Constraint Handling Research Articles

An efficient propositional system for Abductive Logic Programming

Abductive logic programming (ALP) extends logic programming with hypothetical reasoning by means of abducibles, an extension able to handle interesting problems, such as diagnosis, planning, and verification with formal methods. Implementations of this extension have been using Prolog meta-interpreters and Prolog programs with Constraint Handling Rules (CHR). While the latter adds a clean and efficient interface to the host system, it still suffers in performance for large programs. Here, the concern is to obtain a more performant implementation of the SCIFF system following a compiled approach. This paper, as a first step in this long term goal, sets out a propositional ALP system following SCIFF, eliminating the need for CHR and achieving better performance.

An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems

In constrained multi-objective optimization problems, it is challenging to balance the convergence, diversity and feasibility of the population, especially encountering complex infeasible regions. In order to effectively balance the three indicators, from the aspects of the handling of infeasible solution and the quality of individuals, a multi-population co-evolutionary competitive particle swarm optimization algorithm hybridized with infeasible solution transfer and an adaptive technique (ACCPSO) is proposed. Firstly, the information of feasible and infeasible individuals is fully utilized and the individuals are classified by Hamming distance. Then, a novel constraint handling technique based on learning from the promising feasible direction is designed to make individuals cross large infeasible regions and explore more potential feasible regions. Moreover, aiming to provide robust search capability and consequently further generate high-quality solutions, the genetic operators and the particle swarm optimization operator with the competitive mechanism are introduced as operators with an adaptive mechanism. Finally, compared with the state-of-the-art methods, the performance of the proposed algorithm is verified on LIR-CMOP, MW and DTLZ, as well as two real-world problems. The results indicate that ACCPSO exhibits stronger competitiveness in terms of convergence, the solution quality, and distribution diversity on the feasible Pareto front.

NVH multiobjective and robust optimization of electric motor design, including power losses

As part of electric motor design, compromises between NVH considerations, electrotechnical design and performance targets must be made. Electromagnetic excitation within the airgap results in structure-borne and airborne noise transmission to the vehicle. High-frequency tones are characteristic of this noise. Efficient computation methods exist to estimate these vibration and noise levels. From the early design stage, NVH performance can be diagnosed and optimized. The focus on NVH can no longer be separated from efficiency optimization. Simulation workflows and optimization loops, developed for NVH-related targets, are updated to consider copper and iron losses. The modification of the geometrical design must be addressed to reduce both dynamic excitation and energy loss, or at least offer compromises. Electric motor design optimization requires the handling of multiple objectives and constraints from multiple physics. In addition, design robustness must be ensured as part of the industrial process: manufacturing tolerances have to be considered to define a robust optimized design.

A Generalized Framework for Multi-objective-based Constraint Handling Technique

A Generalized Framework for Multi-objective-based Constraint Handling Technique

Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers

This paper presents a new approach for solving FFLP problems using a double parametric form (DPF), which is critical in decision-making scenarios characterized by uncertainty and imprecision. Traditional linear programming methods often fall short in handling the inherent vagueness in real-world problems. To address this gap, an innovative method has been proposed which incorporates fuzzy logic to model the uncertain parameters as TFNs, allowing for a more realistic and flexible representation of the problem space. The proposed method stands out due to its integration of fuzzy arithmetic into the optimization process, enabling the handling of fuzzy constraints and objectives directly. Unlike conventional techniques that rely on crisp approximations or the defuzzification process, the proposed approach maintains the fuzziness throughout the computation, ensuring that the solutions retain their fuzzy characteristics and better reflect the uncertainties present in the input data. In summary, the proposed method has the ability to directly incorporate fuzzy parameters into the optimization framework, providing a more comprehensive solution to FFLP problems. The main findings of this study underscore the method’s effectiveness and its potential for broader application in various fields where decision-making under uncertainty is crucial.

