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This article presents a pioneering mathematical model, fuzzy bipolar hypersoft (FBHS) sets, which combines the bipolarity of parameters with the fuzziness of data. Motivated by the need for a comprehensive framework capable of addressing uncertainty and variability in complex phenomena, our approach introduces a novel method for representing both the presence and absence of parameters through FBHS sets. By employing two mappings to estimate positive and negative fuzziness levels, we bridge the gap between bipolarity, fuzziness, and parameterization, allowing for more realistic simulations of multifaceted scenarios. Compared to existing models like bipolar fuzzy hypersoft (BFHS) sets, FBHS sets offer a more intuitive and user-friendly approach to modeling phenomena involving bipolarity, fuzziness, and parameterization. This advantage is underscored by a detailed comparison and a practical example illustrating FBHS sets' superiority in modeling such phenomena. Additionally, this paper provides an in-depth exploration of fundamental FBHS set operations, highlighting their robustness and applicability in various contexts. Finally, we demonstrate the practical utility of FBHS sets in problem-solving and introduce an algorithm for optimal object selection based on available information sets, further emphasizing the advantages of our proposed framework. [ABSTRACT FROM AUTHOR]

This paper is concerned with two generalized inverse eigenvalue problems for a kind of pseudo‐Jacobi matrix. From a non‐Hermite matrix, an r × r Jacobi matrix, two distinct real eigenvalues, and part of the corresponding eigenvectors, an n × n pseudo‐Jacobi matrix is constructed. Furthermore, an n × n pseudo‐Jacobi matrix can be made by two different eigenpairs and a positive definite diagonal matrix. It is shown that a unique pseudo‐Jacobi matrix can be recovered from partial eigenpairs and certain special mixed eigendata. Two algorithms are provided for the reconstruction of such a pseudo‐Jacobi matrix, and illustrative numerical examples are presented to verify the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose three self-adaptive relaxed CQ-algorithms with projections onto halfspaces for solving a split equality problem. The stepsize of the algorithms is dynamically calculated without any prior information regarding operator norms. Moreover, we prove the strong convergence to the minimum-norm solution of the split equality problem. Finally, we test the validity of our results by conducting some numerical experiments and consider signal recovery problems as applications. [ABSTRACT FROM AUTHOR]

Service composition is a core issue of cloud manufacturing (CMfg) to integrate distributed manufacturing services for customised manufacturing tasks. Existing studies focus on the quality of service (QoS) in composition by assuming that each service is independent with each other. However, the correlation between services determines whether a composition is feasible in practice and is a primary factor of its QoS. This paper considers two typical correlations, composability-oriented correlation and quality-oriented correlation. The composability-oriented correlation is modelled as a group of constraints to decide whether a solution is feasible. The influence of the quality-oriented correlation between two services on the overall QoS of a composition is quantified by a discount percentage based on their correlation degrees. A mathematical model of correlation-aware service composition is then established. To solve this problem, a many-objective memetic algorithm termed HypE-C (Hypervolume Estimation Algorithm for Multiobjective Optimisation involving Correlation) is designed. Three correlation-based local search strategies are established in the frame of HypE (Hypervolume Estimation Algorithm for Multiobjective Optimisation) to achieve better trade-off among multiple conflicting QoS criteria. Experiments demonstrate the effectiveness of the proposed algorithm HypE-C compared with five many-objective algorithms on eliminating infeasible search space and providing high QoS service composition solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a new metaheuristic algorithm called Migration Algorithm (MA), which is helpful in solving optimization problems. The fundamental inspiration of MA is the process of human migration, which aims to improve job, educational, economic, and living conditions, and so on. The mathematical modeling of the proposed MA is presented in two phases to empower the proposed approach in exploration and exploitation during the search process. In the exploration phase, the algorithm population is updated based on the simulation of choosing the migration destination among the available options. In the exploitation phase, the algorithm population is updated based on the efforts of individuals in the migration destination to adapt to the new environment and improve their conditions. MA’s performance is evaluated on fifty-two standard benchmark functions consisting of unimodal and multimodal types and the CEC 2017 test suite. In addition, MA’s results are compared with the performance of twelve well-known metaheuristic algorithms. The optimization results show the proposed MA approach’s high ability to balance exploration and exploitation to achieve suitable solutions for optimization problems. The analysis and comparison of the simulation results show that MA has provided superior performance against competitor algorithms in most benchmark functions. Also, the implementation of MA on four engineering design problems indicates the effective capability of the proposed approach in handling optimization tasks in real-world applications. [ABSTRACT FROM AUTHOR]

