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Journal articles on the topic 'Epsilon-Constraint'

Author: Grafiati

Published: 21 February 2024

Last updated: 19 July 2025

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Bai, Qinbo, Amrit Singh Bedi, Mridul Agarwal, Alec Koppel, and Vaneet Aggarwal. "Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Primal-Dual Approach." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 3682–89. http://dx.doi.org/10.1609/aaai.v36i4.20281.

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Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety constraints. The problem is mathematically formulated as constrained Markov decision process (CMDP). In the literature, various algorithms are available to solve CMDP problems in a model-free manner to achieve epsilon-optimal cumulative reward with epsilon feasible policies. An epsilon-feasible policy implies that it suffers from constraint violation. An important question here is whether we can achieve epsilon-optimal cumulative reward with zero constraint violations or not. To achieve that, we advocate the use of a randomized primal-dual approach to solve the CMDP problems and propose a conservative stochastic primal-dual algorithm (CSPDA) which is shown to exhibit O(1/epsilon^2) sample complexity to achieve epsilon-optimal cumulative reward with zero constraint violations. In the prior works, the best available sample complexity for the epsilon-optimal policy with zero constraint violation is O(1/epsilon^5). Hence, the proposed algorithm provides a significant improvement compared to the state of the art.

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Kai, Liu, and Ramina Malekalipour Kordestanizadeh. "Designing an Agile Closed-Loop Supply Chain with Environmental Aspects Using a Novel Multiobjective Metaheuristic Algorithm." Mathematical Problems in Engineering 2021 (November 2, 2021): 1–13. http://dx.doi.org/10.1155/2021/3811417.

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Success in supply chain implementation depends on the way of dealing with market changes and customer needs. Agility is a concept that has been introduced in recent years to improve the supply chain. On the other hand, paying attention to environmental problems is another issue, and chains are trying to increase their popularity by focusing on this issue. Considering the importance of this issue, designing a multiobjective closed-loop supply chain network has been discussed in this research. The main contribution of this research is the integration of green and agility concepts in supply chain design. In this regard, a mathematical model is presented with economic, environmental, and agility objectives. First, the mathematical model is solved using the Epsilon constraint method, and then, the multiobjective weed algorithm is proposed to solve the model. The results of comparisons between the two methods show that the multiobjective weed algorithm has performed well in terms of various metrics of NPS, SNS, and Max Spread. In terms of the solving time, the average solving time of this algorithm was about 0.1% of the solving time of the Epsilon constraint method. Moreover, all cases show the superiority of the multiobjective weed algorithm over the Epsilon constraint method in solving the proposed mathematical model.

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Feng, Songtao, Michael Dorothy, and Jie Fu. "Learning Nash Equilibrium of Markov Potential Games with a Shared Constraint via Primal-Dual Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 16 (2025): 16577–85. https://doi.org/10.1609/aaai.v39i16.33821.

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The problem of constrained Markov game has recently attracted interests in the study of multi-agent reinforcement learning (MARL). The existing literature has focused on safe MARL problems where safety constraints are imposed for each agent individually. In this work, we consider Markov potential game (MPG) with a shared constraint, where the cost function with respect to the constraint depends on states and joint actions of all agents. We adopt a primal-dual framework to tackle the problem and establish the Slater condition to ensure the strong duality. Moreover, we propose our primal-dual learning algorithm for learning approximate Nash equilibrium in MPG with shared constraint. Thanks to the novel design of the dual update, we provide asymptotic convergence on the weighted output policy. Specifically, we prove that both the value function gap and the constraint violation of the output policy converge at the rate O(epsilon+1/sqrt(T)), where epsilon is the accuracy level of the primal update, and T is the number of iterations. We further show that the weighted output policy outperforms the existing uniformly chosen policy.

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Stanovov, Vladimir, Shakhnaz Akhmedova, and Eugene Semenkin. "Combined fitness–violation epsilon constraint handling for differential evolution." Soft Computing 24, no. 10 (2020): 7063–79. http://dx.doi.org/10.1007/s00500-020-04835-6.

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Mahdi, parvizi Elham Shadkam and Niloofar jahani. "A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS". International Journal on Foundations of Computer Science & Technology (IJFCST) 5, № 5 (2023): 14. https://doi.org/10.5281/zenodo.8143468.

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In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.

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Pérez‐Cañedo, Boris, José Luis Verdegay, and Ridelio Miranda Pérez. "An epsilon‐constraint method for fully fuzzy multiobjective linear programming." International Journal of Intelligent Systems 35, no. 4 (2020): 600–624. http://dx.doi.org/10.1002/int.22219.

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Jin, Bangti, Buyang Li, and Zhi Zhou. "Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint." IMA Journal of Numerical Analysis 40, no. 1 (2018): 377–404. http://dx.doi.org/10.1093/imanum/dry064.