Addressing Constraint Coupling and Autonomous Decision-Making Challenges: An Analysis of Large-Scale UAV Trajectory-Planning Techniques

With the increase in UAV scale and mission diversity, trajectory planning systems faces more and more complex constraints, which are often conflicting and strongly coupled, placing higher demands on the real-time and response capabilities of the system. At the same time, conflicts and strong coupling pose challenges the autonomous decision-making capability of the system, affecting the accuracy and efficiency of the planning system in complex environments. However, recent research advances addressing these issues have not been fully summarized. An in-depth exploration of constraint handling techniques and autonomous decision-making issues will be of great significance to the development of large-scale UAV systems. Therefore, this paper aims to provide a comprehensive overview of this topic. Firstly, the functions and application scenarios of large-scale UAV trajectory planning are introduced and classified in detail according to the planning method, realization function and the presence or absence of constraints. Then, the constraint handling techniques are described in detail, focusing on the priority ranking of constraints and the principles of their fusion and transformation methods. Then, the importance of autonomous decision-making in large-scale UAV trajectory planning is described in depth, and related dynamic adjustment algorithms are introduced. Finally, the future research directions and challenges of large-scale UAV trajectory planning are outlooked, providing directions and references for future research in the fields of UAV clustering and UAV cooperative flight.

Fast machine-learning-enabled size reduction of microwave components using response features

Achieving compact size has emerged as a key consideration in modern microwave design. While structural miniaturization can be accomplished through judicious circuit architecture selection, precise parameter tuning is equally vital to minimize physical dimensions while meeting stringent performance requirements for electrical characteristics. Due to the intricate nature of compact structures, global optimization is recommended, yet hindered by the excessive expenses associated with system evaluation, typically conducted through electromagnetic (EM) simulation. This challenge is further compounded by the fact that size reduction is a constrained problem entailing expensive constraints. This paper introduces an innovative method for cost-effective explicit miniaturization of microwave components on a global scale. Our approach leverages response feature technology, formulating the optimization problem based on a set of characteristic points derived from EM-analyzed responses, combined with an implicit constraint handling approach. Both elements facilitate handling size reduction by transforming it into an unconstrained problem and regularizing the objective function. The core search engine employs a machine-learning framework with kriging-based surrogates refined using the predicted improvement in the objective function as the infill criterion. Our algorithm is demonstrated using two miniaturized couplers and is shown superior over several benchmark routines, encompassing both conventional (gradient-based) and population-based procedures, alongside a machine learning technique. The primary strengths of the proposed framework lie in its reliability, computational efficiency (with a typical optimization cost ranging from 100 to 150 EM circuit analyses), and straightforward setup.

Multi-constrained predictive optimal control for spacecraft attitude stabilization and tracking with performance guarantees

This paper investigates a novel predictive control approach for spacecraft attitude stabilization and tracking problems with consideration of performance constraints, angular velocity limitation and control saturation. First, the prescribed performance control (PPC) structure and barrier Lyapunov function (BLF) are utilized to design the cost function of optimal control problem. Subsequently, a multi-constrained predictive optimal controller for spacecraft attitude stabilization and tracking with performance guarantees is devised via exploiting an explicit receding horizon optimization control strategy under actuator saturation. Compared with the existing methods, the major merit of the proposed one lies in the semi-analytic solving scheme of optimal control problems with high computing efficiency and simultaneous handling of multiple constraints without increasing computational burden. Finally, two illustrative examples are employed to validate the effectiveness of the proposed control method.

