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Journal articles on the topic 'Constraints handling'

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Published: 5 June 2025

Last updated: 16 July 2025

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Kusakci, Ali, and Mehmet Can. "An adaptive ES with a ranking based constraint handling strategy." Yugoslav Journal of Operations Research 24, no. 3 (2014): 307–19. http://dx.doi.org/10.2298/yjor140121035k.

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To solve a constrained optimization problem, equality constraints can be used to eliminate a problem variable. If it is not feasible, the relations imposed implicitly by the constraints can still be exploited. Most conventional constraint handling methods in Evolutionary Algorithms (EAs) do not consider the correlations between problem variables imposed by the constraints. This paper relies on the idea that a proper search operator, which captures mentioned implicit correlations, can improve performance of evolutionary constrained optimization algorithms. To realize this, an Evolution Strategy (ES) along with a simplified Covariance Matrix Adaptation (CMA) based mutation operator is used with a ranking based constraint-handling method. The proposed algorithm is tested on 13 benchmark problems as well as on a real life design problem. The outperformance of the algorithm is significant when compared with conventional ES-based methods.

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Lu, Yuxiao, Arunesh Sinha, and Pradeep Varakantham. "Handling Long and Richly Constrained Tasks through Constrained Hierarchical Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 19 (2024): 21368–77. http://dx.doi.org/10.1609/aaai.v38i19.30132.

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Safety in goal directed Reinforcement Learning (RL) settings has typically been handled through constraints over trajectories and have demonstrated good performance in primarily short horizon tasks. In this paper, we are specifically interested in the problem of solving temporally extended decision making problems such as robots cleaning different areas in a house while avoiding slippery and unsafe areas (e.g., stairs) and retaining enough charge to move to a charging dock; in the presence of complex safety constraints. Our key contribution is a (safety) Constrained Search with Hierarchical Reinforcement Learning (CoSHRL) mechanism that combines an upper level constrained search agent (which computes a reward maximizing policy from a given start to a far away goal state while satisfying cost constraints) with a low-level goal conditioned RL agent (which estimates cost and reward values to move between nearby states). A major advantage of CoSHRL is that it can handle constraints on the cost value distribution (e.g., on Conditional Value at Risk, CVaR) and can adjust to flexible constraint thresholds without retraining. We perform extensive experiments with different types of safety constraints to demonstrate the utility of our approach over leading approaches in constrained and hierarchical RL.

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Hua, Hai Yan, Shu Wen Lin, and Zhen Hui Shen. "A New Method of the Constraints Expression and Handling for Excavator Boom Structural Optimization." Advanced Materials Research 479-481 (February 2012): 1851–56. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1851.

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In allusion to the deficiencies existing in current structural optimization algorithm of excavator boom such as the inefficiency in expressing and handling the constraints, the insufficiency in adopting the task knowledge to direct constraint handling, and the difficulty in obtaining and adopting the optimal process knowledge, a new method of the constraints expression and handling based on cultural algorithm for excavator boom structural optimization is put forward. The mechanism of hierarchical constraints expression and handing is established to improve the efficiency of the constraint handling in the optimal process with the cultural algorithm as frame and the task knowledge as guide. And the hierarchical topographical knowledge is formed to express tacit knowledge in the population space. Then the process of constraints expressing and handling as well as its interaction with the knowledge base is discussed under the direction of dual evolution in cultural algorithm while the aim of acquisition, expression and handling for tacit constraints knowledge in optimal process is realized. Finally, structural optimization of an excavator boom is taken as an example to demonstrate the effectiveness of this method.

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LIU, BING. "SPECIFIC CONSTRAINT HANDLING IN CONSTRAINT SATISFACTION PROBLEMS." International Journal on Artificial Intelligence Tools 03, no. 01 (1994): 79–96. http://dx.doi.org/10.1142/s0218213094000066.

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Abundant literatures exist on consistency techniques for solving Constraint Satisfaction Problems (CSPs). These literatures, however, focused mainly on finding efficient general techniques to achieve network consistency and to solve CSPs. So far, many techniques have been reported, e.g., node consistency, arc consistency, path consistency, k-consistency, forward checking, lookahead, partial lookahead, etc. Not enough attention has been given to individual constraints, and how constraint specific features may be exploited for more efficient consistency check. Many types of constraints exist in real problems, and each has its own features. These features may allow specific consistency techniques to be designed such that they are more efficient than the general algorithms. To analyze this issue, we divide a consistency algorithm into three parts: (1) activating constraints for check; (2) selecting the next constraint to be checked; and (3) checking the selected constraint. We will discuss how constraint specific features may influence each of these aspects and how special handling techniques may be designed to improve the efficiency. In order to allow these individual constraint handling techniques to be used, a new consistency algorithm is also proposed.

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Takami, Hikaru, and Shigeru Obayashi. "A comparator-based constraint handling technique for evolutionary algorithms." AIP Advances 12, no. 5 (2022): 055229. http://dx.doi.org/10.1063/5.0090572.

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Constraint handling is a key task for the successful optimization of design parameters in industrial design problems. This paper proposes a comparator-based constraint handling technique, called the More Less-Violations Method (MLVM), for solving real constrained optimization problems using evolutionary algorithms. The structure of the MLVM is simple and it can easily be integrated into conventional evolutionary algorithms. In the proposed method, constraint weights represent the level of importance of each constraint, enabling evolutionary compliance prioritization. Moreover, an acceptable region formed by the constraint tolerances allows trade-offs between objectives and constraints while preserving diverse solutions and improving optimization performance. These elements enable the appropriate design of industrial optimization problems. An application of this method to problems without constraint tolerances is also proposed. The JAXA/Mazda benchmark problem, developed on a real-world constrained design optimization dataset, is used to assess the performance of the MLVM. The results indicate that the MLVM realizes encouraging optimization performance.

