Статті в журналах: "Minimisation problem"

1

Huy, N. Q., V. Jeyakumar, and G. M. Lee. "Sufficient global optimality conditions for multi-extremal smooth minimisation problems with bounds and linear matrix inequality constraints." ANZIAM Journal 47, no. 4 (April 2006): 439–50. http://dx.doi.org/10.1017/s1446181100010063.

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AbstractIn this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.

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2

Katzourakis, Nikos. "A minimisation problem in L∞ with PDE and unilateral constraints." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 60. http://dx.doi.org/10.1051/cocv/2019034.

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We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system and a prediction of the values of this solution. We pose this problem as a PDE-constrained minimisation problem for a supremal cost functional in L∞, where except for the PDE constraint there is also a unilateral constraint on the parameter. We utilise approximation by PDE-constrained minimisation problems in Lp as p →∞ and the generalised Kuhn-Tucker theory to derive the relevant variational inequalities in Lp and L∞. These results are motivated by the mathematical modelling of the novel bio-medical imaging method of Fluorescent Optical Tomography.

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3

Hawes, Matthew, and Wei Liu. "Design of Fixed Beamformers Based on Vector-Sensor Arrays." International Journal of Antennas and Propagation 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/181937.

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Vector-sensor arrays such as those composed of crossed dipole pairs are used as they can account for a signal’s polarisation in addition to the usual direction of arrival information, hence allowing expanded capacity of the system. The problem of designing fixed beamformers based on such an array, with a quaternionic signal model, is considered in this paper. Firstly, we consider the problem of designing the weight coefficients for a fixed set of vector-sensor locations. This can be achieved by minimising the sidelobe levels while keeping a unitary response for the main lobe. The second problem is then how to find a sparse set of sensor locations which can be efficiently used to implement a fixed beamformer. We propose solving this problem by converting the traditionall1norm minimisation associated with compressive sensing into a modifiedl1norm minimisation which simultaneously minimises all four parts of the quaternionic weight coefficients. Further improvements can be made in terms of sparsity by converting the problem into a series of iteratively solved reweighted minimisations, as well as being able to enforce a minimum spacing between active sensor locations. Design examples are provided to verify the effectiveness of the proposed design methods.

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4

Peldschus, Friedel. "RESEARCH ON THE SENSITIVITY OF MULTI- CRITERION EVALUATION METHODS/SENSIBILITÄTSUNTERSUCHUNGEN ZU METHODEN DER MEHRKRITERIELLEN ENTSCHEIDUNGEN." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 7, no. 4 (August 31, 2001): 276–80. http://dx.doi.org/10.3846/13921525.2001.10531736.

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Investigations into the multi-criterion evaluations have been performed for different purposes for more than 30 years. Nevertheless, up to now there are no common rules how to apply multi-criterion methods of evaluation and how to interpret their results. But the solutions of the problem must be found. The investigations are based on the joint programme LEVI developed by the VGTU and the Leipzig HSTEC. In accordance with the programme, for solving the problem a matrix is created in which all solution variants are evaluated by the same criteria. For the transformation of initial data different methods are used. Besides, the problem solution may be oriented to a choice of a variant and the determination of an optimal sequence or to the determination of the rational behaviour balance of two adversely interested groups. The maximisation, minimisation and mixed problems are distinguished. In case of the last mentioned problems the meanings may be unsuitable and expressions about the maximisation or minimisation too strong. When solving the problem of maximisation by different transformation methods, similar curves are obtained and the results are not dispersed heavily. In case of the minimisation, when solving according to different transformations, a considerable deviation of results has been noticed. The investigations also disclosed that solutions may vary depending on the optimisation goal. Dispersion of results in case of minimisation is stronger than in case of maximisation. When analysing different transformations, the vectorial transformation is regarded as “neutral” and there is no sense to include it into comparison. In case of the minimisation problem, linear transformations should be investigated in a more detailed way.

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5

Khrychev, Dmitry. "Optimal programmed control in energy minimisation problem." E3S Web of Conferences 458 (2023): 01028. http://dx.doi.org/10.1051/e3sconf/202345801028.

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This paper is devoted to the construction of optimal programmed control of the motion of a material point in a medium with a random coefficient of resistance in a homogeneous field of gravity of the Earth. The control objective is to minimise the mathematical expectation of the total mechanical energy of the material point. The problem is solved by two methods proposed by the author in previous works. Both methods assume approximation of the initial stochastic problem by deterministic optimal control problems. In the first case, the transition to approximate deterministic problems is carried out by replacing the parameters representing continuous random variables by discrete-type random variables converging in distribution to the original continuous ones (the method of distribution discretisation). The meaning of such a replacement is that the resulting approximate problem can be considered no longer as a stochastic, but as a deterministic optimal control problem, and can be solved, accordingly, with the help of known standard methods. In the second case, the initial stochastic dynamic system as a result of averaging its equations is replaced first by an infinite system and then, after zeroing all moments of sufficiently high order, by a finite system of equations for mixed moments of the solution and a random parameter (method of moments). The control functions and the optimal values of the quality functional obtained by the two methods were found to be almost identical, and both methods showed good convergence.