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Abstract In this work we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation that involves a fractional derivative of order $\alpha \in (0,1)$ in time. The fully discrete scheme is obtained by applying the conforming linear Galerkin finite element method in space, L1 scheme/backward Euler convolution quadrature in time, and the control variable by a variational-type discretization. With a space mesh size $h$ and time stepsize $\tau $ we establish the following order of convergence for the numerical solutions of the optimal control problem: $O(\tau ^{\min ({1}/{2}+\alpha -\epsilon ,1)}+h^2)$ in the discrete $L^2(0,T;L^2(\varOmega ))$ norm and $O(\tau ^{\alpha -\epsilon }+\ell _h^2h^2)$ in the discrete $L^{\infty }(0,T;L^2(\varOmega ))$ norm, with any small $\epsilon&gt;0$ and $\ell _h=\ln (2+1/h)$. The analysis relies essentially on the maximal $L^p$-regularity and its discrete analogue for the subdiffusion problem. Numerical experiments are provided to support the theoretical results.

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Bozoklar, Emine, and Ebru Yılmaz. "Designing Sustainable Flexible Manufacturing Cells with Multi-Objective Optimization Models." Applied Sciences 14, no. 1 (2023): 203. http://dx.doi.org/10.3390/app14010203.

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Having sustainable and flexible features is crucial for manufacturing companies considering the increasing competition in the globalized world. This study considers three aspects of sustainability, namely economic, social, and environmental factors, in the design of flexible manufacturing cells. Three different multi-objective integer mathematical programming models were developed with the objective of minimizing the costs associated with carbon emissions, inter-cellular movements, machine processing, machine replacement, worker training, and additional salary (bonus). Simultaneously, these models aim to minimize the carbon emission amount of the cells within the environmental dimension scope. The developed models are a goal programming model, an epsilon constraint method, and an augmented epsilon constraint (AUGMECON) method. In these models, alternative routes of parts are considered while assigning parts to machines. The results are obtained using the LINGO 20.0 optimization program with a developed illustrative example. The obtained results are tested and compared by performing sensitivity analyses. The sensitivity analyses include examinations of the effects of changes in part demands, machine capacity values, carbon limit value, and the maximum number of workers in cells.

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Estrin, Ron, and Michael P. Friedlander. "A perturbation view of level-set methods for convex optimization." Optimization Letters 14, no. 8 (2020): 1989–2006. http://dx.doi.org/10.1007/s11590-020-01609-9.

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Abstract Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $$\epsilon $$ ϵ -infeasible points that do not converge to a feasible point as $$\epsilon $$ ϵ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater’s constraint qualification.

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Mavalizadeh, Hani, and Abdollah Ahmadi. "Hybrid expansion planning considering security and emission by augmented epsilon-constraint method." International Journal of Electrical Power & Energy Systems 61 (October 2014): 90–100. http://dx.doi.org/10.1016/j.ijepes.2014.03.004.

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Tartibu, L. K., B. Sun, and M. A. E. Kaunda. "Optimal design study of thermoacoustic regenerator with lexicographic optimization method." Journal of Engineering, Design and Technology 13, no. 3 (2015): 499–519. http://dx.doi.org/10.1108/jedt-09-2012-0039.

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Purpose – This paper aims to illustrate the use of the augmented epsilon-constraint method implemented in general algebraic modelling system (GAMS), aimed at optimizing the geometry of a thermoacoustic regenerator. Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be produced. However, the most inhibiting characteristic of thermoacoustic cooling is their current lack of efficiencies. Design/methodology/approach – Lexicographic optimization is presented as an alternative optimization technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimization objectives instead of giving them a specific (and most of the time, arbitrary) weight. Findings – A practical example is given, in a hypothetical scenario, showing how the proposed optimization technique may help thermoacoustic regenerator designers to identify Pareto optimal solutions when dealing with geometric parameters. This study highlights the fact that the geometrical parameters are interdependent, which support the use of a multi-objective approach for optimization in thermoacoustic. Originality/value – The research output from this paper can be a valuable resource to support designers in building efficient thermoacoustic device. The research illustrates the use of a lexicographic optimization to provide more meaningful results describing the geometry of thermoacoustic regenerator. It applies the epsilon-constraint method (AUGMENCON) to solve a five-criteria mixed integer non-linear problem implemented in GAMS (GAM software).

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Ghasemzadeh, Esmat, Mohammadali Keramati, Safia Mehrinejad, and Azade Mehrani. "Presenting an Optimization Model for Fintech Based on Artificial Intelligence Indices in the Financial Market." Journal of Technology in Entrepreneurship and Strategic Management 2, no. 4 (2023): 69–84. http://dx.doi.org/10.61838/kman.jtesm.2.4.7.