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NAANAA, WADY, and SIMONE PIMONT. "Handling structured and ambiguous constraints in constraint satisfaction problems." Journal of Experimental & Theoretical Artificial Intelligence 10, no. 1 (1998): 91–102. http://dx.doi.org/10.1080/095281398146932.

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Kramer, Oliver. "A Review of Constraint-Handling Techniques for Evolution Strategies." Applied Computational Intelligence and Soft Computing 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/185063.

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Evolution strategies are successful global optimization methods. In many practical numerical problems constraints are not explicitly given. Evolution strategies have to incorporate techniques to optimize in restricted solution spaces. Famous constraint-handling techniques are penalty and multiobjective approaches. Past work has shown that in particular an ill-conditioned alignment between the coordinate system of Gaussian mutation and the constraint boundaries leads to premature convergence. Covariance matrix adaptation evolution strategies offer a solution to this alignment problem. Last, metamodeling of the constraint boundary leads to significant savings of constraint function calls and to a speedup by repairing infeasible solutions. This work gives a brief overview over constraint-handling methods for evolution strategies by demonstrating the approaches experimentally on two exemplary constrained problems.

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Gosain, Anjana, and Kavita Sachdeva. "Handling Constraints Using Penalty Functions in Materialized View Selection." International Journal of Natural Computing Research 8, no. 2 (2019): 1–17. http://dx.doi.org/10.4018/ijncr.2019040101.

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Materialized view selection (MVS) plays a vital role for efficiently making decisions in a data warehouse. This problem is NP-hard and constrained optimization problem. The authors have handled both the space and maintenance cost constraint using penalty functions. Three penalty function methods i.e. static, dynamic and adaptive penalty functions have been used for handling constraints and Backtracking Search Optimization algorithm (BSA) has been used for optimizing the total query processing cost. Experiments were conducted comparing the static, dynamic and adaptive penalty functions on varying the space constraint. The adaptive penalty function method yields the best results in terms of minimum query processing cost and achieves the optimality, scalability and feasibility of the problem on varying the lattice dimensions and on increasing the number of user queries. The authors proposed work has been compared with other evolutionary algorithms i.e. PSO and genetic algorithm and yields better results in terms of minimum total query processing cost of the materialized views.

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SERRANO, ALEJANDRO, and JURRIAAN HAGE. "Constraint handling rules with binders, patterns and generic quantification." Theory and Practice of Logic Programming 17, no. 5-6 (2017): 992–1009. http://dx.doi.org/10.1017/s1471068417000230.

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AbstractConstraint handling rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by λ-tree syntax, in which binding is explicit, and a new ∇ generic quantifier is introduced, which is used to create new fresh constants.

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Adekoya, Adekunle Rotimi, and Mardé Helbig. "Decision-Maker’s Preference-Driven Dynamic Multi-Objective Optimization." Algorithms 16, no. 11 (2023): 504. http://dx.doi.org/10.3390/a16110504.

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DMOOP are optimization problems where elements of the problems, such as the objective functions and/or constraints, change with time. These problems are characterized by two or more objective functions, where at least two objective functions are in conflict with one another. When solving real-world problems, the incorporation of human DM’ preferences or expert knowledge into the optimization process and thereby restricting the search to a specific region of the POF may result in more preferred or suitable solutions. This study proposes approaches that enable DM to influence the search process with their preferences by reformulating the optimization problems as constrained problems. The subsequent constrained problems are solved using various constraint handling approaches, such as the penalization of infeasible solutions and the restriction of the search to the feasible region of the search space. The proposed constraint handling approaches are compared by incorporating the approaches into a DE algorithm and measuring the algorithm’s performance using both standard performance measures for DMOO, as well as newly proposed measures for constrained DMOOP. The new measures indicate how well an algorithm was able to find solutions in the objective space that best reflect the DM’s preferences and the Pareto-optimality goal of DMOA. The results indicate that the constraint handling approaches are effective in finding Pareto-optimal solutions that satisfy the preference constraints of a DM.

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Allmendinger, Richard, and Joshua Knowles. "On Handling Ephemeral Resource Constraints in Evolutionary Search." Evolutionary Computation 21, no. 3 (2013): 497–531. http://dx.doi.org/10.1162/evco_a_00097.

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We consider optimization problems where the set of solutions available for evaluation at any given time t during optimization is some subset of the feasible space. This model is appropriate to describe many closed-loop optimization settings (i.e., where physical processes or experiments are used to evaluate solutions) where, due to resource limitations, it may be impossible to evaluate particular solutions at particular times (despite the solutions being part of the feasible space). We call the constraints determining which solutions are non-evaluable ephemeral resource constraints (ERCs). In this paper, we investigate two specific types of ERC: one encodes periodic resource availabilities, the other models commitment constraints that make the evaluable part of the space a function of earlier evaluations conducted. In an experimental study, both types of constraint are seen to impact the performance of an evolutionary algorithm significantly. To deal with the effects of the ERCs, we propose and test five different constraint-handling policies (adapted from those used to handle standard constraints), using a number of different test functions including a fitness landscape from a real closed-loop problem. We show that knowing information about the type of resource constraint in advance may be sufficient to select an effective policy for dealing with it, even when advance knowledge of the fitness landscape is limited.

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Zhang, Zhihao, Fuyu Guo, Qian Tang, and Jiawei Chen. "Handling robot non-fixed high-velocity handling method." Journal of Physics: Conference Series 2492, no. 1 (2023): 012025. http://dx.doi.org/10.1088/1742-6596/2492/1/012025.