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6

Milovanovic, Milos J., Svetlana S. Raicevic, Dardan O. Klimenta, Nebojsa B. Raicevic, and Bojan D. Perovic. "Determination of Optimal Locations and Parameters of Passive Harmonic Filters in Unbalanced Systems Using the Multiobjective Genetic Algorithm." Elektronika ir Elektrotechnika 30, no. 2 (April 26, 2024): 28–37. http://dx.doi.org/10.5755/j02.eie.36124.

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This paper discusses the problem of optimal placement and sizing of passive harmonic filters to mitigate harmonics in unbalanced distribution systems. The problem is formulated as a nonlinear multiobjective optimisation problem and solved using the multiobjective genetic algorithm. The performance of the proposed algorithm is tested on unbalanced IEEE 13- and 37-bus three-phase systems. The optimal solutions are obtained based on the following objective functions: 1) minimisation of total harmonic distortion in voltage, 2) minimisation of costs of filters, 3) minimisation of voltage unbalances, and 4) a simultaneous minimisation of total harmonic distortion in voltage, costs of filters, and voltage unbalances. Finally, an analysis of the influence of uncertainties of load powers and changes in system frequency and filter parameters on filter efficiency was performed.

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7

Vaidya, Omkarprasad S., L. Ganapathy, and Sushil Kumar. "A cost minimisation model for system reliability allocation." International Journal of Quality & Reliability Management 36, no. 9 (October 7, 2019): 1620–43. http://dx.doi.org/10.1108/ijqrm-07-2018-0199.

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Purpose The purpose of this paper is to consider a nonlinear problem of minimizing the cost of providing reliable systems. The authors assume that the system consists of several components in series, and for each such component, the cost of the component increases exponentially with its reliability. Design/methodology/approach In order to solve this nonlinear optimization problem, the authors propose two approaches. The first approach is based on the concept of adjusting the reliability of a pair of components to minimize the cost of the system. The authors call this procedure as reliability adjustment routine (RAR). Proofs of optimality and convergence for the proposed model are also provided. The second approach solves the problem by using a Lagrangian multiplier. A procedure is developed to obtain the maximum step size to achieve the desired optimal solution in minimum iterations. Proposed approaches are efficient and give exact solutions. Findings Proposed methods enable a decision maker to allocate reliability to the components in series while minimizing the total cost of the system. The developed procedures are illustrated using a numerical example. Although an exponential relationship between the component cost and reliability is assumed, this can be extended to various other nonlinear distributions. Originality/value This cost optimization problem, subject to system component reliability values, assumes the near practical nonlinear pattern of cost vs reliability. Such problems are complex to solve. The authors provide a unique approach called RAR to solve such convoluted problems. The authors also provide an approach to solve such problems by using a Lagrangian multiplier method. Various proofs have been worked out to substantiate the work.

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8

Bisira, Hammed, and Abdellah Salhi. "Reshuffle minimisation to improve storage yard operations efficiency." Journal of Algorithms & Computational Technology 15 (January 2021): 174830262199401. http://dx.doi.org/10.1177/1748302621994010.

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There are many ways to measure the efficiency of the storage area management in container terminals. These include minimising the need for container reshuffle especially at the yard level. In this paper, we consider the container reshuffle problem for stacking and retrieving containers. The problem was represented as a binary integer programming model and solved exactly. However, the exact method was not able to return results for large instances. We therefore considered a heuristic approach. A number of heuristics were implemented and compared on static and dynamic reshuffle problems including four new heuristics introduced here. Since heuristics are known to be instance dependent, we proposed a compatibility test to evaluate how well they work when combined to solve a reshuffle problem. Computational results of our methods on realistic instances are reported to be competitive and satisfactory.

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9

Shang, Zhen, Songzheng Zhao, Yanjun Qian, and Jun Lin. "Exact algorithms for the feedback length minimisation problem." International Journal of Production Research 57, no. 2 (April 24, 2018): 544–59. http://dx.doi.org/10.1080/00207543.2018.1456697.

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10

Darwish, M. A., Abdulrahman R. Alenezi, and Majid M. Aldaihani. "Per-unit cost minimisation of the newsvendor problem." International Journal of Industrial and Systems Engineering 20, no. 4 (2015): 497. http://dx.doi.org/10.1504/ijise.2015.070186.

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11

Omar, Yusuf Sheikh, Anna Jenkins, Marieke van Regteren Altena, Harvey Tuck, Chris Hynan, Ahmed Tohow, Prem Chopra, and David Castle. "Khat Use: What Is the Problem and What Can Be Done?" BioMed Research International 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/472302.