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The aim of this research is to present an optimization model for fintech based on artificial intelligence indices in the financial market. This research is exploratory in nature due to the model presentation and is considered applied since its results are utilized by stakeholders. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed as a metaheuristic method to solve nine problem simulations. The results obtained from this method were then compared with the epsilon-constraint method, and the relationship between the solutions indicated that the developed NSGA-II algorithm is capable of reaching appropriate solutions in a shorter time compared to the epsilon-constraint method, particularly for large-scale problem tests. The outcomes from solving the proposed mathematical model through the presented nine problem simulations were solved using the specified algorithms in GAMS and MATLAB software. The model considered in this research is a bi-objective model aimed at minimizing inter-cell movements and fintech purchases (cell formation) and maximizing the relationships of AI operators with network considerations and operator efficiency on fintechs (operator allocation). This model not only improves the efficiency of fintechs but also provides a novel and effective approach to adapting to various challenges in the financial market. Therefore, utilizing this optimization model can enhance performance and profitability in the financial market and contribute to development and progress in the financial space.

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Agud-Albesa, Lucia, Neus Garrido, Angel A. Juan, Almudena Llorens, and Sandra Oltra-Crespo. "A Weighted and Epsilon-Constraint Biased-Randomized Algorithm for the Biobjective TOP with Prioritized Nodes." Computation 12, no. 4 (2024): 84. http://dx.doi.org/10.3390/computation12040084.

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This paper addresses a multiobjective version of the Team Orienteering Problem (TOP). The TOP focuses on selecting a subset of customers for maximum rewards while considering time and fleet size constraints. This study extends the TOP by considering two objectives: maximizing total rewards from customer visits and maximizing visits to prioritized nodes. The MultiObjective TOP (MO-TOP) is formulated mathematically to concurrently tackle these objectives. A multistart biased-randomized algorithm is proposed to solve MO-TOP, integrating exploration and exploitation techniques. The algorithm employs a constructive heuristic defining biefficiency to select edges for routing plans. Through iterative exploration from various starting points, the algorithm converges to high-quality solutions. The Pareto frontier for the MO-TOP is generated using the weighted method, epsilon-constraint method, and Epsilon-Modified Method. Computational experiments validate the proposed approach’s effectiveness, illustrating its ability to generate diverse and high-quality solutions on the Pareto frontier. The algorithms demonstrate the ability to optimize rewards and prioritize node visits, offering valuable insights for real-world decision making in team orienteering applications.

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Panteleev, A. V., and N. S. Popova. "Development and Application of a Multi-Objective Ant Colony Op-timization Method for Portfolio Problem." Моделирование и анализ данных 14, no. 2 (2024): 80–97. http://dx.doi.org/10.17759/mda.2024140205.

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<p>A numerical method of multi-objective optimization is proposed for an approximate solution of the problem based on the generation of feasible solutions using the continuous ant colony method, non-dominated sorting and the epsilon-constraint technique. Solving a problem means finding the Pareto front. Solutions of typical model examples are given. The applied problem of optimizing an investment portfolio has been solved, in which the initial data are the tabulated average returns and covariance of stocks.</p>

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Zhou, Jinlong, Juan Zou, Jinhua Zheng, Shengxiang Yang, Dunwei Gong, and Tingrui Pei. "An infeasible solutions diversity maintenance epsilon constraint handling method for evolutionary constrained multiobjective optimization." Soft Computing 25, no. 13 (2021): 8051–62. http://dx.doi.org/10.1007/s00500-021-05880-5.

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Laumanns, Marco, Lothar Thiele, and Eckart Zitzler. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method." European Journal of Operational Research 169, no. 3 (2006): 932–42. http://dx.doi.org/10.1016/j.ejor.2004.08.029.

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Pirouz, Behzad, and Esmaile Khorram. "A COMPUTATIONAL APPROACH BASED ON THE \epsilon-CONSTRAINT METHOD IN MULTI-OBJECTIVE OPTIMIZATION PROBLEMS." Advances and Applications in Statistics 49, no. 6 (2016): 453–83. http://dx.doi.org/10.17654/as049060453.

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Stoilova, Svetla. "An Integrated Multi-Criteria and Multi-Objective Optimization Approach for Establishing the Transport Plan of Intercity Trains." Sustainability 12, no. 2 (2020): 687. http://dx.doi.org/10.3390/su12020687.

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The development of the transport plan must take into account various criteria impacting the transport process. The main objective of the study is to propose an integrated approach to determine the transport plan of passenger trains. The methodology consists of five steps. In the first step, the criteria for optimization of the transport plan were defined. In the second step, variants of the transport plan were formulated. In the third step, the weights of the criteria are determined by applying the step-wise weight assessment ratio analysis method (SWARA) multi-criteria method. The multi-objective optimization was conducted in the fourth step. The following multi-objective optimization approaches were used and compared: weighted sum method (WSM), compromise programming method (CP), and the epsilon–constraint method (EC). The study proposes a modified epsilon–constraint method (MEC) by applying normalization of each objective function according to the maximal value of the solution by individual optimization for each objective function, and hybrid methods: hybrid WSM and EC, hybrid WSM and MEC, hybrid CP and EC, and Hybrid CP and MEC. The impact of the variation of passenger flows on the choice of an optimal transport plan was studied in the fifth step. The Laplace’s criterion, Hurwitz’s criterion, and Savage’s criterion were applied to come to a decision. The approbation of the methodology was demonstrated through the case study of Bulgaria’s railway network. Suitable variant of transport plan is proposed.