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Abstract Handling robots are widely used today, and non-fixed handling is more effective than fixed handling in some specific scenarios. The non-fixed handling of robots can increase the load and reduce the precise positioning process of grabbing the object, but the handling velocity is relatively slow for the stability of the object. In addition, it needs to consider the friction and reaction force constraints on the object. This paper proposes a non-fixed high-velocity handling method for the handling robot. First, it deduces the friction and reaction force constraints that maintain the dynamic balance of the object during the handling process into robot dynamic constraints. Then, the time-optimal trajectory planning algorithm based on reachability analysis is used to solve the robot’s time-optimal trajectory that satisfies the dynamic constraints of the object in the handling process. This leads to a markedly improved production efficiency, as the robot concludes the handling process in the shortest possible time. Finally, the experimental handling of the object by the ABB IRB1200 robot verifies this method.

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Prajapati, Raju, and Om Prakash Dubey. "Using Improved Particle Swarm Optimization to Compare Quadratic and Exact Penalty Methods for Nonlinear Programming Problem." International Journal of Students' Research in Technology & Management 13, no. 1 (2025): 07–14. https://doi.org/10.18510/ijsrtm.2025.1312.

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Purpose of the study: Penalty method plays an important role in handling constraints of a Non-Linear Programming Problem (NLPP). There exist varieties in penalty applying procedures. Quadratic and exact penalty methods belong to that class. The present paper computationally compares the performance of quadratic and exact penalty methods when they are implemented on NLPP with inequality constraints. Methodology: We have used some benchmark functions. The constraints are applied arbitrarily to the test functions. An improved version of the metaheuristic Particle Swarm Optimization (PSO) is used to handle the unconstrained NLPP obtained from the constrained NLPP. Main Findings: The results obtained are compared under similar conditions when quadratic and exact penalty methods are used as constraints handling techniques. The computational results are also reported under different ways to use the inertia weight in improved PSO. The paper discusses the computational convergence of these two methods. The condition for the same is also discussed. Applications of this study: The research is applied on NLPP problem. Constrained NLPPs are applicable in industry. Novelty/Originality of this study: The research gives a way to handle constraint between the exact penalty and quadratic penalty methods while solving NLPP using an improved PSO method.

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Gosain, Anjana, and Kavita Sachdeva. "Materialized View Selection for Query Performance Enhancement Using Stochastic Ranking Based Cuckoo Search Algorithm." International Journal of Reliability, Quality and Safety Engineering 27, no. 03 (2019): 2050008. http://dx.doi.org/10.1142/s0218539320500084.

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Materialized view selection (MVS) improves the query processing efficiency and performance for making decisions effectively in a data warehouse. This problem is NP-hard and constrained optimization problem which involves space and cost constraint. Various optimization algorithms have been proposed in literature for optimal selection of materialized views. Few works exist for handling the constraints in MVS. In this study, authors have proposed the Cuckoo Search Algorithm (CSA) for optimization and Stochastic Ranking (SR) for handling the constraints in solving the MVS problem. The motivation behind integrating CS with SR is that fewer parameters have to be fine tuned in CS algorithm than in genetic and Particle Swarm Optimization (PSO) algorithm and the ranking method of SR handles the constraints effectively. For proving the efficiency and performance of our proposed algorithm Stochastic Ranking based Cuckoo Search Algorithm for Materialized View Selection (SRCSAMVS), it has been compared with PSO, genetic algorithm and the constrained evolutionary optimization algorithm proposed by Yu et al. SRCSAMVS outperforms in terms of query processing cost and scalability of the problem.

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Lebbah, Yahia, Claude Michel, Michel Rueher, David Daney, and Jean-Pierre Merlet. "Efficient and Safe Global Constraints for Handling Numerical Constraint Systems." SIAM Journal on Numerical Analysis 42, no. 5 (2005): 2076–97. http://dx.doi.org/10.1137/s0036142903436174.

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Wu, Yu, Jing Wei Liu, and Yue Hong Xie. "Component-Based Ranking Strategy for Evolutionary Optimization with Sparse Constraints." Applied Mechanics and Materials 556-562 (May 2014): 3925–29. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3925.

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Most constraint-handling methods in constrained evolutionary optimization usually take advantage of only the valuable information of feasible solutions, while they don’t exploit adequately the information from infeasible ones. In this paper, a concept of “feasible component” is introduced to recognize the characteristics of diverse information extracted from infeasible solutions. Then a component-based ranking strategy is proposed for evolutionary optimization with sparse constraints by integrating feasible components and the idea of stochastic ranking. Experimental results on several problems with sparse constraints show that the component-based ranking strategy performs better than the stochastic ranking.

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van Hee, Kees, Natalia Sidorova, and Marc Voorhoeve. "Resource-Constrained Workflow Nets." Fundamenta Informaticae 71, no. 2-3 (2006): 243–57. https://doi.org/10.3233/fun-2006-712-306.

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We study concurrent processes modelled as workflow Petri nets extended with resource constrains. Resources are durable units that can be neither created nor destroyed: they are claimed during the handling procedure and then released again. Typical kinds of resources are manpower, machinery, computer memory. We define structural criteria based on traps and siphons for the correctness of workflow nets with resource constraints. We also extend the soundness notion for workflow nets to the workflow nets with resource constraints; extra conditions concern the durability of resources. We prove some properties of sound resource-constrained workflow nets.

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Jiang, Hao, Tien Mai, Pradeep Varakantham, and Huy Hoang. "Reward Penalties on Augmented States for Solving Richly Constrained RL Effectively." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 18 (2024): 19867–75. http://dx.doi.org/10.1609/aaai.v38i18.29962.