An adaptive gravitational search algorithm for optimizing mechanical engineering design and machining problems

The gravitational search algorithm (GSA) is widely used for solving optimization problems because it performs in a superior manner as compared to various competing evolutionary and swarm-based metaheuristics. However, GSA frequently gets trapped in local optima due to a lack of solution diversity. Although chaotic gravitational search algorithm (CGSA) can resolve this issue to some extent but its degraded exploitation rate and convergence speed may not result in desired outcome. To this end, diversity-based chaotic GSA (DCGSA) has exhibited its capability to resolve the issues encountered with GSA and CGSA to a certain extent for unconstrained problems. DCGSA achieves this characteristic through the use of an adaptive gravitational constant, which varies according to the diversity values of the population. Since most real-world problems are subjected to some constraints, it is prudent to improve the performance of GSA in solving constrained optimization problems. The present study integrates the enhanced search capability of DCGSA with a generalized constraint handling mechanism to improve the performance of GSA in solving constrained problems. It is observed that DCGSA significantly outperforms GSA on both CEC (Congress on evolutionary computation) 2006, 2010 and 2017 functions and competes strongly with CGSA. Diversity analysis shows that the capability to balance exploration and exploitation rates is enhanced using CGSA and DCGSA. Furthermore, DCGSA algorithms outperform GSA and CGSA on real-world machining and CEC 2020 mechanical design problems. Comparison with state-of-the-art algorithms is made to analyze the performance of the algorithms from a larger perspective.

Multi-objective optimization of series-parallel system with mixed subsystems failure dependencies using NSGA-II and MOHH

In complex systems, failure dependencies play a crucial role in determining their overall performance. This paper explores the multi-objective optimization of series-parallel systems with mixed failure dependencies. By optimizing system cost and availability, the study aims to identify the most efficient redundancy and repair strategies. Two optimization algorithms, the non-dominated sorting genetic algorithm II (NSGA-II) and a novel multi-objective algorithm named the multi-objective hoopoe heuristic (MOHH), are utilized alongside constraint handling techniques to produce Pareto fronts. These fronts illustrate the trade-offs between cost and availability. Additionally, a fuzzy decision method is utilized to determine the best compromise solutions from each optimization technique. Comparing the results, NSGA-II consistently outperforms MOHH in providing better compromise solutions across five independent runs. However, MOHH demonstrates a better standard deviation in its performance.

A Novel Set-Based Discrete Particle Swarm Optimization for Wastewater Treatment Process Effluent Scheduling.

With the escalating severity of environmental pollution caused by effluent, the wastewater treatment process (WWTP) has gained significant attention. The wastewater treatment efficiency and effluent quality are significantly impacted by effluent scheduling that adjusts the hydraulic retention time. However, the sequential batch and continuous nature of the effluent pose challenges, resulting in complex scheduling models with strong constraints that are difficult to tackle using existing scheduling methods. To optimize maximum completion time and effluent quality simultaneously, this article proposes a restructured set-based discrete particle swarm optimization (RS-DPSO) algorithm to address the WWTP effluent scheduling problem (WWTP-ESP). First, an effective encoding and decoding method is designed to effectively map solutions to feasible schedules using temporal and spatial information. Second, a restructured set-based discrete particle swarm algorithm is introduced to enhance the searching ability in discrete solution space via restructuring the solution set. Third, a constraint handling strategy based on violation degree ranking is designed to reduce the waste of computational resources. Fourth, a Sobel filter based local search is proposed to guide particle search direction to enhance search efficiency ability. The RS-DPSO provides a novel method for solving WWTP-ESP problems with complex discrete solution space. The comparative experiments indicate that the novel designs are effective and the proposed algorithm has superior performance over existing algorithms in solving the WWTP-ESP.

Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.

Chaotic self-adaptive sine cosine multi-objective optimization algorithm to solve microgrid optimal energy scheduling problems