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Cao, Huizhuo, Xuemei Li, Vikrant Vaze, and Xueyan Li. "Multi-Objective Pricing Optimization for a High-Speed Rail Network Under Competition." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 7 (2019): 215–26. http://dx.doi.org/10.1177/0361198119842817.

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Multi-objective pricing of high-speed rail (HSR) passenger fares becomes a challenge when the HSR operator needs to deal with multiple conflicting objectives. Although many studies have tackled the challenge of calculating the optimal fares over railway networks, none of them focused on characterizing the trade-offs between multiple objectives under multi-modal competition. We formulate the multi-objective HSR fare optimization problem over a linear network by introducing the epsilon-constraint method within a bi-level programming model and develop an iterative algorithm to solve this model. This is the first HSR pricing study to use an epsilon-constraint methodology. We obtain two single-objective solutions and four multi-objective solutions and compare them on a variety of metrics. We also derive the Pareto frontier between the objectives of profit and passenger welfare to enable the operator to choose the best trade-off. Our results based on computational experiments with Beijing–Shanghai regional network provide several new insights. First, we find that small changes in fares can lead to a significant improvement in passenger welfare with no reduction in profitability under multi-objective optimization. Second, multi-objective optimization solutions show considerable improvements over the single-objective optimization solutions. Third, Pareto frontier enables decision-makers to make more informed decisions about choosing the best trade-offs. Overall, the explicit modeling of multiple objectives leads to better pricing solutions, which have the potential to guide pricing decisions for the HSR operators.

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Fan, Zhun, Wenji Li, Xinye Cai, et al. "An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions." Soft Computing 23, no. 23 (2019): 12491–510. http://dx.doi.org/10.1007/s00500-019-03794-x.

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Farizal, R. M. Dewi, and D. S. Gabriel. "Supplier evaluation and order allocation using fuzzy analytical hierarchy process and augmented epsilon constraint methods." IOP Conference Series: Materials Science and Engineering 567 (August 15, 2019): 012035. http://dx.doi.org/10.1088/1757-899x/567/1/012035.

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Du, Yawei, Lixin Xie, Jie Liu, Yuxin Wang, Yingjun Xu, and Shichang Wang. "Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method." Desalination 333, no. 1 (2014): 66–81. http://dx.doi.org/10.1016/j.desal.2013.10.028.

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Lolagari, Hossein, Amir Daneshvar, Mahdi Madanchi Zaj, and Fereydon Rahnamay Roodposhti. "Sustainable Financing Model considering Project Risk." Discrete Dynamics in Nature and Society 2022 (September 7, 2022): 1–19. http://dx.doi.org/10.1155/2022/2838913.

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Implementing various projects in each country leads to the development of that country. The necessity of implementing any project is to finance that project through different methods. In this regard, the cost of financing projects, determining the amount of financing from each technique, and the risk of financing projects are among the things that have caused problems for managers and decision makers. This study presents a new sustainable financing model for international projects in Iran. The main objectives are to minimize the financing cost and risk of funding the projects. Based on the proposed conceptual model based on fuzzy hierarchy analysis, it was observed that Iran’s economic conditions, with a weight coefficient of 0.34, have the highest risk in financing projects. Therefore, a two-objective model was designed by determining the weighting coefficients to reduce costs and financing risks. Additionally, the epsilon constraint methods and NSGA II algorithm were used. Comparative results between the two algorithms show that financing projects must be changed to reduce the risk of sustainable financing of international projects, which can lead to an increase in the total cost of financing projects. On the other hand, it was observed that the NSGA II algorithm obtained 32 efficient answers (a combination of how projects are financed). Each of the received answers has advantages over the other solutions obtained. The epsilon constraint method also brought 11 efficient answers, demonstrating that the domestic capital market can provide 54.89% of the deficit budget of the country’s international projects. Furthermore, 44.81% of the project deficit budget can be financed from a foreign bank loan source, and only 0.2% of the budget can be funded through the company’s internal resources.

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Herrero, J. M., G. Reynoso-Meza, M. Martínez, X. Blasco, and J. Sanchis. "A Smart-Distributed Pareto Front Using the ev-MOGA Evolutionary Algorithm." International Journal on Artificial Intelligence Tools 23, no. 02 (2014): 1450002. http://dx.doi.org/10.1142/s021821301450002x.

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Obtaining multi-objective optimization solutions with a small number of points smartly distributed along the Pareto front is a challenge. Optimization methods, such as the normalized normal constraint (NNC), propose the use of a filter to achieve a smart Pareto front distribution. The NCC optimization method presents several disadvantages related with the procedure itself, initial condition dependency, and computational burden. In this article, the epsilon-variable multi-objective genetic algorithm (ev-MOGA) is presented. This algorithm characterizes the Pareto front in a smart way and removes the disadvantages of the NNC method. Finally, examples of a three-bar truss design and controller tuning optimizations are presented for comparison purposes.