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Constrained Reinforcement Learning employs trajectory-based cost constraints (such as expected cost, Value at Risk, or Conditional VaR cost) to compute safe policies. The challenge lies in handling these constraints effectively while optimizing expected reward. Existing methods convert such trajectory-based constraints into local cost constraints, but they rely on cost estimates, leading to either aggressive or conservative solutions with regards to cost. We propose an unconstrained formulation that employs reward penalties over states augmented with costs to compute safe policies. Unlike standard primal-dual methods, our approach penalizes only infeasible trajectories through state augmentation. This ensures that increasing the penalty parameter always guarantees a feasible policy, a feature lacking in primal-dual methods. Our approach exhibits strong empirical performance and theoretical properties, offering a fresh paradigm for solving complex Constrained RL problems, including rich constraints like expected cost, Value at Risk, and Conditional Value at Risk. Our experimental results demonstrate superior performance compared to leading approaches across various constraint types on multiple benchmark problems.

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Koziel, Slawomir, and Zbigniew Michalewicz. "Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization." Evolutionary Computation 7, no. 1 (1999): 19–44. http://dx.doi.org/10.1162/evco.1999.7.1.19.

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During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.

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Chen, Yu-Fang, Vojtěch Havlena, Michal Hečko, Lukáš Holík, and Ondřej Lengál. "A Uniform Framework for Handling Position Constraints in String Solving." Proceedings of the ACM on Programming Languages 9, PLDI (2025): 550–75. https://doi.org/10.1145/3729273.

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We introduce a novel decision procedure for solving the class of position string constraints, which includes string disequalities, ¬prefixof, ¬suffixof, str.at, and ¬str.at. These constraints are generated frequently in almost any application of string constraint solving. Our procedure avoids expensive encoding of the constraints to word equations and, instead, reduces the problem to checking conflicts on positions satisfying an integerconstraint obtained from the Parikh image of a polynomial-sized finite automaton with a special structure. By the reduction to counting, solving position constraints becomes NP-complete and for some cases even falls into PTime. This is much cheaper than the previously used techniques, which either used reductions generating word equations and length constraints (for which modern string solvers use exponential-space algorithms) or incomplete techniques. Our method is relevant especially for automata-based string solvers, which have recently achieved the best results in terms of practical efficiency, generality, and completeness guarantees. This work allows them to excel also on position constraints, which used to be their weakness. Besides the efficiency gains, we show that our framework may be extended to solve a large fragment of ¬contains (in NExpTime), for which decidability has been long open, and gives a hope to solve the general problem. Our implementation of the technique within the Z3-Noodler solver significantly improves its performance on position constraints.

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Barkat Ullah, Abu S. S. M., Ruhul Sarker, and Chris Lokan. "Handling equality constraints in evolutionary optimization." European Journal of Operational Research 221, no. 3 (2012): 480–90. http://dx.doi.org/10.1016/j.ejor.2012.01.047.

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Aguirre, Arturo Hernández, Salvador Botello Rionda, Carlos A. Coello Coello, Giovanni Lizárraga Lizárraga, and Efrén Mezura Montes. "Handling constraints using multiobjective optimization concepts." International Journal for Numerical Methods in Engineering 59, no. 15 (2004): 1989–2017. http://dx.doi.org/10.1002/nme.947.

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Nordin, Axel, Damien Motte, Andreas Hopf, Robert Bjärnemo, and Claus-Christian Eckhardt. "Constraint-handling techniques for generative product design systems in the mass customization context." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 27, no. 4 (2013): 387–99. http://dx.doi.org/10.1017/s0890060413000383.

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AbstractGenerative product design systems used in the context of mass customization are required to generate diverse solutions quickly and reliably without necessitating modification or tuning during use. When such systems are employed to allow for the mass customization of product form, they must be able to handle mass production and engineering constraints that can be time-consuming to evaluate and difficult to fulfill. These issues are related to how the constraints are handled in the generative design system. This article evaluates two promising sequential constraint-handling techniques and the often used weighted sum technique with regard to convergence time, convergence rate, and diversity of the design solutions. The application used for this purpose was a design system aimed at generating a table with an advanced form: a Voronoi diagram based structure. The design problem was constrained in terms of production as well as stability, requiring a time-consuming finite element evaluation. Regarding convergence time and rate, one of the sequential constraint-handling techniques performed significantly better than the weighted sum technique. Nevertheless, the weighted sum technique presented respectable results and therefore remains a relevant technique. Regarding diversity, none of the techniques could generate diverse solutions in a single search run. In contrast, the solutions from different searches were always diverse. Solution diversity is thus gained at the cost of more runs, but no evaluation of the diversity of the solutions is needed. This result is important, because a diversity evaluation function would otherwise have to be developed for every new type of design. Efficient handling of complex constraints is an important step toward mass customization of nontrivial product forms.

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Zhang, Qiang, Shurong Li, and Jianxin Guo. "Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/835098.

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An off-line optimization approach of high precision minimum time feedrate for CNC machining is proposed. Besides the ordinary considered velocity, acceleration, and jerk constraints, dynamic performance constraint of each servo drive is also considered in this optimization problem to improve the tracking precision along the optimized feedrate trajectory. Tracking error is applied to indicate the servo dynamic performance of each axis. By using variable substitution, the tracking error constrained minimum time trajectory planning problem is formulated as a nonlinear path constrained optimal control problem. Bang-bang constraints structure of the optimal trajectory is proved in this paper; then a novel constraint handling method is proposed to realize a convex optimization based solution of the nonlinear constrained optimal control problem. A simple ellipse feedrate planning test is presented to demonstrate the effectiveness of the approach. Then the practicability and robustness of the trajectory generated by the proposed approach are demonstrated by a butterfly contour machining example.

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Sleesongsom, Suwin, and Sujin Bureerat. "Optimal Synthesis of Four-Bar Linkage Path Generation through Evolutionary Computation with a Novel Constraint Handling Technique." Computational Intelligence and Neuroscience 2018 (November 1, 2018): 1–16. http://dx.doi.org/10.1155/2018/5462563.

