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Order release optimisation is essential in production planning, especially in discrete manufacturing. Order release planning models with load-dependent lead times must anticipate the time-dependent work-in-process and output for any given release schedule and thus require an anticipation model that approximates the time-dependent behaviour of queueing systems. We present a generic optimisation model for order release planning in stochastic, non-stationary manufacturing systems that includes a well-defined interface for the anticipation model. We develop two stationary backlog carryover (SBC) approaches to approximate time-dependent queueing behaviour and prove their consistency with the order release model. The resulting nonlinear programming model is shown to be a special case of the well-known clearing function models. A numerical study demonstrates that the optimised order releases for different demand patterns are close to the optimum that results from simulation-based optimisation even for extreme demand and release patterns. The resulting output closely matches the simulated output with some deviations. [ABSTRACT FROM AUTHOR]

High flexibility is an important feature of seru system that has received less attention. In this paper, we discuss how to do such flexible seru system formation, especially focusing on the strategic decision phase. We formulate the flexible seru system formation problem (FSFP) as a nonlinear programming model to evaluate flexibility performance in terms of flexibility–investment cost and flexibility–loss cost. To exactly obtain the optimal solution of the FSFP, we transform the nonlinear model into a linear one and solve it with Gurobi solver. For the large-scale problem, we proposed a parallel Master–Slave adaptive genetic algorithm (PMSA-GA) by transforming it into a two-stage stochastic programming model. The adaptive selection is used to improve the quality of solutions in PMSA-GA. To reduce the computational time, multiple populations of seru formation evolve in parallel with the assistance of the Master–Slave mechanism. Extensive experiments are tested to evaluate the performance of the proposed model and algorithm, and the effect of cost parameters on the system performance is discussed. The results show that the FSFP model takes the property of dynamic demand into account and is more suitable for dynamic demand environments than the task-oriented seru formation (TOSF) strategy from the previous literature. [ABSTRACT FROM AUTHOR]

The edge-cloud computing continuum effectively uses fog and cloud servers to meet the quality of service (QoS) requirements of tasks when edge devices cannot meet those requirements. This paper focuses on the workflow offloading problem in edge-cloud computing and formulates this problem as a nonlinear mathematical programming model. The objective function is to minimize the monetary cost of executing a workflow while satisfying constraints related to data dependency among tasks and QoS requirements, including security and deadlines. Additionally, it presents a genetic algorithm for the workflow offloading problem to find near-optimal solutions with the cost minimization objective. The performance of the proposed mathematical model and genetic algorithm is evaluated on several real-world workflows. Experimental results demonstrate that the proposed genetic algorithm can find admissible solutions comparable to the mathematical model and outperforms particle swarm optimization, bee life algorithm, and a hybrid heuristic-genetic algorithm in terms of workflow execution costs. [ABSTRACT FROM AUTHOR]

Shakedown analysis with Melan's theorem is an important approach to predicting the ultimate load-bearing capacity of heterogeneous materials under varying loads. However, this approach entails dealing with a large-scale nonlinear mathematical programming problem with numerous element-wise yielding constraints and unknown time-independent beneficial residual stress variables, resulting in a substantial computational burden. The well-known basis reduction method expresses the unknown time-independent beneficial residual stress as a linear combination of a set of self-equilibrium stress (SES) bases, and the corresponding coefficients are the unknowns. This method is effective only if the set of SES basis vectors is small and easily available. Based on the representative volume element (RVE) and FEM-cluster based analysis (FCA) method, this paper proposes a FEM cluster-based basis reduction method to fast predict the shakedown domain of heterogeneous materials. The novel data-driven clustering method is introduced to divide the RVE into several clusters. The SES basis is constructed by applying the cluster eigenstrain to RVE under periodic boundary conditions. Numerical experiments show that the unknown time-independent beneficial residual stress can be well represented with this small set of SES basis vectors. In this way, the unknown variables are reduced dramatically. In addition, to further reduce the number of nonlinear constraints, a constraint reduction strategy based on the reduced-order model of FCA is implemented to remove the element-wise yielding constraints for the elements far from yielding. Several numerical examples demonstrate its efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Rigid retaining walls with polyline backs are possibly used in filling engineering, and some types of these walls may have better stability than ordinary gravity walls with planar backs. Aiming at the active earth pressure on polyline-back walls under the translation mode, an analytical method within the frame of limit equilibrium is provided according to the potential two slip surfaces intersected in the retained backfill. The proposed method focuses on the minimum slide-resisting factor of safety of the polyline-back wall to be the objective function, and it can be performed easily using the nonlinear programming approach. Analysis results of some examples show that the proposed earth pressure is close to those obtained using the test and numerical methods with an average error of about 15%. The platform width and the ratio of the upper to lower wall height in the counterweight wall have more obvious influences on earth pressure than the slip surfaces. The overall and local critical slip surfaces are considerably influenced by the lower-back and backfill surface inclinations, respectively. The counterweight wall is the optimum configuration for the overall sliding stability among the compared five polyline-back walls due to its outward-extending platform and positively inclined lower back. Practical Applications: This work provides a calculation method for the active earth pressure on rigid walls with polyline backs under wall translation, which holds practical significance for geotechnical engineers or practitioners in filling engineering such as embankments. The proposed method can analytically solve the active earth pressure on different segments of the polyline back of gravity walls and the two critical slip surfaces intersected in the retained soil. As a result, the slide-resisting stability of the wall can be analyzed in the design. The proposed method can be used further to compare possible different types of polyline backs of a wall and then for the quick optimization design of the gravity wall. Analysis results of an example show that the counterweight wall is the optimum configuration for overall sliding stability due to its outward-extending platform and positively inclined lower back. In brief, this work can provide a significant reference for the practical design of rigid walls with polyline backs, such as counterweight walls and hunchbacked walls, based on the easily operated limit equilibrium methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the applicability of Zermelo's equation within the context of 3D commercial aircraft trajectory optimization problems. The associated optimal control problem includes two singular controls, specifically aerodynamic path angle and throttle setting, and one regular control, specifically heading angle. Using Pontryagin's maximum principle and the direct adjoining method, we show that the optimal heading angle is defined by Zermelo's equation. The significance of the presented analysis is that Zermelo's equation holds for 3D commercial aircraft flights, even in the presence of standard state-inequality constraints and a more general objective function. With the help of Zermelo's equation, the control problem is initially analyzed for a 3D time-optimal climb-phase scenario, which is solved by an indirect approach. Through the analysis of the switching function, we demonstrate the dependency of the optimal aerodynamic path angle on the optimal heading angle. Next, by tackling a 3D time-fuel-optimal free-routing flight, solved by a direct approach, we show that Zermelo's equation can help reduce the overall dimension of the associated nonlinear programming. To successfully handle the initial guess in both indirect and direct problems, it is proposed a diminutive nonlinear programming technique as a fast and robust initializer. This simple-yet-effective initializer provides sufficient information about the optimal controls and state dynamics required for initializing a direct optimization, as well as the optimal switching times and co-states required for initializing an indirect optimization. • Demonstrating the applicability of Zermelo's equation to constrained optimization of 3D aircraft flights. • Solving 3D time-optimal problem in climb phase with Zermelo's identity using an Indirect method. • Solving 3D time-fuel-optimal free-routing problem with Zermelo's identity using a new Direct transcription method. • Brief discussion on aNLP for initialization of both Indirect and Direct methods. [ABSTRACT FROM AUTHOR]