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The chewing of khat leaves is an established tradition in East Africa but is much less prevalent in other areas of the world and is mostly limited to Somali communities. However, our understanding of what constitutes problematic khat use in the Somali community in Victoria, Australia, is limited. The objectives of this study were to better understand the views of Somali community representatives and primary care practitioners regarding problematic khat use, to consider relevant harm minimisation strategies, and to develop resources to assist individuals with problematic khat use and their families. Qualitative research methods were used to investigate the experiences and perceptions of khat use among Somalis and mainstream primary care practitioners. Six focus groups were conducted with 37 members of the Somali community and 11 primary care practitioners. Thematic analysis was used to analyse transcripts. Various indicators of the problematic use of khat were identified, including adverse physical and mental health effects, social isolation, family breakdown, and neglect of social responsibilities. Potential harm minimisation strategies were identified including the adoption of health promotion through education, outreach to the community, and the use of universal harm minimisation strategies specifically tailored to khat use.

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12

Adamson, Duncan, Argyrios Deligkas, Vladimir Gusev, and Igor Potapov. "On the Hardness of Energy Minimisation for Crystal Structure Prediction*." Fundamenta Informaticae 184, no. 3 (February 15, 2022): 181–203. http://dx.doi.org/10.3233/fi-2021-2096.

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Crystal Structure Prediction (CSP) is one of the central and most challenging problems in materials science and computational chemistry. In CSP, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as “NP-Hard and very challenging” without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of CSP with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the CSP removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of CSP. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.

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13

Montoya-Torres, Jairo R., and Fabián Vargas-Nieto. "Solving a Bi-Criteria Hybrid Flowshop Scheduling Problem Occurring in Apparel Manufacturing." International Journal of Information Systems and Supply Chain Management 4, no. 2 (April 2011): 42–60. http://dx.doi.org/10.4018/jisscm.2011040103.

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This paper studies the problem of production scheduling in a company belonging to the apparel industry, where textile labels are manufactured through the process of thermal transfer. The problem is modelled as a flexible flowshop with two stages. The objectives are the maximisation of system productivity (or minimisation of makespan) and the minimisation of the number of production orders with late delivery. This paper proposes a scheduling procedure based on a bi-objective genetic algorithm. An experimental study was performed using real data from the enterprise. Since validation results showed the efficiency and effectiveness of the proposed procedure, a decision-aid tool is designed. The algorithm is implemented at the enterprise and allows improved key performance metrics.

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14

Mohapatra, Sudhir Kumar, and Srinivas Prasad. "Using chemical reaction optimisation for test case minimisation problem." International Journal of Software Engineering, Technology and Applications 2, no. 1 (2017): 22. http://dx.doi.org/10.1504/ijseta.2017.086971.

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15

Prasad, Srinivas, and Sudhir Kumar Mohapatra. "Using chemical reaction optimisation for test case minimisation problem." International Journal of Software Engineering, Technology and Applications 2, no. 1 (2017): 22. http://dx.doi.org/10.1504/ijseta.2017.10008007.

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16

Bosch, P., J. P. Contreras, and J. Munizaga-Rosas. "Feasibility and cost minimisation for a lithium extraction problem." Computers & Operations Research 115 (March 2020): 104724. http://dx.doi.org/10.1016/j.cor.2019.05.029.

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17

Peng, C. Y., and J. W. Li. "Fast sparse representation model for l1-norm minimisation problem." Electronics Letters 48, no. 3 (2012): 162. http://dx.doi.org/10.1049/el.2011.3466.

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18

LIU, HAIFENG, JIHUA ZHU, and JIGEN PENG. "TWO NEW LOWER BOUNDS FOR THE SPARK OF A MATRIX." Bulletin of the Australian Mathematical Society 96, no. 3 (June 8, 2017): 353–60. http://dx.doi.org/10.1017/s000497271700034x.

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The $l_{0}$-minimisation problem has attracted much attention in recent years with the development of compressive sensing. The spark of a matrix is an important measure that can determine whether a given sparse vector is the solution of an $l_{0}$-minimisation problem. However, its calculation involves a combinatorial search over all possible subsets of columns of the matrix, which is an NP-hard problem. We use Weyl’s theorem to give two new lower bounds for the spark of a matrix. One is based on the mutual coherence and the other on the coherence function. Numerical examples are given to show that the new bounds can be significantly better than existing ones.

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19

Wu, Xiao, and Xianping Guo. "First Passage Optimality and Variance Minimisation of Markov Decision Processes with Varying Discount Factors." Journal of Applied Probability 52, no. 2 (June 2015): 441–56. http://dx.doi.org/10.1239/jap/1437658608.