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This paper presents a novel constraint handling technique for optimum path generation of four-bar linkages using evolutionary algorithms (EAs). Usually, the design problem is assigned to minimize the error between desired and obtained coupler curves with penalty constraints. It is found that the currently used constraint handling technique is rather inefficient. In this work, we propose a new technique, termed a path repairing technique, to deal with the constraints for both input crank rotation and Grashof criterion. Three traditional path generation test problems are used to test the proposed technique. Metaheuristic algorithms, namely, artificial bee colony optimization (ABC), adaptive differential evolution with optional external archive (JADE), population-based incremental learning (PBIL), teaching-learning-based optimization (TLBO), real-code ant colony optimization (ACOR), a grey wolf optimizer (GWO), and a sine cosine algorithm (SCA), are applied for finding the optimum solutions. The results show that new technique is a superior constraint handling technique while TLBO is the best method for synthesizing four-bar linkages.

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Brosowsky, Mathis, Florian Keck, Olaf Dünkel, and Marius Zöllner. "Sample-Specific Output Constraints for Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 6812–21. http://dx.doi.org/10.1609/aaai.v35i8.16841.

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It is common practice to constrain the output space of a neural network with the final layer to a problem-specific value range. However, for many tasks it is desired to restrict the output space for each input independently to a different subdomain with a non-trivial geometry, e.g. in safety-critical applications, to exclude hazardous outputs sample-wise. We propose ConstraintNet—a scalable neural network architecture which constrains the output space in each forward pass independently. Contrary to prior approaches, which perform a projection in the final layer, ConstraintNet applies an input-dependent parametrization of the constrained output space. Thereby, the complete interior of the constrained region is covered and computational costs are reduced significantly. For constraints in form of convex polytopes, we leverage the vertex representation to specify the parametrization. The second modification consists of adding an auxiliary input in form of a tensor description of the constraint to enable the handling of multiple constraints for the same sample. Finally, ConstraintNet is end-to-end trainable with almost no overhead in the forward and backward pass. We demonstrate ConstraintNet on two regression tasks: First, we modify a CNN and construct several constraints for facial landmark detection tasks. Second, we demonstrate the application to a follow object controller for vehicles and accomplish safe reinforcement learning in this case. In both experiments, ConstraintNet improves performance and we conclude that our approach is promising for applying neural networks in safety-critical environments.

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Chocat, Rudy, Loïc Brevault, Mathieu Balesdent, and Sébastien Defoort. "Modified Covariance Matrix Adaptation – Evolution Strategy algorithm for constrained optimization under uncertainty, application to rocket design." International Journal for Simulation and Multidisciplinary Design Optimization 6 (2015): A1. http://dx.doi.org/10.1051/smdo/2015001.

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The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ) optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.

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Angantyr, Anders, and Jan-Olov Aidanpää. "Constrained Optimization of Gas Turbine Tilting Pad Bearing Designs." Journal of Engineering for Gas Turbines and Power 128, no. 4 (2005): 873–78. http://dx.doi.org/10.1115/1.2179463.

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This paper presents the constrained optimization of the tilting pad bearing design on a gas turbine rotor system. A real coded genetic algorithm with a robust constraint handling technique is used as the optimization method. The objective is to develop a formulation of the optimization problem for the late bearing design of a complex rotor-bearing system. Furthermore, the usefulness of the search method is evaluated on a difficult problem. The effects considered are power loss and limiting temperatures in the bearings as well as the dynamics at the system level, i.e., stability and unbalance responses. The design variables are the bearing widths and radial clearances. A nominal design is the basis for comparison of the optimal solution found. An initial numerical experiment shows that finding a solution that fulfills all the constraints for the system design is likely impossible. Still, the optimization shows the possibility of finding a solution resulting in a reduced power loss while not violating any of the constraints more than the nominal design. Furthermore, the result also shows that the used search method and constraint handling technique works on this difficult problem.

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Cinar, Ahmet, and Mustafa Kiran. "The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Problems." International Arab Journal of Information Technology 17, no. 5 (2020): 799–807. http://dx.doi.org/10.34028/iajit/17/5/13.

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The constraints are the most important part of many optimization problems. The metaheuristic algorithms are designed for solving continuous unconstrained optimization problems initially. The constraint handling methods are integrated into these algorithms for solving constrained optimization problems. Penalty approaches are not only the simplest way but also as effective as other constraint handling techniques. In literature, there are many penalty approaches and these are grouped as static, dynamic and adaptive. In this study, we collect them and discuss the key benefits and drawbacks of these techniques. Tree-Seed Algorithm (TSA) is a recently developed metaheuristic algorithm, and in this study, nine different penalty approaches are integrated with the TSA. The performance of these approaches is analyzed on well-known thirteen constrained benchmark functions. The obtained results are compared with state-of-art algorithms like Differential Evolution (DE), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Genetic Algorithm (GA). The experimental results and comparisons show that TSA outperformed all of them on these benchmark functions

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DUCK, GREGORY J. "SMCHR: Satisfiability modulo constraint handling rules." Theory and Practice of Logic Programming 12, no. 4-5 (2012): 601–18. http://dx.doi.org/10.1017/s1471068412000208.

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AbstractConstraint Handling Rules (CHRs) are a high-level rule-based programming language for specification and implementation of constraint solvers. CHR manipulates a global store representing a flat conjunction of constraints. By default, CHR does not support goals with a more complex propositional structure including disjunction, negation, etc., or CHR relies on the host system to provide such features. In this paper we introduce Satisfiability Modulo Constraint Handling Rules (SMCHR): a tight integration of CHR with a modern Boolean Satisfiability (SAT) solver for quantifier-free formulae with an arbitrary propositional structure. SMCHR is essentially a Satisfiability Modulo Theories (SMT) solver where the theory T is implemented in CHR. The execution algorithm of SMCHR is based on lazy clause generation, where a new clause for the SAT solver is generated whenever a rule is applied. We shall also explore the practical aspects of building an SMCHR system, including extending a “built-in” constraint solver supporting equality with unification and justifications.