A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container. Moreover, specified ratios between the placed spheres of different radii must be satisfied. A corresponding mixed-integer nonlinear programming model is formulated. It enables the exact solution of small instances. For larger instances, a heuristic strategy is proposed, which relies on techniques for the generation of feasible points and the decomposition of open dimension problems. Numerical results are presented to demonstrate the viability of the approach. [ABSTRACT FROM AUTHOR]

Given a finite set of distinct points in R n and a positive weight for each point, primal and dual algorithms are developed for finding the Euclidean ball of minimum radius so that the weighted Euclidean distance between the center of the ball and each point is less than or equal to the radius of the ball. Each algorithm is based on a directional search method in which the search path at each iteration is either a ray or a two-dimensional circular arc in R n . At each iteration, a search path is constructed by intersecting bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional spheres. Each search path preserves complementary slackness and primal (dual) feasibility for the primal (dual) algorithm. The step size along each search path is determined explicitly. Test problems up to 1000 dimensions and 10,000 points were solved to optimality by both primal and dual algorithms. Computational results also show that these algorithms outperform several open-source SOCP codes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weighted nonlinear complementarity problem which is the extension of the general complementarity problems and contains a wide class of optimization problems. Based on the weighted complementarity function, we reformulate the weighted nonlinear complementarity problem as an unconstrained minimization problem and present the steepest descent-based neural network to solve it. Under mild conditions, we derive some results related to the asymptotic stability of the neural network. Numerical experiments indicate that the proposed algorithm is quite effective. [ABSTRACT FROM AUTHOR]

In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two-body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm. [ABSTRACT FROM AUTHOR]

The new energy system constructed by energy storage and photovoltaic power generation system can effectively solve the problem of transformer overload operation in some enterprises. It can not only reduce the cost of electricity, but also realize low-carbon emission reduction. However, due to its low return on investment, the willingness of enterprises to install new energy is not high. In this paper, we first establish a load forecasting model to users whose transformers are overloaded or about to be overloaded, which are potential customers with new energy installation needs. Then, Optimal configuration models of PV and energy storage systems based on nonlinear programming are developed for these potential customers. The optimal installed capacity of the PV energy storage and the optimal charging and discharging strategy for the energy storage system can be obtained. This optimization strategy ensures that the electricity consumption of the enterprise does not exceed the rated capacity, and effectively reduces the enterprise's basic tariff and electricity price to achieve cost reduction and efficiency. Finally, taking a building materials production factory as an example, we obtain the optimal plan for the new energy capacity, as well as the economic benefits of the plan and the specific strategy of energy storage charging and discharging for this factory. [ABSTRACT FROM AUTHOR]

In many recent applications, sparse solutions of the optimization problems are favoured over non-sparse solutions with comparable objective values. A standard method to induce the sparsity of the solution is based on the use of the $ \ell _0 $ ℓ 0 norm in the objective. However, if the underlying optimization problem is nonlinear, the solution of the nonlinear (sparse) $ \ell _0 $ ℓ 0 -optimization problem is difficult. Therefore, it is often approximated using the convex $ \ell _1 $ ℓ 1 -norm although this can lead to suboptimal solutions for the sparsity of the solution. In this paper, we follow another direction. We present exact reformulations (with respect to the $ \ell _0 $ ℓ 0 norm) and their relaxations leading to standard nonlinear but nonconvex programmes. We discuss and relate the relations between the different reformulations with repect to the original problem. We accompany our theoretical results by some numerical tests using randomly generated datasets. [ABSTRACT FROM AUTHOR]

