in buildings. The study reveals that the DRL approach, integrated with electric vehicle charging systems, excels in responsiveness and reducing energy consumption. In contrast, the PDCBO method enhances control by allowing for the artificial definition and continuous optimization of constraints on energy usage and comfort during the operation, facilitated by algorithmic design. By synthesizing the strengths of both methods and considering electric vehicle integration and tailored adaptive control constraints, enhanced outcomes are achievable. This paper proposes that specific control strategies be developed for different building types to address diverse real-world requirements effectively.

From Single-Objective to Bi-Objective Maximum Satisfiability Solving

The declarative approach is key to efficiently finding optimal solutions to various types of NP-hard real-world combinatorial optimization problems. Most work on practical declarative solvers—ranging from classical integer programming to finite-domain constraint optimization and maximum satisfiability (MaxSAT)—has focused on optimization under a single objective; fewer advances have been made towards efficient declarative techniques for multi-objective optimization problems. Motivated by significant recent advances in practical solvers for MaxSAT, in this work we develop BiOptSat, an exact declarative approach for finding Pareto-optimal solutions to bi-objective optimization problems, with propositional logic as the underlying constraint language. BiOptSat can be viewed as an instantiation of the lexicographic method. The approach makes use of a single Boolean satisfiability solver that is incrementally employed throughout the entire search procedure, allowing for finding a single Pareto-optimal solution, finding one representative solution for each non-dominated point, and enumerating all Pareto-optimal solutions. We detail several algorithmic instantiations of BiOptSat, each building on recent algorithms proposed for single-objective MaxSAT. We empirically evaluate the instantiations compared to recently-proposed alternative approaches to multi-objective MaxSAT solving on several real-world domains from the literature, showing the practical benefits of our approach.

Two-Warehouse Inventory Model: Interval Valued Costs, Advanced Payment, Stock-Dependent Demand, and Partial Backlogging

A great deal of inventory costs are typically unpredictable because of the unpredictability of a competitive market. The fluctating demand from customer's and the unpredictability of the market economy make it difficult for researchers and operation research practitioners to appropriately replicate an inventory problem. In order to prevail this type of unpredictability circumstances, in this paper, we have represented the inventory parameters as interval. Using this concept, we progressed a two-warehouse inventory model for deteriorating items with a fixed Shelf life, partially backlogging shortages and interval-valued deterioration rate. In addition to this the parameters like ordering cost, purchase cost, shortage cost, deterioration cost for both the rented and owned warehouse except the backlogging parameter have been considered as interval-valued. The uncertainty in the inventory parameters motivated us to view them as interval-valued in the present research. Based on the assumptions, the cost function of this problem is a highly nonlinear constraint optimization problem. Mathematica is used to tackle this nonlinear optimization problem. A numerical example has been presented to demonstrate the computational result. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.

Design of a Multi-loop PI Controller for Minimum Phase System Level Regulation in a Quadruple Tank: A Method for Constraint Optimization

Design of a Multi-loop PI Controller for Minimum Phase System Level Regulation in a Quadruple Tank: A Method for Constraint Optimization

Semi-supervised metric learning incorporating weighted triplet constraint and Riemannian manifold optimization for classification

Semi-supervised metric learning incorporating weighted triplet constraint and Riemannian manifold optimization for classification

Cooperative Path Planning for Multiplayer Reach‐Avoid Games under Imperfect Observation Information

This article investigates a reach‐avoid game and proposes a cooperative path planning algorithm for a target–pursuers (TP) coalition to capture an evader. In the game, the target aims to bait and escape from the evader, and the pursuer aims to capture the evader. Due to imperfect observations, the TP coalition has uncertain information of the evader's state, while the evader is assumed to have perfect observation. The game model is constructed by formulating the optimization problems for each player in a receding horizon fashion. Then, to counter the evader effectively, the TP coalition constructs a virtual evader using the belief information from a Kalman filter. And a chance constraint optimization problem is constructed to predict the virtual evader's trajectory under uncertainties. The TP coalition can capture the actual evader by generating a robust counter‐strategy against the virtual evader with a chance constraint feasible set. Next, to compute the Nash equilibrium of the TP coalition's subjective game, an iterative algorithm is designed that combines the iterative best response and the distributed alternating direction method of multiplier algorithms. Finally, the effectiveness of the algorithm is validated through simulations and experiments.