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This paper deals with the first passage optimality and variance minimisation problems of discrete-time Markov decision processes (MDPs) with varying discount factors and unbounded rewards/costs. First, under suitable conditions slightly weaker than those in the previous literature on the standard (infinite horizon) discounted MDPs, we establish the existence and characterisation of the first passage expected-optimal stationary policies. Second, to further distinguish the expected-optimal stationary policies, we introduce the variance minimisation problem, prove that it is equivalent to a new first passage optimality problem of MDPs, and, thus, show the existence of a variance-optimal policy that minimises the variance over the set of all first passage expected-optimal stationary policies. Finally, we use a computable example to illustrate our main results and also to show the difference between the first passage optimality here and the standard discount optimality of MDPs in the previous literature.

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Wu, Xiao, and Xianping Guo. "First Passage Optimality and Variance Minimisation of Markov Decision Processes with Varying Discount Factors." Journal of Applied Probability 52, no. 02 (June 2015): 441–56. http://dx.doi.org/10.1017/s0021900200012560.

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This paper deals with the first passage optimality and variance minimisation problems of discrete-time Markov decision processes (MDPs) with varying discount factors and unbounded rewards/costs. First, under suitable conditions slightly weaker than those in the previous literature on the standard (infinite horizon) discounted MDPs, we establish the existence and characterisation of the first passage expected-optimal stationary policies. Second, to further distinguish the expected-optimal stationary policies, we introduce the variance minimisation problem, prove that it is equivalent to a new first passage optimality problem of MDPs, and, thus, show the existence of a variance-optimal policy that minimises the variance over the set of all first passage expected-optimal stationary policies. Finally, we use a computable example to illustrate our main results and also to show the difference between the first passage optimality here and the standard discount optimality of MDPs in the previous literature.

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21

Oeri, Hans, and David Goluskin. "Convex computation of maximal Lyapunov exponents." Nonlinearity 36, no. 10 (September 1, 2023): 5378–400. http://dx.doi.org/10.1088/1361-6544/acecf5.

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Abstract We describe an approach for finding upper bounds on an ODE dynamical system’s maximal Lyapunov exponent (LE) among all trajectories in a specified set. A minimisation problem is formulated whose infimum is equal to the maximal LE, provided that trajectories of interest remain in a compact set. The minimisation is over auxiliary functions that are defined on the state space and subject to a pointwise inequality. In the polynomial case—i.e. when the ODE’s right-hand side is polynomial, the set of interest can be specified by polynomial inequalities or equalities, and auxiliary functions are sought among polynomials—the minimisation can be relaxed into a computationally tractable polynomial optimisation problem subject to sum-of-squares constraints. Enlarging the spaces of polynomials over which auxiliary functions are sought yields optimisation problems of increasing computational cost whose infima converge from above to the maximal LE, at least when the set of interest is compact. For illustration, we carry out such polynomial optimisation computations for two chaotic examples: the Lorenz system and the Hénon–Heiles system. The computed upper bounds converge as polynomial degrees are raised, and in each example we obtain a bound that is sharp to at least five digits. This sharpness is confirmed by finding trajectories whose leading Lyapunov exponents approximately equal the upper bounds.

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22

Keshavarz, Taha, and Nasser Salmasi. "Makespan minimisation in flexible flowshop sequence-dependent group scheduling problem." International Journal of Production Research 51, no. 20 (October 15, 2013): 6182–93. http://dx.doi.org/10.1080/00207543.2013.825055.

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23

Das, S., and Monisha Borthakur. "A Mixed Constrained (Identical) Vehicle Routing Problem for Time Minimisation." OPSEARCH 43, no. 1 (March 2006): 31–48. http://dx.doi.org/10.1007/bf03398758.

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24

Kuimova, Yelena I., and Dmitriy A. Ryabov. "Multi-criteria problem of optimization." Vestnik Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics, no. 3 (2019): 214–16. http://dx.doi.org/10.34216/2073-1426-2019-25-3-214-216.

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General subjects of teaching technics connected with minimisation by metrics are under consideration.The effectiveness of studying the possibilities of mathematical modelling in applied economical problems depends not only on studying the basic section of operation research, but also on the skill of finding the resolution of non-typical situation independently. Comparative analysis of different approaches to reduction of multicriteria problem to a single-criterion problem for further use of classical optimisation techniques.Comparative analysis of different approaches to the reduction of a multi-criteria problem to a single-criterion problem is carried out for the further use of classical methods for finding of optimal solution. The study of complex optimisation problems contributes to the development of nonstandard creative thinking and abilities of the future specialists in general volume of professional training of student.

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25

Yaotian, Shen, and Yan Shusen. "Existence and boundedness of a minimiser for a constrained minimisation problem on Rn with limiting exponent." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 122, no. 3-4 (1992): 221–35. http://dx.doi.org/10.1017/s0308210500021089.

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SynopsisWe use the concentration compactness principle to study the existence of a minimiser of the minimisation problem where u =(u1, …, uN), . We also prove the boundedness of the minimiser of l1 by using the reverse Holder inequality.