This paper pertains to the finite-element lower bound limit analysis (FELA-LB) of vertical strip anchors embedded in cohesionless and cohesive soils and subjected to static and earthquake forces (using pseudostatic analysis) to estimate the optimal horizontal pullout capacity using nonlinear programming (NLP) technique for isolating the optimal solution. In the developed procedure, a mesh of finite-number triangular elements and assuming a linear stress field that satisfies all the equations of internal equilibrium at all points within the soil medium, elemental interface equilibrium, boundary conditions and no-yield conditions at all the nodal points, has been adopted. In contrast to the use of linear programming (LP), as used in the early phase of the development of FELA of stability problems, in the adopted optimization scheme (NLP), the nonlinear no-yield conditions are incorporated directly, eliminating the necessity of successive linearization of the no-yield constraints. The convergence of the solutions (by varying the number of elements in the soil mesh) and extensibility of the selected stress field (by extending the mesh of elements) has been checked and ensured. The correctness of the estimated lower bound has been checked by comparing the obtained solutions with those reported in the literature. Parametric studies showing the effect of the embedment depth of the vertical anchor, soil properties, and earthquake acceleration on the horizontal pullout capacity of the vertical anchor have also been presented in the paper. Practical Applications: Anchor plates are used in the design and construction of foundation for retaining walls, sheet piles, bulkheads, transmission towers, bridge abutments, and buried pipelines to withstand the horizontal, vertical, or inclined loads. The present study adds to the existing state of art for the design and installation of anchor systems subjected to static and seismic conditions and may improve the performance of such foundation systems. [ABSTRACT FROM AUTHOR]

Copyright of Transportation Science & Technolgy is the property of Transportation Science & Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study. [ABSTRACT FROM AUTHOR]

This article focuses on air defense in maritime environment, which involves protecting friendly naval assets from aerial threats. Specifically, we define and address the Naval Air Defense Planning (NADP) problem, which consists of maneuvering decisions of the ships and scheduling weapons and sensors to the threats in order to maximize the total expected survival probability of friendly units. The NADP problem is more realistic and applicable than previous studies, as it considers features such as sensor assignment requirements, weapon and sensor blind sectors, sequence‐dependent setup times, and ship's infrared/radar signature. In this study, a mixed‐integer nonlinear programming model of the NADP problem is presented and heuristic solution approaches are developed. Computational results demonstrate that these heuristic approaches are both fast and efficient in solving the NADP problem. [ABSTRACT FROM AUTHOR]

In this article, the Chebyshev pseudo-spectral (CPS) method is presented for solving Troesch’s problem, which is a singular, highly sensitive, and nonlinear boundary problem and occurs in the consideration of the confinement of a plasma column by radiation pressure. Here, a continuous time optimization (CTO) problem corresponding to Troesch’s problem is first proposed. Then, the Chebyshev pseudo-spectral method is used to convert the CTO problem to a discrete-time optimization problem its optimal solution can be found by nonlinear programming methods. The feasibility and convergence of the generated approximate solutions are analyzed. The proposed method is used to solve various kinds of Troesch’s equations. The obtained results have been compared with approximate solutions resulting from well known numerical methods. It can be confirmed that the numerical solutions resulting from this method are completely acceptable and accurate, compared with other techniques. [ABSTRACT FROM AUTHOR]

On the basis of predecessors' coordination optimization of active and reactive power in distribution network, For the necessity of the optimal operation in the distribution network, part of power generated from photovoltaic (PV) cannot be sold to users, and cannot enjoy subsidies. Similarly, the network loss in the power transmission will also bring a certain economic loss. This paper comprehensively considers the economic loss caused by the network loss and PV abandon of the distribution system, and establishes a model to minimize the economic loss. To solve this problem efficiently, the method of DistFlow equation and mixed integer second order cone programming (MISOCP) is used to solve the problem, in this method, the original mixed integer nonlinear programming non-convex problem is transformed into a convex problem, which makes the optimization problem easy to solve. The modified IEEE 33 and IEEE 69 distribution networks are tested by the above method. The optimized results are able to meet the target and have very small relaxation gaps, and the voltage level is also optimized. This coordinated optimization approach helps to optimize the economic operation for active distribution networks with PVs. [ABSTRACT FROM AUTHOR]

Background Purpose Methods Results Conclusion In magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming.In this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile.This study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO‐SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively.The simulation study demonstrated that the magnetic field was improved from 462  to 3.6 ppm, utilizing merely 1.2 kg of iron in a 40 cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%.The results indicated that the proposed method is expected to be effective for passive shimming. [ABSTRACT FROM AUTHOR]