Legalized routing is an essential part of PCB automatic routing. It solves the problem of wiring conflicts and obtains routing results that comply with the constraints of design rules. Traditional legalized routing problems mostly use trial backtracking methods, but with increasing design complexity and design rules, avoiding wiring conflicts between networks has become increasingly challenging. This paper proposes a legalized routing algorithm based on linear programming to obtain the optimal wiring trajectory under specified topological constraints. First, the corresponding routing model was established based on numerous routing rules, and a routing grid diagram was found using obstacles as grid points. Secondly, a global routing algorithm was used to obtain the estimated wiring path, and integer linear programming was used to realize the mathematical modeling of the legalized routing problem. Finally, a multi-line simultaneous routing strategy was used to design and implement a detailed routing algorithm, optimizing the routing results. We use C++ to complete the coding work and thoroughly test the PCB use cases of different sizes. The experimental results show that our algorithm still maintains a 100% routing success rate, good time performance, and excellent routing quality with large-scale use cases compared with the trial backtracking method. [ABSTRACT FROM AUTHOR]

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

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.)

With the rapid development of social platforms and human activities, people are now interested to solve their problems with the help of the social crowd-powered system. So, crowdsourcing has become a promising way of solving problems in a distributed manner within a specific time. Crowd workers pick up a task (simple or complex) and solve it with competing interest or collaboratively and receive an incentive (as monetary or non-monetary). In paid crowdsourcing platforms, crowd workers solve complex tasks and get remunerations through prior bidding or prior announcement of fee decided by the requester (task provider). For decomposable tasks, a single winner may not provide a significant solution to the requester due to the insufficient knowledge. So, we induce collaboration in competitive crowdsourcing markets to better handle decomposable-type tasks. In this paper, we propose an envelope game-based mechanism that ensures if the tasks are decomposable then the workers will be encouraged to collaborate with their subtasks and share their remunerations. This mechanism also increases the chance of receiving more number of cost-effective solutions. Thus both the requester and crowd workers get benefits from the system. The effectiveness of the proposed mechanism is evaluated through empirical analysis on simulated environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

There have been many algorithms for solving the shortest path problems through necessary nodes set, but most of them are insufficient when applied to the circumstances with extra hard constraints. To solve this problem, this paper puts forward a random search algorithm based on depth first search mechanism. The mathematical models are provided by users according to actual situation, and they are abstracted as undirected weighted graphs. Some related variables such as the beginning node, the end node, necessary nodes and extra hard constraints are defined by path planning requirements, and they are saved as adjacency matrix. In the searching process, the feasibility of the path is determined in real time to meet the requirements of extra hard constraints. Finally, the optimal shortest path solution is obtained. Simulation and actual results show that the algorithm effectively avoids the influence of intermediate path under extra hard constraints and generate a shortest path, which means that this algorithm can greatly improve problem solvability. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology 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.)

Peak height detection is critical for blade tip clearance (BTC) measurement based on capacitive probes. However, the noise interference of the complicated working environments and instabilities of the rotation speed make high-precision peak detection a challenge. To solve this problem, a novel self-adaptive, multi-peak detection algorithm is proposed in this paper. The adaptive dual thresholds are used to identify the single peak and pre-estimate its peak parameters for the segmentation of the peak support region and the selection basis of the wavelet parameters. Then, based on the prior pre-estimation information, the wavelet matching is performed on the segmented single peak adaptively for eight times, and the derived mathematical models of the wavelet matching are fitted using the obtained matching coefficients to get precise peak parameters such as peak height and peak position. The blade tip clearance is calculated from the peak height through the calibration curve. The experiments show that the BTC measurement error of the proposed algorithm is under 15 μm, with the clearance ranging from to , and the proposed algorithm has preferable stability to comparable algorithms with the rotation speed ranging from 1000 rpm to 4000 rpm. This implies that the proposed algorithm has high anti-noise performance and good adaptability to rotation speed change. [ABSTRACT FROM AUTHOR]