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Asamba, Samwel O. "Conditions for Convex Optimization in $L^p$-Spaces." Journal of Advances in Mathematics and Computer Science 40, no. 4 (2025): 90–96. https://doi.org/10.9734/jamcs/2025/v40i41991.

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This paper establishes the optimality conditions for convex optimization in $L^p$-spaces. We prove that if a lower semi-continuous function $\vartheta$ : L $\rightarrow$ $\mathbb{R}$ is Lipschitz continuous in an $L^p$-space L, then it is weakly lower semi-continuous and must attain a unique global minimizer for the convex optimization problem $\frac{min}{q{\epsilon}G}$ $\vartheta$(q) on a sequentially bounded convex constraint set . We also provide further necessary conditions for optimality using the concepts of compactness and coercivity of semi-continuous functions on sequentially bounded domains. Additionally, we prove the existence of minimizers using the concepts of Gateux and Frchet differentiability.

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Hanson, Brandon, Misha Rudnev, Ilya Shkredov, and Dmitrii Zhelezov. "The sum-product problem for integers with few prime factors." Compositio Mathematica 161, no. 3 (2025): 427–46. https://doi.org/10.1112/s0010437x24007735.

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Abstract It was asked by E. Szemerédi if, for a finite set $A\subset {\mathbb {Z}}$ , one can improve estimates for $\max \{|A+A|,|A\cdot A|\}$ , under the constraint that all integers involved have a bounded number of prime factors, that is, each $a\in A$ satisfies $\omega (a)\leq k$ . In this paper we show that this maximum is at least of order $|A|^{\frac {5}{3}-o_\epsilon (1)}$ provided $k\leq (\log |A|)^{1-\varepsilon }$ for any $\varepsilon \gt 0$ . In fact, this will follow from an estimate for additive energy which is best possible up to factors of size $|A|^{o(1)}$ .

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Abdelaziz, Fouad Ben, Mohamed Amer, and Hazim El-Baz. "An Epsilon Constraint Method for selecting Indicators for use in Neural Networks for Stock Market Forecasting." INFOR: Information Systems and Operational Research 52, no. 3 (2014): 116–25. http://dx.doi.org/10.3138/infor.52.3.116.

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Aghaei, J., N. Amjady, and H. A. Shayanfar. "Multi-objective electricity market clearing considering dynamic security by lexicographic optimization and augmented epsilon constraint method." Applied Soft Computing 11, no. 4 (2011): 3846–58. http://dx.doi.org/10.1016/j.asoc.2011.02.022.

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Ostovari, Alireza, Lyes Benyoucef, Hichem Haddou Benderbal, and Xavier Delorme. "Multi-Objective Workforce and Process Planning For Socio-Economic Sustainable RMS: Lp-metric vs Epsilon Constraint." Procedia Computer Science 232 (2024): 456–64. http://dx.doi.org/10.1016/j.procs.2024.01.045.

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Cui, Shuang, Kai Han, Jing Tang, He Huang, Xueying Li, and Aakas Zhiyuli. "Practical Parallel Algorithms for Submodular Maximization Subject to a Knapsack Constraint with Nearly Optimal Adaptivity." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (2023): 7261–69. http://dx.doi.org/10.1609/aaai.v37i6.25885.

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Submodular maximization has wide applications in machine learning and data mining, where massive datasets have brought the great need for designing efficient and parallelizable algorithms. One measure of the parallelizability of a submodular maximization algorithm is its adaptivity complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose the first combinatorial algorithm achieving an (8+epsilon)-approximation under O(log n) adaptive complexity, which is optimal up to a factor of O(loglog n). Moreover, under slightly larger adaptivity, we also propose approximation algorithms with nearly optimal query complexity of O(n), while achieving better approximation ratios. We show that our algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our approach is demonstrated by extensive experiments on real-world applications.

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Dwijendra, Ngakan Ketut Acwin, Muhaned Zaidi, I. Gusti Ngurah Kerta Arsana, et al. "A Multi-Objective Optimization Approach of Smart Autonomous Electrical Grid with Active Consumers and Hydrogen Storage System." Environmental and Climate Technologies 26, no. 1 (2022): 1067–79. http://dx.doi.org/10.2478/rtuect-2022-0080.

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Abstract In this paper, a multi objective optimization approach is studied for optimal energy scheduling of the smart autonomous electrical grid with participation of active consumers (ACs) and hydrogen storage system (HSS). The objective functions consist of: 1) minimizing the costs and 2) maximizing reliability. The ACs participation are modelled through demand reduction approach based on offer price to peak demand management. The proposed optimization is solved by epsilon-constraint method and LINMAP decision making strategy. The 21-node test system is employed to analyse the efficiency of the proposed approach at two case studies. The obtained results shown the high effectiveness of smart autonomous electrical grid with participation of ACs and HSS to supply the demand.

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Otsuki, Yu, Dan Li, Santanu S. Dey, Masahiro Kurata, and Yang Wang. "Finite element model updating of an 18-story structure using branch-and-bound algorithm with epsilon-constraint." Journal of Civil Structural Health Monitoring 11, no. 3 (2021): 575–92. http://dx.doi.org/10.1007/s13349-020-00468-3.