The summary receiver operating characteristic (SROC) curve has been recommended as one important meta-analytical summary to represent the accuracy of a diagnostic test in the presence of heterogeneous cutoff values. However, selective publication of diagnostic studies for meta-analysis can induce publication bias (PB) on the estimate of the SROC curve. Several sensitivity analysis methods have been developed to quantify PB on the SROC curve, and all these methods utilize parametric selection functions to model the selective publication mechanism. The main contribution of this article is to propose a new sensitivity analysis approach that derives the worst-case bounds for the SROC curve by adopting nonparametric selection functions under minimal assumptions. The estimation procedures of the worst-case bounds use the Monte Carlo method to approximate the bias on the SROC curves along with the corresponding area under the curves, and then the maximum and minimum values of PB under a range of marginal selection probabilities are optimized by nonlinear programming. We apply the proposed method to real-world meta-analyses to show that the worst-case bounds of the SROC curves can provide useful insights for discussing the robustness of meta-analytical findings on diagnostic test accuracy. [ABSTRACT FROM AUTHOR]

The study considers issues of elaborating and validating a technique of autonomous vehicle motion planning based on sequential trajectory and speed optimization. This method includes components such as representing sought-for functions by finite elements (FE), vehicle kinematic model, sequential quadratic programming for nonlinear constrained optimization, and Gaussian N-point quadrature integration. The primary novelty consists of using the inverse approach for obtaining vehicle trajectory and speed. The curvature and speed are represented by integrated polynomials to reduce the number of unknowns. For this, piecewise functions with two and three degrees of freedom (DOF) are implemented through FE nodal parameters. The technique ensures higher differentiability compared to the needed in the geometric and kinematic equations. Thus, the generated reference curves are characterized by simple and unambiguous forms. The latter fits best the control accuracy and efficiency during the motion tracking phase. Another advantage is replacing the nodal linear equality constraints with integral nonlinear ones. This ensures the non-violation of boundary limits within each FE and not only in nodes. The optimization technique implies that the spatial and time variables must be found separately and staged. The trajectory search is accomplished in the restricted allowable zone composed by superposing an area inside the external and internal boundaries, based on keeping safe distances, excluding areas for moving obstacles. Thus, this study compares two models that use two and three nodal DOF on optimization quality, stability, and rapidity in real-time applications. The simulation example shows numerous graph results of geometric and kinematic parameters with smoothed curves up to the highest derivatives. Finally, the conclusions are made on the efficiency and quality of prognosis, outlining the similarities and differences between the two applied models. [ABSTRACT FROM AUTHOR]

Malnutrition has led to growth retardation in many adolescents and health deterioration in adults all over the world. Recently, there has been increasing attention on balanced diets as a preventive measure. This study evaluates the daily diet of a student, aiming to optimize the amino acid score (AAS) across three meals per day. By using balanced diet criteria as constraints, we established a single-objective nonlinear programming model, maximizing AAS as the objective function. The model was solved by using a simulated annealing algorithm, and we obtained a diet that is both balanced and high in AAS. This study helps to raise awareness about individual nutritional needs and provides guidance for dietary structure improvements, thereby contributing to global public health enhancement. [ABSTRACT FROM AUTHOR]

Mine ventilation is crucial for ensuring safe production in mines, as it is integral to the entire underground mining process. This study addresses the issues of high energy consumption, regulation difficulties, and unreasonable regulation schemes in mine ventilation systems. To this end, we construct an optimization model for mine ventilation network regulation using mixed-integer nonlinear programming (MINLP), focusing on objectives such as minimizing energy consumption, optimal regulation locations and modes, and minimizing the number of regulators. We analyze the construction methods of the mathematical optimization model for both selected and unselected fans. To handle high-order terms in the MINLP model, we propose a variable discretization strategy that introduces 0-1 binary variables to discretize fan branches' air quantity and frequency regulation ratios. This transformation converts high-order terms in the constraints of fan frequency regulation into quadratic terms, making the model suitable for solvers based on globally accurate algorithms. Example analysis demonstrate that the proposed method can find the optimal solution in all cases, confirming its effectiveness. Finally, we apply the optimization method of ventilation network regulation based on MINLP to a coal mine ventilation network. The results indicate that the power of the main fan after frequency regulation is 71.84 kW, achieving a significant energy savings rate of 65.60% compared to before optimization power levels. Notably, ventilation network can be regulated without adding new regulators, thereby reducing management and maintenance costs. This optimization method provides a solid foundation for the implementation of intelligent ventilation systems. [ABSTRACT FROM AUTHOR]

The article addresses the energy consumption minimization problem in wireless powered communication networks (WPCNs) and proposes a time allocation scheme, named DaTA, which is based on the Different Target Simultaneous Wireless Information and Power Transfer (DT-SWIPT) scheme such that the wireless station can share the remaining energy after transmission to the Hybrid Access Point (HAP) to those who have not transmitted to the HAP to minimize the energy consumption of the WPCN. In addition to proposing a new frame structure, the article also considers the Signal-to-Noise (SNR) constraint to guarantee that the HAP can successfully receive data from wireless stations. In the article, the problem of minimization of energy consumption is formulated as a nonlinear programming model. We employ the SQP (Sequential Quadratic Programming) algorithm to figure out the optimal solution. Moreover, a heuristic method is proposed as well to obtain a near-optimal solution in a shorter time. The simulation results showed that the proposed scheme outperforms the related work in terms of energy consumption and energy efficiency. [ABSTRACT FROM AUTHOR]