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HOLZBAUR, CHRISTIAN, MARIA GARCIA DE LA BANDA, PETER J. STUCKEY, and GREGORY J. DUCK. "Optimizing compilation of constraint handling rules in HAL." Theory and Practice of Logic Programming 5, no. 4-5 (2005): 503–31. http://dx.doi.org/10.1017/s1471068405002413.

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In this paper we discuss the optimizing compilation of Constraint Handling Rules (CHRs). CHRs are a multi-headed committed choice constraint language, commonly applied for writing incremental constraint solvers. CHRs are usually implemented as a language extension that compiles to the underlying language. In this paper we show how we can use different kinds of information in the compilation of CHRs to obtain access efficiency, and a better translation of the CHR rules into the underlying language, which in this case is HAL. The kinds of information used include the types, modes, determinism, functional dependencies and symmetries of the CHR constraints. We also show how to analyze CHR programs to determine this information about functional dependencies, symmetries and other kinds of information supporting optimizations.

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Abdullah, Muhammad, John Anthony Rossiter, and Alia Farhana Abdul Ghaffar. "IMPROVED CONSTRAINT HANDLING APPROACH FOR PREDICTIVE FUNCTIONAL CONTROL USING AN IMPLIED CLOSED-LOOP PREDICTION." IIUM Engineering Journal 22, no. 1 (2021): 323–38. http://dx.doi.org/10.31436/iiumej.v22i1.1538.

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Predictive Functional Control is a simple alternative to the traditional PID controller which has the capability to handle process constraints more systematically. Nevertheless, the most basic form of PFC has suffered from ill-posed prediction due to its simplicity in formulation and assumption of constant future input dynamics. Although some constraints can be satisfied, nevertheless the performance may be very conservative due to this issue. The main objective of this paper is to improve the constrained performance of a PFC controller with a minimum modification of the existing formulation. Specifically, a novel constraint handling approach for PFC is proposed based on an implied closed-loop prediction. Instead of assuming a constant input as deployed in the conventional open-loop prediction, the implied closed-loop input dynamics are utilised to detect future constraint violations. In addition, a future perturbation is introduced into the prediction structure as an extra degree of freedom for satisfying the constraints. Two simulation results confirm that the proposed approach gives far less conservative constraint handling and thus better control performance compared to the nominal PFC. Furthermore, this novel implementation also alleviates the well-known tuning difficulties and prediction inconsistency issues that are associated with conventional PFC when handling constraints. ABSTRAK: Kawalan Kefungsian Ramalan adalah alternatif mudah kepada kawalan tradisional PID yang mempunyai kekangan keupayaan bagi mengawal proses secara lebih tersusun. Namun, keadaan paling asas pada kesan PFC adalah daripada ramalan tak teraju-rapi yang disebabkan oleh formula ringkas dan anggapan dinamik input yang sama bagi masa depan. Walau kekangan ini dapat diatasi, namun prestasi akan berubah secara konservatif disebabkan oleh isu ini. Objektif utama kajian ini adalah bagi membaiki kekangan prestasi kawalan PFC dengan modifikasi minimum formula yang ada. Secara spesifik, pendekatan nobel kawalan PFC dicadangkan berdasarkan ramalan lingkaran-tertutup. Selain anggapan input tetap seperti yang dilakukan pada ramalan lingkaran-terbuka yang konservatif, dinamik input yang dibuat pada lingkaran-tertutup telah digunakan bagi mengesan kekangan masa depan yang bertentangan. Tambahan, gangguan yang bakal berlaku pada masa depan telah diperkenalkan ke dalam struktur ramalan sebagai tambahan darjah pada kebebasan bagi mengatasi kekangan. Dua dapatan simulasi kajian menyetujui pendekatan yang dicadangkan dan menyebabkan sangat kurang kekangan pengendalian pada sistem konservatif, oleh itu kawalan yang lebih bagus pada prestasi berbanding pada PFC nominal. Selain itu, pendekatan nobel ini juga menghilangkan kesukaran pelarasan yang dikenali ramai dan ramalan isu tidak konsisten yang terdapat pada PFC konvensional apabila mengendali kekangan.

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Amin, Ruhul. "Handling Instance Spanning Constraints in Compliance Management." ABC Journal of Advanced Research 8, no. 2 (2019): 95–108. http://dx.doi.org/10.18034/abcjar.v8i2.522.

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Instance spanning constraints refers to instruments to establish controls during multiple instances in or several processes. Many business entities crave an established ISC support system. Take, for instance, the bundling and unbundling of cargo from various logistics processes or the dependence of various examinations in medical treatment systems. During such systems, non-compliance with the ISC would lead to immense consequences and penalties, which can be fatal if it occurs in the medical field. ISC can also occur from process execution logs. Business execution store execution information for the process instance and, consequently, the characteristics of the execution logs. Discovering ISC early enough helps in supporting ISC design and execution. The purpose of this study is to contribute towards the categorization of the ISC and hence contribute to the digitalized ISC and its compliance management.

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Byrne, A., M. Sniedovich, and L. Churilov. "Handling Soft Constraints via Composite Concave Programming." Journal of the Operational Research Society 49, no. 8 (1998): 870. http://dx.doi.org/10.2307/3009968.

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Mérigot, Quentin, and Édouard Oudet. "Handling Convexity-Like Constraints in Variational Problems." SIAM Journal on Numerical Analysis 52, no. 5 (2014): 2466–87. http://dx.doi.org/10.1137/130938359.