Researchers are increasingly focusing on renewable energy due to its high reliability, energy independence, efficiency, and environmental benefits. This paper introduces a novel multi-objective framework for the short-term scheduling of microgrids (MGs), which addresses the conflicting objectives of minimizing operating expenses and reducing pollution emissions. The core contribution is the development of the Chaotic Self-Adaptive Sine Cosine Algorithm (CSASCA). This algorithm generates Pareto optimal solutions simultaneously, effectively balancing cost reduction and emission mitigation. The problem is formulated as a complex multi-objective optimization task with goals of cost reduction and environmental protection. To enhance decision-making within the algorithm, fuzzy logic is incorporated. The performance of CSASCA is evaluated across three scenarios: (1) PV and wind units operating at full power, (2) all units operating within specified limits with unrestricted utility power exchange, and (3) microgrid operation using only non-zero-emission energy sources. This third scenario highlights the algorithm’s efficacy in a challenging context not covered in prior research. Simulation results from these scenarios are compared with traditional Sine Cosine Algorithm (SCA) and other recent optimization methods using three test examples. The innovation of CSASCA lies in its chaotic self-adaptive mechanisms, which significantly enhance optimization performance. The integration of these mechanisms results in superior solutions for operation cost, emissions, and execution time. Specifically, CSASCA achieves optimal values of 590.45 €ct for cost and 337.28 kg for emissions in the first scenario, 98.203 €ct for cost and 406.204 kg for emissions in the second scenario, and 95.38 €ct for cost and 982.173 kg for emissions in the third scenario. Overall, CSASCA outperforms traditional SCA by offering enhanced exploration, improved convergence, effective constraint handling, and reduced parameter sensitivity, making it a powerful tool for solving multi-objective optimization problems like microgrid scheduling.

Adaptive gain design for Zero-Order Hold discrete-time implementation of explicit reference governor

Explicit reference governor (ERG) is an add-on unit that provides constraint handling capability to pre-stabilized systems. The main idea behind ERG is to manipulate the derivative of the applied reference in continuous time such that the satisfaction of state and input constraints is guaranteed at all times. However, ERG should be practically implemented in discrete-time. This paper studies the discrete-time implementation of ERG, and provides conditions under which the feasibility and convergence properties of the ERG framework are maintained when the updates of the applied reference are performed in discrete time. Specifically, using Zero-Order Hold (ZOH) discretization method, we develop an adaptive algorithm to adjust the gain of the discretized term based on actual measurements to maintain all properties of ERG when implemented in discrete-time. The proposed approach is validated via extensive simulation and experimental studies.

Modular control architecture for safe marine navigation: Reinforcement learning with predictive safety filters

Many autonomous systems are safety-critical, making it essential to have a closed-loop control system that satisfies constraints arising from underlying physical limitations and safety aspects in a robust manner. However, this is often challenging to achieve for real-world systems. For example, autonomous ships at sea have nonlinear and uncertain dynamics and are subject to numerous time-varying environmental disturbances such as waves, currents, and wind. There is increasing interest in using machine learning-based approaches to adapt these systems to more complex scenarios, but there are few standard frameworks that guarantee the safety and stability of such systems. Recently, predictive safety filters (PSF) have emerged as a promising method to ensure constraint satisfaction in learning-based control, bypassing the need for explicit constraint handling in the learning algorithms themselves. The safety filter approach leads to a modular separation of the problem, allowing the use of arbitrary control policies in a task-agnostic way. The filter takes in a potentially unsafe control action from the main controller and solves an optimization problem to compute a minimal perturbation of the proposed action that adheres to both physical and safety constraints. In this work, we combine reinforcement learning (RL) with predictive safety filtering in the context of marine navigation and control. The RL agent is trained on path-following and safety adherence across a wide range of randomly generated environments, while the predictive safety filter continuously monitors the agents' proposed control actions and modifies them if necessary. The combined PSF/RL scheme is implemented on a simulated model of Cybership II, a miniature replica of a typical supply ship. Safety performance and learning rate are evaluated and compared with those of a standard, non-PSF, RL agent. It is demonstrated that the predictive safety filter is able to keep the vessel safe, while not prohibiting the learning rate and performance of the RL agent.