This paper attempts to propose two adaptive nonmonotone trust-region algorithms in the multiobjective optimization (MO) case. The first proposed trust-region algorithm uses a modified maximum nonmonotone technique, which takes a convex combination of the maximum value of some preceding successful iterates and the function value in the current iterate. The second one employs the average nonmonotone technique, which takes a weighted average of the successive function values. Under some suitable assumptions, the convergence of the sequences generated by the trust-region algorithms that use the aforementioned nonmonotone techniques to a critical point is shown. Using some well-known test problems, we compare our proposed adaptive nonmonotone MO algorithms with some other MO trust-region algorithms. To conduct a thorough comparison in this regard, some performance criteria are used. These numerical results confirm a significant advantage of applying the proposed adaptive nonmonotone trust-region algorithms in solving MO problems. Finally, the proposed algorithms are implemented to optimize one of the optimization problems of the abrasive water-jet machining process. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tensor sparse principal component analysis (TSPCA) by obtaining principal components which are linear combinations of a small subset of the original features for tensorial data. The core mathematical model can be formulated as a nonsmooth nonconvex optimization problem with a polynomial objective function, and with the sparsity constraint and the unit Euclidean spherical constraint. By employing the tools in tensor analysis, along with the variational properties for the involved $ \ell _{0} $ ℓ 0 -norm, the optimality condition of TSPCA is analysed in terms of stationary points. To well resolve the problem, we reformulate the stationary conditions into the Lagrange stationary equation system via the property of the projection operator onto the sparsity constraint set. With special emphasis on the Jacobian nonsingularity of the corresponding nonlinear system, we propose the Lagrange–Newton algorithm for pursuing the stationary point, which serves as a promising approximation of the optimal solution to TSPCA. The locally quadratic convergence rate is also established under mild conditions. Numerical experiments illustrate the effectiveness of our proposed TSPCA approach in terms of the solution accuracy as well as the computation time. [ABSTRACT FROM AUTHOR]

Fixture layout is an essential factor in intelligent manufacturing in the shipbuilding industry, affecting assembly quality and efficiency. Its optimization has become an urgent problem in the assembly process of compliant parts. Traditional fixture layout depends on workers' experience, which leads to butt clearance along the assembly interface. Thus, this article proposes a butt clearance control-oriented fixture layout optimization (BCCFLO) methodology. First, a method for calculating the part dimensional variation under the influence of fixture layout and fixture locating error is developed. Then, a constrained multi-objective integer nonlinear programming (CMINP) model is innovatively formulated to optimize the fixture layout. Furthermore, the non-dominated sorting genetic algorithm-II based on Latin hypercube sampling is designed to address the CMINP model. The case study illustrates and validates that the fixture layout achieved by the proposed method could significantly control the butt clearance for large compliant part assembly in the shipbuilding industry. [ABSTRACT FROM AUTHOR]

This paper overviews the development of a framework for the optimization of black-box mixed-integer functions subject to bound constraints. Our methodology is based on the use of tailored surrogate approximations of the unknown objective function, in combination with a trust-region method. To construct suitable model approximations, we assume that the unknown objective is locally quadratic, and we prove that this leads to fully-linear models in restricted discrete neighborhoods. We show that the proposed algorithm converges to a first-order mixed-integer stationary point according to several natural definitions of mixed-integer stationarity, depending on the structure of the objective function. We present numerical results to illustrate the computational performance of different implementations of this methodology in comparison with the state-of-the-art derivative-free solver NOMAD. [ABSTRACT FROM AUTHOR]

Mixed-Integer Formulations for Power Production Problems The unit commitment problem is a complex mixed-integer nonlinear program that originates in the field of power production. Although it arises in a monopolistic system, there is still great attention to this problem even in a free-market regime, where it constitutes only a subproblem of larger ones. Historically, it was usually solved by Lagrangian relaxation methods. However, the advances achieved by commercial solvers of mixed-integer (linear and convex) programming problems have made such approaches an attractive option. T. Bacci, A. Frangioni, C. Gentile, and K. Tavlaridis-Gyparakis present the first mixed-integer nonlinear programming formulation with a polynomial number of both variables and constraints that describes the convex hull of the feasible solutions of the unit commitment problem with a single thermal generation unit, comprising all typical constraints and convex power generation costs. Proving that the formulation is exact requires a new result about the convex envelope of specially structured functions that can have independent interest. This new formulation for a single power generation unit is used to derive three new formulations for the general unit commitment problem whose effectiveness has been tested against the state-of-art formulation. The unit commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon. Operational constraints of each unit depend on its type and can be rather complex. For thermal units, typical ones concern minimum and maximum power output, minimum up- and down-time, start-up and shut-down limits, ramp-up and ramp-down limits, and nonlinear objective function. In this work, we present the first mixed-integer nonlinear program formulation that describes the convex hull of the feasible solutions of the single-unit commitment problem comprising all the above constraints and convex power generation costs. The new formulation has a polynomial number of both variables and constraints, and it is based on the efficient dynamic programming algorithm proposed by Frangioni and Gentile together with the perspective reformulation. The proof that the formulation is exact is based on a new extension of a result previously only available in the polyhedral case, which is potentially of interest in itself. We then analyze the effect of using it to develop tight formulations for the more general UC problem. Because the formulation is rather large, we also propose two new formulations, based on partial aggregations of variables, with different trade-offs between quality of the bound and cost of solving the continuous relaxation. Our results show that navigating these trade-offs may lead to improved performances. Funding: A. Frangioni acknowledges the partial financial support by the European Union Horizon 2020 research and innovation programme [Grant 773897 "plan4res"]. A. Frangioni and C. Gentile acknowledge the partial financial support by the European Union Horizon 2020 Marie Skłodowska-Curie Actions [Grant 764759 "MINOA"]. T. Bacci, A. Frangioni, and C. Gentile acknowledge the partial financial support by the Italian Ministry of Education program MIUR-PRIN [Grant 2015B5F27W "Nonlinear and Combinatorial Aspects of Complex Networks"]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2435. [ABSTRACT FROM AUTHOR]