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26

Shen, Yaotian, and Shusen Yan. "A singularly perturbed elliptic problem involving supercritical Sobolev exponent." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 4 (1998): 809–19. http://dx.doi.org/10.1017/s030821050002179x.

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This paper deals with −Δu + εuq−1 = u2*−1, , where q > 2*, ε > 0. We first show that the minimiser of the associated minimisation problem blows up at the global minimum point of H(x, x), where H(y, x) is the regular part of the Green's function. We then prove that for each strictly local minimum point x0 of H(x, x), this problem has a solution concentrating at x0 as ε→0.

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Fadeeva, A. M. "Risk minimisation methods in shaping the optimal range of treadmills." Vestnik Universiteta, no. 11 (January 7, 2022): 149–56. http://dx.doi.org/10.26425/1816-4277-2021-11-149-156.

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The article presents a solution to the problem of integrating risk minimisation methods in the process of forming the optimal range of treadmill models in a retail enterprise. The problem of multi-criteria optimisation was solved using the generalised criterion method. The formulated problem was therefore broken down into a number of specific tasks, each of which was solved by selecting specific methods. Risks were minimised by mathematical methods, taking into account the economic performance of the enterprise. Recommendations were also offered for customers wishing to purchase one of the treadmill models chosen from the analysis and the best option for ordering via the online shop with home delivery.

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Ayanbayev, Birzhan, Ilja Klebanov, Han Cheng Lie та T. J. Sullivan. "Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems". Inverse Problems 38, № 2 (28 грудня 2021): 025005. http://dx.doi.org/10.1088/1361-6420/ac3f81.

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Abstract The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.

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29

Alyami, Maryam. "Existence of solution for a singular fractional boundary value problem of Kirchhoff type." Filomat 36, no. 17 (2022): 5803–12. http://dx.doi.org/10.2298/fil2217803a.

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In this work, we investigate the existence of solution for some nonlinear singular problem of Kirchhoff type involving Riemann-Liouville Fractional Derivative and the p-Laplacian operator. The main tools are based on the variational method, precisely, we use the minimisation of the corresponding functional in a suitable fractional spaces. Our main result significantly complement and improves the previous ones due to [6] and [31].

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Guardiola, Carlos, Benjamín Pla, Varun Pandey, and Richard Burke. "On the potential of traffic light information availability for reducing fuel consumption and NOx emissions of a diesel light-duty vehicle." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 234, no. 4 (August 2, 2019): 981–91. http://dx.doi.org/10.1177/0954407019867167.

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The paper addresses the impact of traffic light information availability in terms of fuel consumption and emissions by means of comparing three different scenarios that a driver of a diesel light-duty vehicle may face when trying to cover a particular route of 1 km with two traffic lights in between. The first scenario is that the driver does not know in advance the state of the traffic lights. The second scenario assumes that the driver knows the state of the traffic lights but has no modelling nor computation capabilities to solve the associated optimal control problem. In the third scenario, the driver knows in advance the state of the traffic lights and is also able to solve the corresponding optimal control problem that leads to fuel consumption or NOx emission minimisation. In this study, the vehicle-speed trajectories associated with the previously described three scenarios have been computed and then tested in a Euro 5 Diesel vehicle installed in a chassis dynamometer. The obtained results show that traffic light information is essential for fuel minimisation in urban conditions, promoting reductions of 7.5–12% and 13–32% for fuel consumption and NOx emissions in the studied case. In addition, differences in the engine-operating conditions for high efficiency and low NOx emissions may lead to extremely high fuel consumption when NOx minimisation is foreseen or viceversa.

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Hussein, M. S., D. Lesnic, and M. Ivanchov. "Free Boundary Determination in Nonlinear Diffusion." East Asian Journal on Applied Mathematics 3, no. 4 (November 2013): 295–310. http://dx.doi.org/10.4208/eajam.100913.061113a.

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AbstractFree boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the lsqnonlin routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.

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32

Coladas, L., Z. Li, and S. Wang. "Optimality conditions for multiobjecttve and nonsmooth minimisation in abstract spaces." Bulletin of the Australian Mathematical Society 50, no. 2 (October 1994): 205–18. http://dx.doi.org/10.1017/s0004972700013678.

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In this paper we study optimality conditions for an efficient solution in various senses of a general multiobjective optimisation problem in abstract spaces. We utilise properties of the Clarke's generalised differential and properties of a conesubconvexlike function to derive a few necessary and/or sufficient conditions for a feasible solution to be a weak minimum (a minimum, a strong minimum or a proper minimum) of the vector optimisation problem. The results in this paper are extensions and refinements of some known results in vector optimisation.

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33

Basupi, Innocent, Zoran Kapelan, and David Butler. "Reducing life-cycle carbon footprints in the redesign of water distribution systems." Journal of Water and Climate Change 4, no. 3 (April 18, 2013): 176–92. http://dx.doi.org/10.2166/wcc.2013.004.