Equilibrium Interaction Strategies for Integrated Energy System Incorporating Demand-Side Management Based on Stackelberg Game Approach

This paper analyzes the balanced interaction strategy of an integrated energy system (IES) operator and an industrial user in the operation process of the IES under the demand-side management (DSM) based on game theory. Firstly, we establish an electric–thermal IES, which includes a power grid, a heat grid and a natural gas grid. Secondly, a two-stage Stackelberg dynamic game model is proposed to describe the game behavior of IES operators and industrial users in the process of participating in DSM. The interactions between the IES operator (leader) and the user (follower) are formulated into a one-leader–one-follower Stackelberg game, where optimization problems are formed for each player to help select the optimal strategy. A pricing function is adopted for regulating time-of-use (TOU), which acts as a coordinator, inducing users to join the game. Then, for the complex two-stage dynamic game model established, the lower user-side constraint optimization problem is replaced by its KKT condition, so that the two-stage hierarchical optimization problem is transformed into a single-stage mixed-integer nonlinear optimization model, and the branch-and-bound method is introduced to solve it. Finally, the equilibrium strategies and income values of both sides of the game are obtained through a case simulation, and the dynamic equilibrium strategy curves under different capacity configurations are obtained through the sensitivity analysis of key parameters. The equilibrium income of the IES is USD 93.859, while the equilibrium income of industrial users in the park is USD 92.720. The simulation results show that the proposed method and model are effective.

Exploring constraint qualification-free optimality conditions for linear second-order cone programming

Exploring constraint qualification-free optimality conditions for linear second-order cone programming

RevGraphVAMP: A protein molecular simulation analysis model combining graph convolutional neural networks and physical constraints

Molecular dynamics simulation is a crucial research domain within the life sciences, focusing on comprehending the mechanisms of biomolecular interactions at atomic scales. Protein simulation, as a critical subfield, often utilizes MD for implementation, with trajectory data play a pivotal role in drug discovery. The advancement of high-performance computing and deep learning technology becomes popular and critical to predict protein properties from vast trajectory data, posing challenges regarding data features extraction from the complicated simulation data and dimensionality reduction. Simultaneously, it is essential to provide a meaningful explanation of the biological mechanism behind dimensionality. To tackle this challenge, we propose a new unsupervised model named RevGraphVAMP to intelligently analyze the simulation trajectory. This model is based on the variational approach for Markov processes (VAMP) and integrates graph convolutional neural networks and physical constraint optimization to enhance the learning performance. Additionally, we introduce attention mechanism to assess the importance of key interaction region, facilitating the interpretation of molecular mechanism. In comparison to other VAMPNets models, our model showcases competitive performance, improved accuracy in state transition prediction, as demonstrated through its application to two public datasets and the Shank3-Rap1 complex, which is associated with autism spectrum disorder. Moreover, it enhanced dimensionality reduction discrimination across different substates and provides interpretable results for protein structural characterization.

Validating and speeding up x-ray tomographic inversions in tokamak plasmas

X-ray tomography is a precious tool in tokamaks that provides rich information about the core plasma, such as local impurity concentration, electron temperature and density as well as magnetic equilibrium (ME) and magnetohydrodynamic activity. Nevertheless, inferring the local plasma emissivity from a sparse set of line-integrated measurements is an ill-posed problem that requires dedicated regularization and validation methods. Besides, speeding up the inversion algorithm in order to be compatible with real-time control systems is a challenging task with traditional approaches. In this contribution, in a first part we introduce tools aiming at validating and speeding up the x-ray tomographic inversions based on Tikhonov regularization, including ME constraint and parameter optimization, taking the WEST geometry as an example. In a second part, an alternative approach compatible with real-time, based on a set of neural networks is proposed and compared with the Tikhonov approach for an experimental case.