In this paper, we studied a generalized Nash equilibrium problem where the constraint conditions were limited to a certain probability. The existence of an equilibrium solution for the vector-valued optimization problem was verified using Ky Fan’s inequality and Lusin’s theorem, considering the conditions of lower semi-continuity and concavity. Based on the study of the variational inequality method, we proposed a new algorithm to solve the problem. Furthermore, we analyzed the convergence of the algorithm. Finally, we applied the model to examine the economic benefits of digital currency issuance, corroborating the algorithm’s effectiveness with a concrete numerical example. [ABSTRACT FROM AUTHOR]

Nonlinear optimal control problems governed by variable-order fractional integro-differential equations constitute an important subgroup of optimal control problems. This group of problems is often difficult or impossible to solve analytically because of the variable-order fractional derivatives and fractional integrals. In this article, we utilized the expansion of Lagrange polynomials in terms of Chebyshev polynomials and the power series of Chebyshev polynomials to find an approximate solution with high accuracy. Subsequently, by employing collocation points, the problem was transformed into a nonlinear programming problem. In addition, variable-order fractional derivatives in the Caputo sense were represented by a new operational matrix, and an operational matrix represented fractional integrals. As a result, the mentioned integro-differential optimal control problem becomes a nonlinear programming problem that can be easily solved with the repetitive optimization method. In the end, the proposed method is illustrated by numerical examples that demonstrate its efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, optimal gliding trajectories are analyzed, formulating an optimal control problem to be solved computationally via nonlinear programming. A multi-objective terminal cost function that minimizes the velocity, altitude, horizontal flight path angle, and the error of a desired terminal point is formulated. The results are validated via Monte Carlo simulations, analyzing the influence of the variations in the lift-to-drag ratios in the atmospheric entry. The results show feasible solutions for minimizing the distance to the desired final point, which have significant practical implications for the controlled gliding entry of a spaceplane on Mars. In this sense, the results also show that the longitudes of the landing points do not change too much for almost all trajectories, while the latitude of these points is in the interval of about 4 degrees for the majority of the trajectories. This suggests that it is possible to implement an optimal control approach with reasonable accuracy for the controlled gliding entry of a spaceplane on Mars, even in the presence of some uncertainties regarding the aerodynamic performance of the spacecraft, such as the lift-to-drag ratio. [ABSTRACT FROM AUTHOR]

The optimization of process systems within the field of Chemical Engineering often confronts uncertainties that can exert significant influences on the performance and dependability of the obtained solutions. This research endeavors to investigate the application of Bayesian optimization in the realm of constrained mixed integer nonlinear problems. A comparative analysis was conducted, exploring different surrogate models, and evaluating diverse kernel functions and acquisition functions. Furthermore, a sampling strategy was devised to assess the enhancement achieved by the acquisition function. The findings of this article reveal the superior performance of sparse Gaussian processes in conjunction with computationally inexpensive acquisition functions, thereby highlighting their suitability for addressing mixed integer nonlinear programming problems characterized by noisy functions and stochastic behavior. Consequently, this article presents a computationally efficient approach to effectively tackle the challenges associated with data‐driven mixed integer nonlinear programming problems within the domain of Process System Engineering. [ABSTRACT FROM AUTHOR]

Aiming at the problem of multiple constraints and low solving efficiency in the process of vehicle path tracking, an improved hp-adaptive Radau pseudospectral method (I-hp-ARPM) which uses a double-layer optimization iteration strategy and the residual of differential algebraic constraints at sampling points with a Gaussian distribution as the error evaluation criterion is proposed. Firstly, a four-DOF vehicle motion model is established. Secondly, on the basis of establishing algebraic differential constraints and path constraints and satisfying the optimization objective function, the I-hp-ARPM is used to transform the optimal control problem (OCP) into a general nonlinear programming problem for solution. Finally, the effectiveness of the proposed method is verified compared with the traditional hp-adaptive pseudospectral method. The simulation results and the virtual test show that there are peak values at 3.5 s and 4.8 s, as well as 6 s, for both the steering wheel angle and the sideslip angle with the condition of μ = 0.8. And also, there are peak values at the times of 3.5 s and 5.5 s, as well as 7.5 s, with the condition of μ = 0.4. This indicates the vehicle can track the reference path well with the control of the proposed algorithm. Both the initial and final constraints, as well as the path constraint, meet the requirements. The proposed method can generate the optimal trajectory that meets various constraint requirements. This method provides a design basis for path tracking of autonomous vehicles and has significance in engineering. [ABSTRACT FROM AUTHOR]

There is considered the possibility of solving the problem of choosing the optimal width of curved emergency corridors, both sides of which are parts of an ellipse to further minimize the mixing of human flows (and, accordingly, to prevent congestion in people's movement) during evacuation in case of fire or other emergencies. The issue of changing the corridor width along its length is considered in two ways: one-dimensional unconditional optimization and the classical Kuhn-Tucker theorem. A sequence of steps is proposed to implement the task of finding the optimal corridor width.