The paper aims to present an integrated approach to solve the decision-making problem under the probabilistic hesitant fuzzy information (PHFI) features, which is an extension of the hesitant fuzzy set. The considered PHFI not only allows multiple opinions, but also associates occurrence probability to each opinion, which increases the reliability of the information. Motivated by these features of PHFI, an approach is presented to solve the decision problem with partial known information about the attribute and expert weights. In addition, an algorithm for finding some missing values in the preference information is presented and stated their properties. Afterward, the Hamy mean operator has been used to aggregate the different collective information into a single one. Also, we presented a COPRAS method to the PHFI for ranking the given alternatives. The presented algorithm has been demonstrated through a case study of cloud vendor selection and its validity has been revealed by comparing the approach results with the several existing algorithm results. [ABSTRACT FROM AUTHOR]

Nowadays organizations outsource transportation of goods or services to reduce cost which leads to a particular type of problem called open location-routing. Also, each logistic organization possesses a limited number of specific vehicles that may not be enough in certain circumstances. This issue indicates the importance of simultaneously considering both open and closed routs. On the other hand, the growing concerns about the detrimental environmental impacts of human activities reveal the necessity of paying attention to environmental issues in logistics. In this study, a bi-objective mathematical programming model is proposed for two-echelon close and open location-routing problem (2E-COLRP) including two echelons of factories, depots and customers to minimize costs and CO2 emissions. The proposed model finds the optimal routs, optimal number of vehicles and facilities as well as the locations of facilities. The augmented epsilon constraint method is used as an exact method to solve the small-sized problems. Due to complexity of model, two metaheuristic algorithms named MOGWO and NSGA-II are utilized to tackle the problems. The efficiency of two aforementioned algorithms is evaluated in terms of several indices considering 22 problem instances with various sizes. The results show that MOGWO performs better than NSGA-II. [ABSTRACT FROM AUTHOR]

Multiple external representations (MERs) play an important role in the learning field of mathematics. Whereas the cognitive theory of multimedia learning and the integrative text and picture comprehension model assume that the heterogeneous combination of symbolic and analogous representations fosters learning; the design, functions, and tasks framework holds that learning benefits depend on the specific functions of MERs. The current paper describes a conceptual replication study of one of the few studies comparing single representations, heterogeneous, and homogeneous MERs in the context of mathematics learning. In a balanced incomplete block design, the participants were provided single representations (a graphic, text, or formula) or a heterogeneous (e.g., text + graphic) or homogeneous (text + formula) combination of these to solve linear system of equations problems. In accordance with previous research, performance was superior in conditions providing MERs compared to single‐representation conditions. Moreover, heterogeneous MERs led to time savings over homogeneous MERs which triggered an increase in cognitive load. Contrary to previous research, text was the least fixated representation whereas the graphical representation proved to be most beneficial. With regard to practical implications, experts should be fostered through more challenging homogeneous MERs whereas novices should be supported through the accessible graphic contained in heterogeneous MERs. Lay Description: What is already known about this topic: Providing multiple instead of single representations can foster mathematics learning.However, some combinations of representations hamper the performance of novice learners.The classical multimedia view explains the positive effect of combining text with picture.Recent research suggests the combination of multiple symbolic representations (text and formula). What this paper adds: The study replicated the effect of multiple symbolic representations for equation solving.In contrast to former research, each representation (text, formula, and graphic) was functionally equivalent.Tasks with differently coded representations were solved faster and with less mental effort.Gaze behavior indicated that students mostly used the graphical representation. Implications for practice and/or policy: Beginners should be supported with a graphic when solving equations.Experts should be challenged with a combination of symbolic representations to benefit the most. [ABSTRACT FROM AUTHOR]