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Water distribution systems (WDSs) contribute to undesirable greenhouse gas (GHG) emissions that are generated through their component fabrication, construction, operation and disposal processes. The concentration of GHGs in the atmosphere is strongly associated with global warming and climate change. In order to meet the consequent challenge of limiting GHG emissions, the problem of WDS redesign is formulated here as a multi-objective optimisation problem. The three objectives are as follows: (1) minimisation of total redesign cost, (2) maximisation of the WDS resilience, and (3) minimisation of GHG emissions. The resilience index serves as a measure of the WDS's intrinsic capability to ensure continuity of supply to users after sudden failure conditions, whilst the GHG emissions serve as a measure of environmental performance and climate change mitigation. The output from the non-dominated sorting genetic algorithm (NSGA2) optimisation process is a Pareto front containing optimal solutions traded-off in terms of the three objectives analysed. This methodology was applied on the New York Tunnels and the Anytown Network problems. The results obtained demonstrate that the redesign approach leads to cost-effective and resilient solutions that can also mitigate climate change compared with the single-objective (least cost) and other multi-objective redesigns over the long-term planning horizon.

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34

Elliott, J., and J. Peraire. "Constrained, multipoint shape optimisation for complex 3D configurations." Aeronautical Journal 102, no. 1017 (September 1998): 365–76. http://dx.doi.org/10.1017/s0001924000065143.

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AbstractA method for performing three-dimensional, multipoint, lift-constrained drag minimisation for complex aircraft configurations is presented. Parameters representing the aircraft geometry are the design variables used in the solution of an optimisation problem. The compressible Euler equations for the flow are discretised on automatically generated unstructured meshes, and the sensitivities of the objective function and the constraints with respect to the design parameters are efficiently calculated using the discrete adjoint method. In addition, the solution algorithm has been parallelised making the approach feasible for practical applications. Several constrained minimisation strategies are discussed and some numerical tests are carried out for a lift-constrained, two-dimensional problem. The strategy found to work best is demonstrated for the three-dimensional optimisation of a wing-body configuration operating in transonic and supersonic conditions. It is concluded that Euler-based optimisation can be useful as a first step in the design process but that most applications involving transonic flows do require viscous flow modelling to avoid unrealistic pressure distributions.

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35

Vo, Q. B., and N. Y. Foo. "Reasoning about Action: An Argumentation - Theoretic Approach." Journal of Artificial Intelligence Research 24 (October 1, 2005): 465–518. http://dx.doi.org/10.1613/jair.1602.

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We present a uniform non-monotonic solution to the problems of reasoning about action on the basis of an argumentation-theoretic approach. Our theory is provably correct relative to a sensible minimisation policy introduced on top of a temporal propositional logic. Sophisticated problem domains can be formalised in our framework. As much attention of researchers in the field has been paid to the traditional and basic problems in reasoning about actions such as the frame, the qualification and the ramification problems, approaches to these problems within our formalisation lie at heart of the expositions presented in this paper.

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36

Szłapczyński, Rafał, and Hossein Ghaemi. "Framework of an Evolutionary Multi-Objective Optimisation Method for Planning a Safe Trajectory for a Marine Autonomous Surface Ship." Polish Maritime Research 26, no. 4 (December 1, 2019): 69–79. http://dx.doi.org/10.2478/pomr-2019-0068.

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Abstract This paper represents the first stage of research into a multi-objective method of planning safe trajectories for marine autonomous surface ships (MASSs) involved in encounter situations. Our method applies an evolutionary multi-objective optimisation (EMO) approach to pursue three objectives: minimisation of the risk of collision, minimisation of fuel consumption due to collision avoidance manoeuvres, and minimisation of the extra time spent on collision avoidance manoeuvres. Until now, a fully multi-objective optimisation has not been applied to the real-time problem of planning safe trajectories; instead, this optimisation problem has usually been reduced to a single aggregated cost function covering all objectives. The aim is to develop a method of planning safe trajectories for MASSs that is able to simultaneously pursue the three abovementioned objectives, make decisions in real time and without interaction with a human operator, handle basic types of encounters (in open or restricted waters, and in good or restricted visibility) and guarantee compliance with the International Regulations for Preventing Collisions at Sea. It should also be mentioned that optimisation of the system based on each criterion may occur at the cost of the others, so a reasonable balance is applied here by means of a configurable trade-off. This is done throughout the EMO process by means of modified Pareto dominance rules and by using a multi-criteria decision-making phase to filter the output Pareto set and choose the final solution

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37

Bokhari, M. A. "On certain sequences of least squares approximants." Bulletin of the Australian Mathematical Society 37, no. 3 (June 1988): 415–22. http://dx.doi.org/10.1017/s0004972700027039.

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A sequence of certain rational functions is determined where each member solves an ℓ2-minimisation problem on a “large” set of roots of unity. The sequence is compared with another sequence of L2-rational approximants. Our main result extends a result of Rivlin on Walsh type equiconvergence.