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Luus, Rein, Kelly Sabaliauskas, and Ihor Harapyn. "Handling inequality constraints in direct search optimization." Engineering Optimization 38, no. 4 (2006): 391–405. http://dx.doi.org/10.1080/03052150500431642.

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Byrne, A., M. Sniedovich, and L. Churilov. "Handling soft constraints via composite concave programming." Journal of the Operational Research Society 49, no. 8 (1998): 870–77. http://dx.doi.org/10.1057/palgrave.jors.2600592.

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Zheng, Xu, Jianzhong Li, and Hong Gao. "Handling Interservice Time Constraints in Wireless Networks." International Journal of Distributed Sensor Networks 11, no. 8 (2015): 280109. http://dx.doi.org/10.1155/2015/280109.

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Gray, Jeff, Ted Bapty, Sandeep Neema, and James Tuck. "Handling crosscutting constraints in domain-specific modeling." Communications of the ACM 44, no. 10 (2001): 87–93. http://dx.doi.org/10.1145/383845.383864.

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Liu, Hai-Lin, Chaoda Peng, Fangqing Gu, and Jiechang Wen. "A Constrained Multi-Objective Evolutionary Algorithm Based on Boundary Search and Archive." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 01 (2015): 1659002. http://dx.doi.org/10.1142/s0218001416590023.

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In this paper, we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problems (CMOPs), named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. Moreover, a novel constraint handling scheme based on the boundary search and archive is proposed. Each subproblem has one archive, including a subpopulation and a temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation, while the temporary register consists of those individuals ever found before. To improve the efficiency of the algorithm, the boundary search method is designed. This method makes the feasible individuals with a higher probability to perform genetic operator with the infeasible individuals. Especially, when the constraints are active at the Pareto solutions, it can play its leading role. Compared with two algorithms, i.e. CMOEA/D-DE-CDP and Gary’s algorithm, on 18 CMOPs, the results show the effectiveness of the proposed constraint handling scheme.

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Lv, Yongjing, Kaiwen Li, Hong Zhao, and Hongtao Lei. "A Multi-Stage Constraint-Handling Multi-Objective Optimization Method for Resilient Microgrid Energy Management." Applied Sciences 14, no. 8 (2024): 3253. http://dx.doi.org/10.3390/app14083253.

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In recent years, renewable energy has seen widespread application. However, due to its intermittent nature, there is a need to develop energy management systems for its scheduling and control. This paper introduces a multi-stage constraint-handling multi-objective optimization method tailored for resilient microgrid energy management. The microgrid encompasses diesel generators, energy storage systems, renewable energy sources, and various load types. The intelligent management of generators, batteries, switchable loads, and controllable loads ensures a reliable power supply for the critical loads. Beyond operational costs, our model also considers grid dependency as a key objective, making it particularly suited for energy management in extreme environments such as islands, border regions, and military bases. Managing complex controls of generators, batteries, switchable loads, and controllable loads presents challenging constraints that the management strategy must meet. To tackle this challenge, we propose an multi-objective optimization algorithm with multi-stage constraint-handling strategy to handle the high-dimensional complex constraints of the resilient energy management problem. Our proposed approach demonstrates superior performance compared to nine leading constrained multi-objective optimization algorithms across various test scenarios. Furthermore, the benefits of our method become increasingly evident as the complexity of the problem increases. Compared to the classical NSGA-II, the proposed NSGA-II-MC method achieved a 49.7% improvement in the Hypervolume metric on large-scale problems.

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Zhang, Kai, Siyuan Zhao, Hui Zeng, and Junming Chen. "Two-Stage Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization." Mathematics 13, no. 3 (2025): 470. https://doi.org/10.3390/math13030470.

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The core issue in handling constrained multi-objective optimization problems (CMOP) is how to maintain a balance between objectives and constraints. However, existing constrained multi-objective evolutionary algorithms (CMOEAs) often fail to achieve the desired performance when confronted with complex feasible regions. Building upon this theoretical foundation, a two-stage archive-based constrained multi-objective evolutionary algorithm (CMOEA-TA) based on genetic algorithms(GA) is proposed. In CMOEA-TA, First stage: The archive appropriately relaxes constraints based on the proportion of feasible solutions and constraint violations,compelling the population to explore more search space. Second stage: Sharing valuable information between the archive and the population, while embedding constraint dominance principles to enhance the feasibility of solutions. In addition an angle-based selection strategy was used to select more valuable solutions to increase the diversity of the population. To verify its effectiveness, CMOEA-TA was tested on 54 CMOPs in 4 benchmark suites and 7 state-of-the-art algorithms were compared. The experimental results show that it is far superior to seven competitors in inverse generation distance (IGD) and hypervolume (HV) metrics.

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Huang, Gang, Min Hu, Xueying Yang, Xun Wang, Yijun Wang, and Feiyao Huang. "A Review of Constrained Multi-Objective Evolutionary Algorithm-Based Unmanned Aerial Vehicle Mission Planning: Key Techniques and Challenges." Drones 8, no. 7 (2024): 316. http://dx.doi.org/10.3390/drones8070316.

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UAV mission planning is one of the core problems in the field of UAV applications. Currently, mission planning needs to simultaneously optimize multiple conflicting objectives and take into account multiple mutually coupled constraints, and traditional optimization algorithms struggle to effectively address these difficulties. Constrained multi-objective evolutionary algorithms have been proven to be effective methods for solving complex constrained multi-objective optimization problems and have been gradually applied to UAV mission planning. However, recent advances in this area have not been summarized. Therefore, this paper provides a comprehensive overview of this topic, first introducing the basic classification of UAV mission planning and its applications in different fields, proposing a new classification method based on the priorities of objectives and constraints, and describing the constraints of UAV mission planning from the perspectives of mathematical models and planning algorithms. Then, the importance of constraint handling techniques in UAV mission planning and their advantages and disadvantages are analyzed in detail, and the methods for determining individual settings in multiple populations and improvement strategies in constraint evolution algorithms are discussed. Finally, the method from the related literature is presented to compare in detail the application weights of constrained multi-objective evolutionary algorithms in UAV mission planning and provide directions and references for future research.