Gas production and pressure from shale gas wells are highest early in the extraction process and decay rapidly over time. Skid-mounted compression equipment (SCE) in the shale gas gathering and transportation system (SGTS) can adapt to production changes in gas wells and can be deployed flexibly, improving equipment utilization. This paper examines the effects of node pressure and equipment type on the deployment scheme of SCE. Using a specific shale gas field production block as a case study, this paper proposes a method for multicycle operation and pressurizing deployment optimization in the SGTS, establishing a mixed-integer nonlinear programming (MINLP) model. Solving this optimization model yields the optimal deployment scheme of SCE at different times, the number of compression equipment, and the equipment utilization rate. The results show that in shale gas field production, SCE can be deployed flexibly, and most equipment utilization rates are above 0.8, with a maximum of 0.99. This not only achieves efficient use of equipment but also reduces the purchase cost, fully reflecting the importance of SCE in the SGTS. A sensitivity analysis was conducted to consider the impact of different costs and type combinations of SCE on the total production cost, and the results showed that the total cost of eight types was 6.28% lower than that of two types of booster equipment combinations. [ABSTRACT FROM AUTHOR]

Cooling water systems (CWSs) are extensively utilized in various industries to eliminate the excess heat and converse energy. Studies on CWSs mainly concentrated on finding the optimal cooler network structure. In addition, some works also considered the optimal design under varied operation conditions. However, in these works, once the optimal design of the cooler's network is determined, its arrangement remains fixed and cannot be adapted to accommodate diverse operating conditions. In this work, a flexible topology network concept is proposed to make the adjustment of network structure possible under different operation conditions. The CWS with integrated air cooler and flexible topology network has better overall performance, represented by a mixed integer nonlinear programming (MINLP) model that require advanced tools such as GAMS software. Case studies revealed that the proposed methodology can realize better energy-saving performance, and improve the economic performance under varied operation conditions. The impact of critical flexible nodes on system configuration and economy is achieved by sensitivity analysis. [ABSTRACT FROM AUTHOR]

This study is the first time devoted to seek an online optimal tracking solution for unknown nonlinear singularly perturbed systems based on single network adaptive critic (SNAC) design. Firstly, a novel identifier with more efficient parametric multi-time scales differential neural network (PMTSDNN) is developed to obtain the unknown system dynamics. Then, based on the identification results, the online optimal tracking controller consists of an adaptive steady control term and an optimal feedback control term is developed by using SNAC to solve the Hamilton–Jacobi–Bellman (HJB) equation online. New learning law considering filtered parameter identification error is developed for the PMTSDNN identifier and the SNAC, which can realize online synchronous learning and fast convergence. The Lyapunov approach is synthesized to ensure the convergence characteristics of the overall closed loop system consisting of the PMTSDNN identifier, the SNAC and the optimal tracking control policy. Three examples are provided to illustrate the effectiveness of the investigated method. [ABSTRACT FROM AUTHOR]

This note comments on the study of [Diri Kenger, Zülal, Çağrı Koç, and Eren Özceylan. 2020. "Integrated Disassembly Line Balancing and Routing Problem." International Journal of Production Research 58 (23): 7250–7268.] which studies an integrated disassembly line balancing and routing problem and develops two mixed integer linear programming (MILP) models and three mixed integer nonlinear programming (MINLP) models to handle five different scenarios, respectively. The purpose is twofold. First, we demonstrate that the two MILP models can be separated into two parallel subproblems whose optimal solutions can be combined to obtain the optimal solution of the original models. Second, we show that the three MINLP models can be linearised and propose two different linearisation techniques to reformulate them as equivalent MILP models. Computational results indicate that the linearised model outperforms the original nonlinear model in most cases. [ABSTRACT FROM AUTHOR]

This paper introduces a solution method for the multimission selective maintenance problem (SMP) that combines column-generation (CG) and genetic algorithms (GAs). The multimission SMP is an optimisation problem that arises when a system performs a sequence of missions separated by breaks of finite duration. During these finite breaks, only a subset of possible maintenance actions can be performed due to resource limitations. The problem is in deciding what actions to perform during each break duration such that the system meets or exceeds a minimum target reliability for all missions. The resulting optimisation problems are usually modelled as mixed integer nonlinear mathematical programmes, which are hard to solve. They are usually solved using metaheuristics. We propose a solution method based on CG framework in which the subproblems are solved using a GA. By integrating the GA within the classical CG framework, high-quality solutions can be obtained very quickly. The proposed solution method is capable of solving systems composed of both parallel and k-out-of-n:G subsystems. This hybrid CG algorithm is shown to obtain near optimal solutions and outperform other metaheuristic solution methods; it is also shown to be capable of solving large-scale systems composed of many subsystems and hundreds of components in a reasonable amount of time. [ABSTRACT FROM AUTHOR]