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Sreenu, Karnam, and Sreelatha Malempati. "MFGMTS: Epsilon Constraint-Based Modified Fractional Grey Wolf Optimizer for Multi-Objective Task Scheduling in Cloud Computing." IETE Journal of Research 65, no. 2 (2018): 201–15. http://dx.doi.org/10.1080/03772063.2017.1409087.

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Morabi, Zahra Sorayanezhad, Mohammad Saleh Owlia, Mahdi Bashiri, and Mohammad Hadi Doroudyan. "Multi-objective design of X¯ control charts with fuzzy process parameters using the hybrid epsilon constraint PSO." Applied Soft Computing 30 (May 2015): 390–99. http://dx.doi.org/10.1016/j.asoc.2015.01.065.

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Bıçakcı, İsmail, Yusuf Tansel İç, Esra Karasakal, and Berna Dengiz. "A Multi-Objective Mathematical Model for Level of Repair Analysis with Lead Times and Multi-Transportation Modes." International Journal of Information Technology & Decision Making 21, no. 01 (2021): 423–40. http://dx.doi.org/10.1142/s0219622021500632.

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In the event of failure of the product, level of repair analysis (LORA) is used to determine (1) whether the defective component should be discarded or repaired and (2) where this repair is made. In the literature, these repair operations are made with the aim of minimizing the total life cycle cost of the product. In this paper, we develop a multi-objective decision model that minimizes both the repair time (affected by lead times) and the repair costs. Our proposed model also considers the movement of the defective components to be performed by multiple transportation modes such as highway, railway, and airway. We use the epsilon constraint method to generate the Pareto frontier and analyze the trade-off between total repair costs and total repair time. We demonstrate the approach on an example problem.

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Alikhani, Masoomeh, and Hamed Fazlollahtabar. "A Mathematical Model for Optimizing Organizational Learning Capability." Advances in Operations Research 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/490210.

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Learning capability is the basis of evolution in every organization. Since the simplification and development of learning level in any organization seems to be necessary, in this paper we represent a mathematical model to maximize organizational learning capability. The proposed mathematical model focuses on required cost, labor, and capital, for implementation of ten effective factors on learning capability in different parts of an organization so that they are effective in learning capability with least cost for organization. To measure the factors in different parts of an organization some metrics are introduced. Computational tests confirm the effectiveness of the model. The model is optimized by epsilon constraint while it is multiobjective one. The validation of the model is also reported to emphasize the validity and applicability of the proposed methodology.

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Yuan, Yu, Pengcheng Wang, and Minghui Wang. "Multi-Objective Stochastic Synchronous Timetable Optimization Model Based on a Chance-Constrained Programming Method Combined with Augmented Epsilon Constraint Algorithm." Mathematical Problems in Engineering 2022 (August 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/9222636.

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The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.

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Villacrés, Ricardo, та Diego Carrión. "Optimizing Real and Reactive Power Dispatch Using a Multi-Objective Approach Combining the ϵ-Constraint Method and Fuzzy Satisfaction". Energies 16, № 24 (2023): 8034. http://dx.doi.org/10.3390/en16248034.

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Optimal power dispatch is essential to improve the power system’s safety, stability, and optimal operation. The present research proposes a multi-objective optimization methodology to solve the real and reactive power dispatch problem by minimizing the active power losses and generation costs based on mixed-integer nonlinear programming (MINLP) using the epsilon constraint method and fuzzy satisficing approach. The proposed methodology was tested on the IEEE 30-bus system, in which each objective function was modeled and simulated independently to verify the results with what is obtained via Digsilent Power Factory and then combined, which no longer allows for the simulation of Digsilent Power Factory. One of the main contributions was demonstrating that the proposed methodology is superior to the one available in Digsilent Power Factory, since this program only allows for the analysis of single-objective problems.

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Dwijendra, Ngakan Ketut Acwin, Wongchai Anupong, Ahmed Majed Althahabi, et al. "Optimal Dispatch of the Energy Demand in Electrical Distribution Grid with Reserve Scheduling." Environmental and Climate Technologies 27, no. 1 (2023): 80–91. http://dx.doi.org/10.2478/rtuect-2023-0007.

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Abstract The operation of the electrical systems is a major problem for electrical companies’ subject to uncertainties threatening. In this study, the optimal management of the energy demand in the electrical distribution grid is done by interval optimization approach under electrical price uncertainty. The management of the energy demand is implemented via incentive-based modelling of the demand response programs (DRPs). The incentive-based modelling as reserve, and based on bid price for reduction of the electrical demand at peak hours is proposed. The interval optimization approach is used for the minimization of the electrical price uncertainty effects. The main objective in the proposed approach is minimizing operation cost; epsilon-constraint method is utilized to solve the problem. Finally, an electrical distribution grid has been used at various case studies to numerical simulation results and positive effects of the proposed modelling under uncertainties.