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38

Xu, Xiaoqing, Wentian Cui, Jun Lin, and Yanjun Qian. "Robust makespan minimisation in identical parallel machine scheduling problem with interval data." International Journal of Production Research 51, no. 12 (June 2013): 3532–48. http://dx.doi.org/10.1080/00207543.2012.751510.

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39

Stoica, Adrian-Mihail, and Isaac Yaesh. "STATIC OUTPUT FEEDBACK REVISITED." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 13, no. 1-2 (2021): 216–31. http://dx.doi.org/10.56082/annalsarscimath.2021.1-2.216.

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The synthesis problem of static output feedback controllers within the anisotropic-norm setup is revisited. A tractable synthesis approach involving iterations over a convex optimisation problem is suggested, similarly to existing results for the H∞-norm minimisation case. The results are formulated by a couple of Linear Matrix Inequalities coupled via a bilinear equality, revealing, as in the H∞ case the duality of between the control-type and filtering type LMIs and allowing a tractable iterative method to cope with practical static output feedback synthesis problems. The resulting optimisation scheme is then applied to a flight control problem, where the merit of the anisotropic norm setup is shown to provide a useful trade-off between closed loop response and feedback gains

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40

Stoica, Adrian-Mihail, and Isaac Yaesh. "STATIC OUTPUT FEEDBACK REVISITED." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 13, no. 1-2 (2021): 216–31. http://dx.doi.org/10.56082/annalsarscimath.2022.1-2.216.

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Анотація:

The synthesis problem of static output feedback controllers within the anisotropic-norm setup is revisited. A tractable synthesis approach involving iterations over a convex optimisation problem is suggested, similarly to existing results for the H∞-norm minimisation case. The results are formulated by a couple of Linear Matrix Inequalities coupled via a bilinear equality, revealing, as in the H∞ case the duality of between the control-type and filtering type LMIs and allowing a tractable iterative method to cope with practical static output feedback synthesis problems. The resulting optimisation scheme is then applied to a flight control problem, where the merit of the anisotropic norm setup is shown to provide a useful trade-off between closed loop response and feedback gains

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41

Liu, Cheng-Hsiang. "Approximate trade-off between minimisation of total weighted tardiness and minimisation of carbon dioxide (CO2) emissions in bi-criteria batch scheduling problem." International Journal of Computer Integrated Manufacturing 27, no. 8 (September 10, 2013): 759–71. http://dx.doi.org/10.1080/0951192x.2013.834479.

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42

Clayton, R. P., and R. F. Martinez-Botas. "Application of generic algorithms in aerodynamic optimisation design procedures." Aeronautical Journal 108, no. 1090 (December 2004): 611–20. http://dx.doi.org/10.1017/s0001924000000440.

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AbstractDirect optimisation techniques using different methods are presented and compared for the solution of two common flows: a two dimensional diffuser and a drag minimisation problem of a fixed area body. The methods studied are a truncated Newton algorithm (gradient method), a simplex approach (direct search method) and a genetic algorithm (stochastic method). The diffuser problem has a known solution supported by experimental data, it has one design performance measure (the pressure coefficient) and two design variables. The fixed area body also has one performance measure (the drag coefficient), but this time there are four design variables; no experimental data is available, this computation is performed to assess the speed/progression of solution.In all cases the direct search approach (simplex method) required significantly smaller number of evaluations than the generic algorithm method. The simplest approach, the gradient method (Newton) performed equally to the simplex approach for the diffuser problem but it was unable to provide a solution to the four-variable problem of a fixed area body drag minimisation. The level of robustness obtained by the use of generic algorithm is in principle superior to the other methods, but a large price in terms of evaluations has to be paid.

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43

Srše, Jure, Marko Perkovič, and Aleksander Grm. "Minimisation of Propeller-Induced Sediment Resuspension with Rip-Rap System." Časopis Pomorskog fakulteta Kotor - Journal of Maritime Sciences 24, no. 1 (May 25, 2023): 12–21. http://dx.doi.org/10.56080/jms230502.

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Sediment resuspension caused by the movement of propellers during manoeuvring is a major problem in daily port operations. Negative impacts include: Marine flora and fauna, sediment erosion that weakens berth structures, sediment deposits that require dredging. Later, this leads to delays in port operations. Several authors have proposed different methods to cope with this problem. This paper presents methods and tools to determine the critical propeller jet velocities, which are the most important parameter to determine the size of the bank stabilisation system. The tool is a bridge simulator that can be used to simulate the intrusive departure manoeuvre of a ship. The ship motion data are analysed to determine the critical shear stress of the sediment particles. The critical velocity induced by the propeller jet is determined using the German method.

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44

Strachan, L. F., L. M. Freitas dos Santos, D. J. Leak, and A. G. Livingston. "Minimisation of biomass in an extractive membrane bioreactor." Water Science and Technology 34, no. 5-6 (September 1, 1996): 273–80. http://dx.doi.org/10.2166/wst.1996.0560.