Robust optimization of hypoid gear contact performance considering tooth form error: Design sensitivity and Pareto front

Optimization of hypoid gear contact performance is challenging due to its nonconvex nature and the handling of non-linear constraints involving complex gear contact behavior. In addition, the contact performance in the existing optimization schemes is highly reliant on the manufacturing quality, for example, the uncertain tooth form errors induced by machining tolerances and blade wear are usually ignored. To tackle these problems, a robust optimization methodology is proposed for hypoid gear contact performance. A finite element/contact mechanics model is established, which considers the stochastic tooth form errors following a Gaussian distribution model. The non-linear constraints are incorporated to avoid edge contact under loaded conditions, and tooth surface interference due to error. This methodology guarantees the feasible solution space and reduces the optimization complexity by the independent identification model. The identification model of the optimal solution is flexible in the parameter selection while keeping tooth depth. This non-deterministic problem is optimized based on the pattern search method. The Pareto front and design sensitivity analysis demonstrate the effectiveness and robustness of the proposed optimization methodology.

Handling of constraints in multiobjective blackbox optimization

Handling of constraints in multiobjective blackbox optimization

Constrained multiobjective optimization design for ordinary shovel attachment of hydraulic excavator based on evolutionary algorithm

Shovel attachment is one of the most commonly used working attachments in hydraulic excavators. Its mechanical design remains a challenging optimization problem. To tackle this issue, the optimizing model of ordinary shovel attachment is firstly established which contains twenty-three design variables, six objective functions, and sixty-three constraints. Then, an improved decomposition-based constrained many-objective evolution algorithm is proposed, which integrates advanced push & pull search constraint handling technique and differential evolution operator to deal with the optimization problems of shovel attachment. Finally, the proposed algorithm has demonstrated its superior optimization ability for designing shovel attachments through the case studies of a 70-ton face-shovel hydraulic excavator, outperforming seventeen state-of-the-art constrained multiobjective evolutionary algorithms. Furthermore, the first quantitative comparison between ordinary shovel attachment and TriPower shovel attachment under the same main machine is presented by the optimized results. The result demonstrates the complexity of the optimal design for shovel attachment and the effectiveness of multiobjective evolutionary algorithm.

Surrogate-assisted constrained hybrid particle swarm optimization algorithm for propane pre-cooled mixed refrigerant LNG process optimization

The propane pre-cooled mixed refrigerant (C3MR) process is one of the most widely used and efficient natural gas liquefaction processes. However, optimization of this process involves various design and operational constraints, complex thermodynamics, and hence nonconvex in nature. Therefore, it's computationally expensive, often involving trial and error approaches. Existing optimization algorithms often possess flaws such as insufficient accuracy and premature convergence, leading to suboptimal solutions that may violate essential process constraints. This article proposes a novel method to optimize the C3MR process that handles the computational complexity, meets the constraints, and achieves feasible solutions quickly. The proposed method includes modified feasibility-based constraint handling and radial basis function network-assisted surrogate modeling and optimization, where the power consumption is optimized using a hybrid of the particle swarm optimization (PSO) and social learning PSO algorithm. The proposed algorithm achieves the optimum power consumption (121109.31 kW), which is 21.5 % less than the base case (154200 kW). The optimization results are compared with similar optimization algorithms, where the proposed algorithm outperformed the other algorithm regarding optimal solution, convergence, and speed. The results from this study are compared to previous studies from the literature, which validate the accuracy and applicability of the proposed method.

Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions

Pontryagin's Minimum Principle (PMP) is a powerful tool for solving Nonlinear Model Predictive Control problems (NMPC), enabling the handling of time-varying input constraints and cost functions. However, applying PMP encounters challenges when state constraints must be satisfied. This arises because the optimal trajectory often requires a blend of unconstrained and constrained arcs with unknown junction points. To address this issue, relaxation methods are frequently explored, where state constraints are replaced with penalty functions. The contributions of this paper are as follows. First, a method of penalty functions allowing for coping with soft state constraints is examined. We prove the recursive feasibility of this method and demonstrate its efficiency in a numerical example. Second, the finite-time practical stability for the optimal reference tracking NMPC problem is addressed. By appropriately choosing the terminal cost, one can guarantee the convergence of the state vector to a predefined neighbourhood of the target state.