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Jumintono, J., Mohammed Abdulkreem Salim, Ming-Hung Lin, Mohammed Hayder Alshalal, Muneam Hussein Ali, and Hassan Taher Braiber. "Multi-Criteria Problems of Energy Consumption in Buildings Considering Technical and Economic Indices." Environmental and Climate Technologies 27, no. 1 (2023): 379–90. http://dx.doi.org/10.2478/rtuect-2023-0028.

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Abstract This study focuses on economic modelling of the energy consumption in buildings considering controllable appliances scheduling in stand-alone electrical grids. The economic modelling is implemented via coordination of the energy generation of the renewable energies with controllable appliances by using demand shifting strategy (DSS). On the other side, uncertainty and stochastic modelling of the renewable energies are considered in the optimal coordination. Also, optimal coordination is modelled by multi-criteria problems of the technical and economic indices. Solving of the multi-criteria problem is done by fuzzy and augmented epsilon-constraint methods. To investigate the effectiveness of the proposed model, it is applied on a 25-node test system through defining two scenarios. The obtained results show that modelling the optimal coordination to supply the demand of the grid can increase the efficiency of the system.

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Le, Vu-anh, and Mehmet Dik. "Topology-Preserving Scaling in Data Augmentation." Maltepe Journal of Mathematics 7, no. 1 (2025): 9–26. https://doi.org/10.47087/mjm.1615296.

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We propose an algorithmic framework for dataset normalization in data augmentation pipelines that preserves topological stability under non-uniform scaling transformations. Given a finite metric space $ X \subset \mathbb{R}^n $ with Euclidean distance $ d_X $, we consider scaling transformations defined by scaling factors $ s_1, s_2, \ldots, s_n > 0 $. Specifically, we define a scaling function $ S $ that maps each point $ x = (x_1, x_2, \ldots, x_n) \in X $ to \[ S(x) = (s_1 x_1, s_2 x_2, \ldots, s_n x_n). \] Our main result establishes that the bottleneck distance $ d_B(D, D_S) $ between the persistence diagrams $ D $ of $ X $ and $ D_S $ of $ S(X) $ satisfies: \[ d_B(D, D_S) \leq (s_{\max} - s_{\min}) \cdot \operatorname{diam}(X), \] where $ s_{\min} = \min_{1 \leq i \leq n} s_i $, $ s_{\max} = \max_{1 \leq i \leq n} s_i $, and $ \operatorname{diam}(X) $ is the diameter of $ X $. Based on this theoretical guarantee, we formulate an optimization problem to minimize the scaling variability $ \Delta_s = s_{\max} - s_{\min} $ under the constraint $ d_B(D, D_S) \leq \epsilon $, where $ \epsilon > 0 $ is a user-defined tolerance. We develop an algorithmic solution to this problem, ensuring that data augmentation via scaling transformations preserves essential topological features. We further extend our analysis to higher-dimensional homological features, alternative metrics such as the Wasserstein distance, and iterative or probabilistic scaling scenarios. Our contributions provide a rigorous mathematical framework for dataset normalization in data augmentation pipelines, ensuring that essential topological characteristics are maintained despite scaling transformations.

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Agnoletto, Elian J., Daniel Silva de Castro, Rodolpho V. A. Neves, Ricardo Quadros Machado, and Vilma A. Oliveira. "An Optimal Energy Management Technique Using the $\epsilon$ -Constraint Method for Grid-Tied and Stand-Alone Battery-Based Microgrids." IEEE Access 7 (2019): 165928–42. http://dx.doi.org/10.1109/access.2019.2954050.

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Cao, Yan, Qiangfeng Wang, Jiang Du, Sayyad Nojavan, Kittisak Jermsittiparsert, and Noradin Ghadimi. "Optimal operation of CCHP and renewable generation-based energy hub considering environmental perspective: An epsilon constraint and fuzzy methods." Sustainable Energy, Grids and Networks 20 (December 2019): 100274. http://dx.doi.org/10.1016/j.segan.2019.100274.

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Attaran, Seyed Mohammad, Rubiyah Yusof, and Hazlina Selamat. "A novel optimization algorithm based on epsilon constraint-RBF neural network for tuning PID controller in decoupled HVAC system." Applied Thermal Engineering 99 (April 2016): 613–24. http://dx.doi.org/10.1016/j.applthermaleng.2016.01.025.

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Devi, S. Prasanna, S. Manivannan, and K. Suryaprakasa Rao. "Comparison of nongradient methods with hybrid Taguchi-based epsilon constraint method for multiobjective optimization of cylindrical fin heat sink." International Journal of Advanced Manufacturing Technology 63, no. 9-12 (2012): 1081–94. http://dx.doi.org/10.1007/s00170-012-3985-7.

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Esmaeel Nezhad, Ali, Abdollah Ahmadi, Mohammad Sadegh Javadi, and Mohammadreza Janghorbani. "Multi-objective decision-making framework for an electricity retailer in energy markets using lexicographic optimization and augmented epsilon-constraint." International Transactions on Electrical Energy Systems 25, no. 12 (2015): 3660–80. http://dx.doi.org/10.1002/etep.2059.