Repetitive group inspection of production lots is considered to develop the failure censored plan with minimal expected sampling effort using prior information. Optimal reliability test plans are derived for the family of log-location-scale lifetime distributions, whereas a limited beta distribution is assumed to model the proportion nonconforming, p. A highly efficient and quick step-by-step algorithm is proposed to solve the underlying mixed nonlinear programming problem. Conventional repetitive group plans are often very effective in reducing the average sample number with respect to other inspection schemes, but sample sizes may increase under certain conditions such as high censoring. The inclusion of previous knowledge from past empirical results contributes to drastically reduce the amount of sampling required in life testing. Moreover, the use of expected sampling risks significantly improves the assessment of the actual producer and consumer sampling risks. Several tables and figures are presented to analyse the effect of the available prior evidence about p. The results show that the proposed lot inspection scheme clearly outperforms the standard repetitive group plans obtained under the traditional approach based on conventional risks. Finally, an application to the manufacture of integrated circuits is included for illustrative purposes. [ABSTRACT FROM AUTHOR]

Improved lognormal reliability test plans are proposed for lot sentencing. A mixed integer nonlinear programming problem is stated and solved in order to find the duration of the reliability test based on lognormal failure count data that minimises the inspection effort. The maximum number of failures tolerated by the decision maker and the necessary number of devices to be tested are also determined. The producer and consumer risks are limited in advanced, whereas the cost function is essentially a linear combination of the required sample size and test time. The minimum-cost test for device reliability demonstration provides the best criterion to decide the acceptability of manufacturing processes and submitted lots. A quick and effective iterative algorithm is suggested to obtain the optimal reliability demonstration test plan. The developed methodology is applied to the production of microelectronic chips, semiconductor lasers and ball bearings for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we address a new optimal plate design problem in steel production, in which slab selection is jointly considered. On the basis of the underlying features, the problem is formulated as a mixed integer nonlinear programming (MINLP) model with generalized disjunctive programming (GDP) constraints. A logic-based outer approximation (L-OA) algorithm is proposed to solve the problem. Specifically, a two-stage heuristic method is designed to initialise the L-OA algorithm. Numerical results are presented to demonstrate that the proposed L-OA algorithm and the heuristic method are effective and computationally efficient. [ABSTRACT FROM AUTHOR]

Nonlinear optimal control problems governed by variable-order fractional integro-differential equations constitute an important subgroup of optimal control problems. This group of problems is often difficult or impossible to solve analytically because of the variable-order fractional derivatives and fractional integrals. In this article, we utilized the expansion of Lagrange polynomials in terms of Chebyshev polynomials and the power series of Chebyshev polynomials to find an approximate solution with high accuracy. Subsequently, by employing collocation points, the problem was transformed into a nonlinear programming problem. In addition, variable-order fractional derivatives in the Caputo sense were represented by a new operational matrix, and an operational matrix represented fractional integrals. As a result, the mentioned integro-differential optimal control problem becomes a nonlinear programming problem that can be easily solved with the repetitive optimization method. In the end, the proposed method is illustrated by numerical examples that demonstrate its efficiency and accuracy.

The relevance of this study is determined by the growing worldwide interest in renewable energy sources against the backdrop of depleting fossil fuel reserves. This study aims to develop an innovative technology for managing biofuel production from wood waste, including a set of interrelated economic and mathematical models focused on maximizing the fuel and energy efficiency of biofuels depending on the location of waste generation, feedstock moisture content, and distance to the biofuel production site. This technology should also combine the main directions of international research in the field of environmental responsibility of countries in terms of carbon dioxide (CO2) emissions and the Paris Climate Agreement. The methodological basis of the research comprises the authors’ innovative technology based on a set of interconnected economic and mathematical models and managerial decision-making systems, methods for nonlinear programming, system analysis, an information approach to the analysis of systems, accepted technological processes, norms, and standards established in the international practice of the timber industry. This innovative technology was implemented in practice using the capabilities of the MathCad and MS Excel software products. The article determines the optimal operating parameters of timber industry enterprises at which the specific thermal energy of the produced biofuel exceeds by at least 15% the thermal energy spent on processing this biofuel as an energy carrier. Wood waste biofuel production is profitable if the distance for feedstock transportation to the production site does not exceed 80 km and the relative humidity of the raw materials does not exceed 60%. Doi: 10.28991/ESJ-2024-08-03-03 Full Text: PDF

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace's production capacity and the steelmaking converter's consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods. [ABSTRACT FROM AUTHOR]

Orthogonal Nonnegative Matrix Factorization (ONMF) with orthogonality constraints on a matrix has been found to provide better clustering results over existing clustering problems. Because of the orthogonality constraint, this optimization problem is difficult to solve. Many of the existing constraint-preserving methods deal directly with the constraints using different techniques such as matrix decomposition or computing exponential matrices. Here, we propose an alternative formulation of the ONMF problem which converts the orthogonality constraints into non-convex constraints. To handle the non-convex constraints, a penalty function is applied. The penalized problem is a smooth nonlinear programming problem with quadratic (convex) constraints that can be solved by a proper optimization method. We first make use of an optimization method with two gradient projection steps and then apply a post-processing technique to construct a partition of the clustering problem. Comparative performance analysis of our proposed approach with other available clustering methods on randomly generated test problems and hard synthetic data-sets shows the outperformance of our approach, in terms of the obtained misclassification error rate and the Rand index. [ABSTRACT FROM AUTHOR]