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Bian, Chao, Qinglong Liu, Xuan Zhang, et al. "An efficient mixed constrained Bayesian optimization for handling known and unknown constraints." Advanced Engineering Informatics 62 (October 2024): 102704. http://dx.doi.org/10.1016/j.aei.2024.102704.

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Liu, Linzhong, Haibo Mu, and Juhua Yang. "Generic constraints handling techniques in constrained multi-criteria optimization and its application." European Journal of Operational Research 244, no. 2 (2015): 576–91. http://dx.doi.org/10.1016/j.ejor.2015.01.051.

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HOTHAZIE, Mihai-Vladut, Georgiana ICHIM, and Mihai-Victor PRICOP. "Development and validation of constraints handling in a Differential Evolution optimizer." INCAS BULLETIN 12, no. 1 (2020): 59–66. http://dx.doi.org/10.13111/2066-8201.2020.12.1.6.

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Research work requires independent, portable optimization tools for many applications, most often for problems where derivability of objective functions is not satisfied. Differential evolution optimization represents an alternative to the more complex, encryption based genetic algorithms. Various packages are available as freeware, but they lack constraints handling, while constrained optimizations packages are commercially available. However, the literature devoted to constraints treatment is significant and the current work is devoted to the implementation of such an optimizer, to be applied in low-fidelity optimization processes. The parameter free penalty scheme is adopted for implementation, and the code is validated against the CEC2006 benchmark test problems and compared with the genetic algorithm in MATLAB. Our paper underlines the implementation of constrained differential evolution by varying two parameters, a predefined parameter for feasibility and the scaling factor, to ensure the convergence of the solution.

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Kulkarni, Anand J., and K. Tai. "A Probability Collectives Approach with a Feasibility-Based Rule for Constrained Optimization." Applied Computational Intelligence and Soft Computing 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/980216.

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This paper demonstrates an attempt to incorporate a simple and generic constraint handling technique to the Probability Collectives (PC) approach for solving constrained optimization problems. The approach of PC optimizes any complex system by decomposing it into smaller subsystems and further treats them in a distributed and decentralized way. These subsystems can be viewed as a Multi-Agent System with rational and self-interested agents optimizing their local goals. However, as there is no inherent constraint handling capability in the PC approach, a real challenge is to take into account constraints and at the same time make the agents work collectively avoiding the tragedy of commons to optimize the global/system objective. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. Moreover, a rule-based procedure is incorporated to handle solutions based on the number of constraints violated and drive the convergence towards feasibility. Two specially developed cases of the Circle Packing Problem with known solutions are solved and the true optimum results are obtained at reasonable computational costs. The proposed algorithm is shown to be sufficiently robust, and strengths and weaknesses of the methodology are also discussed.

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Abdullah, Mohd Noor, A. H. A. Bakar, Hazlie Mokhlis, and Jasrul Jamani Jamian. "An Efficient Constraint Handling Approach for Economic Load Dispatch Problem with Non-Smooth Cost Function." Applied Mechanics and Materials 785 (August 2015): 490–94. http://dx.doi.org/10.4028/www.scientific.net/amm.785.490.

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Increasing of the power demand and fuel cost in power generation required an advanced algorithm for scheduling the output of generating unit in economical manner. The economic load dispatch problem (ELD) problem consists several operational and system constraints such as prohibited operating zones (POZs) and ramp-rate limit that need to handle wisely by optimization algorithm. Previously, the penalty function is widely used to satisfy the power balance and other constraints by augmenting the objective function with the penalized function. However, it required a proper penalty factor tuning and depends on the size of problem. This paper proposes an efficient constraint handling based on the repairing or adjusting infeasible solution into feasible solution in every iterative process. The simulation results show that the proposed constraints handling approach is better than penalty function approach in term of convergence characteristic and robustness.

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Rosso, Marco M., Raffaele Cucuzza, Fabio Di Trapani, and Giuseppe C. Marano. "Nonpenalty Machine Learning Constraint Handling Using PSO-SVM for Structural Optimization." Advances in Civil Engineering 2021 (February 15, 2021): 1–17. http://dx.doi.org/10.1155/2021/6617750.

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Firstly formulated to solve unconstrained optimization problems, the common way to solve constrained ones with the metaheuristic particle swarm optimization algorithm (PSO) is represented by adopting some penalty functions. In this paper, a new nonpenalty-based constraint handling approach for PSO is implemented, adopting a supervised classification machine learning method, the support vector machine (SVM). Because of its generality, constraint handling with SVM appears more adaptive both to nonlinear and discontinuous boundary. To preserve the feasibility of the population, a simple bisection algorithm is also implemented. To improve the search performances of the algorithm, a relaxation function of the constraints is also adopted. In the end part of this paper, two numerical literature benchmark examples and two structural examples are discussed. The first structural example refers to a homogeneous constant cross-section simply supported beam. The second one refers to the optimization of a plane simply supported Warren truss beam. The obtained results in terms of objective function demonstrate that this new approach represents a valid alternative to solve constrained optimization problems even in structural optimization field. Furthermore, as demonstrated by the Warren truss beam problem, this new algorithm provides an optimal structural design which represents also a good solution from the technical point of view with a trivial rounding-off that does not jeopardize significantly the optimization design process.

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