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Buss, Armands, Arturs Suleiko, Normunds Jekabsons, Juris Vanags, and Dagnija Loca. "Constraint Handling and Flow Control in Stirred Tank Bioreactors with Magnetically Coupled Impellers." Materials Science Forum 1071 (October 18, 2022): 189–96. http://dx.doi.org/10.4028/p-w35yei.

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In this study, Computational Fluid Dynamics (CFD), applied to a non-Newtonian fluid, was developed to characterize gas-liquid interaction and mixing process in a 15 m3 (working volume) bioreactor. The bioreactor was equipped with four arrangements of standard Rushton, Pitch-blade and Scaba® impellers. Gas-liquid hydrodynamics was estimated based on CFD results. The chosen operating conditions were defined by the settings used for production of xanthan gum via fermentation route by Xanthomonas campestris. The mixing process was simulated by using the k-epsilon turbulence model, Multiple Reference Frame and Population Balance Model approaches. The simulation results have been compared and analyzed by isosurfaces, volume fractions, velocity graphs, torques and flow analysis calculations. Obtained results revealed that for the Pitched-Pitched-Pitched arrangement to avoid the constraint-imposed overload torque limitations impeller diameter size should be reduced by 10%. The use of Rushton-Rushton-Rushton impeller arrangement was discouraged for non-Newtonian pseudoplastic fluid mixing, whereas Pitched-Rushton-Scaba and Scaba-Rushton-Pitched impeller arrangements were both acceptable.

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Shi, Wenjuan, Hongjun Liu, and Zhaolu Wang. "Polarization-Independent Large Third-Order-Nonlinearity of Orthogonal Nanoantennas Coupled to an Epsilon-Near-Zero Material." Nanomaterials 11, no. 12 (2021): 3424. http://dx.doi.org/10.3390/nano11123424.

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The nonlinear optical response of common materials is limited by bandwidth and energy consumption, which impedes practical application in all-optical signal processing, light detection, harmonic generation, etc. Additionally, the nonlinear performance is typically sensitive to polarization. To circumvent this constraint, we propose that orthogonal nanoantennas coupled to Al-doped zinc oxide (AZO) epsilon-near-zero (ENZ) material show a broadband (~1000 nm bandwidth) large optical nonlinearity simultaneously for two orthogonal polarization states. The absolute maximum value of the nonlinear refractive index n2 is 7.65 cm2∙GW−1, which is 4 orders of magnitude larger than that of the bare AZO film and 7 orders of magnitude larger than that of silica. The coupled structure not only realizes polarization independence and strong nonlinearity, but also allows the sign of the nonlinear response to be flexibly tailored. It provides a promising platform for the realization of ultracompact, low-power, and highly nonlinear all-optical devices on the nanoscale.

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Vaisi, Bahareh, Hiwa Farughi, and Sadigh Raissi. "Schedule-Allocate and Robust Sequencing in Three-Machine Robotic Cell under Breakdowns." Mathematical Problems in Engineering 2020 (October 30, 2020): 1–24. http://dx.doi.org/10.1155/2020/4597827.

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The purpose of this paper is to model two problems comprising schedule-allocate (in case of producing identical parts) and sequencing of parts (in case of producing different parts). The first model is used for minimizing the cycle time and operational cost, and the second one for minimizing both the mean and standard deviation of the total production cost as well the cycle time, in an unreliable three-machine robotic cell which confronted with many uncertainty factors. In the current article, mathematical modelling and simulation-based optimization method have been presented to schedule-allocate similar parts and trace the optimal sequence of different parts. Several solution procedures, including epsilon-constraint method and multiobjective particle swarm optimization algorithm, for identical parts case and response surface methodology for different parts case are applied. The results derived from solving numerical examples revealed some advantages in terms of time to attain the optimal solution.

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Praneetpholkrang, Panchalee, and Sarunya Kanjanawattana. "A Novel Approach for Determining Shelter Location-Allocation in Humanitarian Relief Logistics." International Journal of Knowledge and Systems Science 12, no. 2 (2021): 52–68. http://dx.doi.org/10.4018/ijkss.2021040104.

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This study proposes a methodology that integrates the epsilon constraint method (EC) and artificial neural network (ANN) to determine shelter location-allocation. Since shelter location-allocation is a critical part of disaster response stage, fast decision-making is very important. A multi-objective optimization model is formulated to simultaneously minimize total cost and minimize total evacuation time. The proposed model is solved by EC because it generates the optimal solutions without intervention of decision-makers during the solution process. However, EC requires intensive computational time, especially when dealing with large-scale data. Thus, ANN is combined with EC to facilitate prompt decision-making and address the complexity. Herein, ANN is supervised by the optimal solutions generated by EC. The applicability of the proposed methodology is demonstrated through a case study of shelter allocation in response to flooding in Surat Thani, Thailand. It is plausible to use this proposed methodology to improve disaster response for the benefit of victims and decision-makers.

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