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Many traditional biological methods for the treatment of wastewater cope poorly with toxic, volatile organic compounds. The extractive membrane bioreactor is a novel process for the treatment of industrial wastewaters containing such compounds which combines extraction across a silicone rubber membrane with biodegradation. Previous work has shown that there is a problem in this system with excess biofilm growth on the membrane surface, resulting in reduced flux of organic substrate across the membrane. The work presented here shows that addition of sodium chloride to the biomedium increases the maintenance energy requirement of the degradative microorganisms and results, in a carbon-limited situation, in a reduction in biofilm growth. Flux of organic substrate was shown to remain high under reduced biofilm growth conditions.

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45

Le, Hoang Son, Rini Akmeliawati, and Gustavo Carneiro. "Domain Generalisation with Domain Augmented Supervised Contrastive Learning (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (May 18, 2021): 15821–22. http://dx.doi.org/10.1609/aaai.v35i18.17907.

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Domain generalisation (DG) methods address the problem of domain shift, when there is a mismatch between the distributions of training and target domains. Data augmentation approaches have emerged as a promising alternative for DG. However, data augmentation alone is not sufficient to achieve lower generalisation errors. This project proposes a new method that combines data augmentation and domain distance minimisation to address the problems associated with data augmentation and provide a guarantee on the learning performance, under an existing framework. Empirically, our method outperforms baseline results on DG benchmarks.

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46

Zhou, Hongming, Ya-Chih Tsai, Shenquan Huang, Yarong Chen, and Fuh-Der Chou. "Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times." Mathematical Problems in Engineering 2021 (April 17, 2021): 1–15. http://dx.doi.org/10.1155/2021/8891322.

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The single-machine scheduling problem with fixed periodic preventive maintenance, in which preventive maintenance is implemented periodically to maintain good machine operational status and decrease the cost caused by sudden machine failure, is studied in this paper. The adopted objective function is to minimise the total weighted completion time, which is representative of the minimisation of the global holding/inventory cost in the system. This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion time problem. To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed. Computational experiments show that the proposed heuristic can rapidly achieve optimal results for small-sized problems and obtain near-optimal solutions with tight average relative percentage deviation for large-sized problems.

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47

Sajjadmanesh, Mojtaba, Hassen Aydi, Eskandar Ameer, and Choonkil Park. "The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain." Fractal and Fractional 6, no. 2 (January 27, 2022): 66. http://dx.doi.org/10.3390/fractalfract6020066.

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In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.

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48

Vycital, Vaclav, Michal Ptacek, David Topolanek, and Petr Toman. "On Minimisation of Earthing System Touch Voltages." Energies 12, no. 20 (October 11, 2019): 3838. http://dx.doi.org/10.3390/en12203838.

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Finding cost efficient earthing system design with acceptable level of safety might be quite tedious work. Thus, many earthing system engineers try to find the most suitable design either by employing only their best experience or taking advantage of some more complex optimisation programs. Although both approaches might work well under certain circumstances, they might fail either due to counter-intuitiveness of the specific situation or by misunderstanding of the applied optimisation method, its limitations etc. Thus, in this paper, the earthing system design optimisation problem was addressed by analysing optimisation simulation results together with conducted sensitivity analysis. In the paper, a simple double ring earthing system was optimised while using five different optimisation methods. The earthing system was placed in different horizontally stratified soil models and the earthing system was optimised by minimising touch voltages instead of commonly minimised earth potential rise. The earthing system was modelled by Ansys Maxwell software. Apart from using Ansys Maxwell built-in optimisers, the possible solution space has also been mapped by performing sensitivity analysis with changing the earthing system design dimensions and the results of optimisation were compared and validated. It was found out that the Sequential Non-Linear Programming Optimisation technique was quite superior to the other techniques. Additionally, in most cases, the Ansys Maxwell optimiser was able to found optimal solution; however, in some cases, based on the initial conditions, it might get stuck in local minima or the results might be influenced by the solution noise. Additionally, some quite non intuitive dependencies of earthing system electrodes positions had been found when different spatial dimensions constraints are used.

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49

Nafiah, Faris, Mohammad O. Tokhi, Gholamhossein Shirkoohi, Fang Duan, Zhanfang Zhao, and Owen Rees-Lloyd. "Determining Feature Extraction Parameters for Pulsed Eddy Current Sensor: A Minimisation Problem Approach." IEEE Sensors Journal 21, no. 22 (November 15, 2021): 26124–31. http://dx.doi.org/10.1109/jsen.2021.3119466.

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50

Thevenin, Simon, Nicolas Zufferey, and Jean-Yves Potvin. "Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility." International Journal of Production Research 55, no. 6 (May 8, 2016): 1588–606. http://dx.doi.org/10.1080/00207543.2016.1181285.

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