Summary: Mathematical model parameter estimation of solar photovoltaic (PV) cell, module and array represent a prodigious challenge in recent researches, where analytical, metaheuristic and hybrid techniques play a vital role for parameter extraction by using manufacturer's datasheet and experimental data, although the precise and highly reliable solution identification is still a complex problem to be solved. In this paper, a new Emperor Penguin Optimisation‐ (EPO) based parameter estimation approach for a single‐diode Rp solar PV model is presented that is cohesively analysed under different sets of temperature and irradiance (G). Validation of the proposed technique is perceived on the analysis of performance characteristics, that is, current‐voltage (I‐V) and power‐voltage (P‐V) of KC200GT, PWP201, and STP6 120‐36 PV modules under various simulation conditions. Moreover, estimated results are compared with the experimental data and several established estimation techniques in the literature for validation and demonstrate the proposed technique with highly precise outcomes having reduced computational cost for the PV model parameter extraction problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse, model, and solve the rescheduling problem in dynamic permutation flow shop environments while considering several criteria to optimize. Searching optimal solutions in multiobjective optimization problems may be difficult as these objectives are expressing different concepts and are not directly comparable. Thus, it is not possible to reduce the problem to a single-objective optimization, and a set of efficient (nondominated) solutions, a so-called Pareto front, must be found. Moreover, in manufacturing environments, disruptive changes usually emerge in scheduling problems, such as machine breakdowns or the arrival of new jobs, causing a need for fast schedule adaptation. In this paper, a mathematical model for this type of problem is proposed and a restarted iterated Pareto greedy (RIPG) metaheuristic is used to find the optimal Pareto front. To demonstrate the appropriateness of this approach, the algorithm is applied to a benchmark specifically designed in this study, considering three objective functions (makespan, total weighted tardiness, and steadiness) and three classes of disruptions (appearance of new jobs, machine faults, and changes in operational times). Experimental studies indicate the proposed approach can effectively solve rescheduling tasks in a multiobjective environment. [ABSTRACT FROM AUTHOR]

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University 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.)

In modern conditions, due to the vastness of the territory of Kazakhstan, with a certain probability, natural disasters such as earthquakes, floods, avalanches, as well as accidents, destruction of buildings, epidemics, release of chemical toxic substances at industrial enterprises, fires in educational and medical institutions are possible, which justifies the relevance of modern methods and technologies for solving the problem of evacuation. The peculiarity of this work lies in the formation of an integrated approach for organizing the evacuation process both in peacetime as training for the event of an emergency situation (emergency), and in the event of the emergency itself. A conceptual diagram of an evacuation system is proposed that uses heterogeneous sources for receiving and transmitting information about the onset of an emergency. The input and output sources for receiving and transmitting information about the number of people in the building are determined. The main purpose of the system is to form an operational real-time evacuation plan. This work is the result of a phased implementation of an integrated evacuation system, which consists in building a mathematical model and a method for solving the problem of maximum flow in the network. A mathematical model has been developed for the optimal flow distribution along the Grindshiels network with the analysis of the flow formation and the characteristics of people’s motion in enclosed spaces. A game-theoretic approach and mathematical methods of the theory of hydraulic networks for finding an equilibrium state in flow-distribution networks have been developed. An algorithm for solving the evacuation problem using the graph approach is proposed. The results of this paper make it possible to systematically organize training evacuations, prepare resources, train the personnel responsible for evacuation in order to quickly respond in an emergency and carry out the evacuation process in order to avoid major consequences. [ABSTRACT FROM AUTHOR]

Copyright of Application Research of Computers / Jisuanji Yingyong Yanjiu is the property of Application Research of Computers Edition 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.)

Dynamic Travelling Salesman Problem (DTSP) is a novel type of TSP where the number of cities in the problem domain changes unpredictably. The approaches to handling dynamism in those DTSPs, has been solving the problems as they were static and recreating the models after each change. In this respect, multi-agent based strategies along with intelligent approaches provide an opportunity to deal with those difficulties. The proposed approach in this paper is based on the modification of existing solutions according to changes in the city domain. Thereby problem is not resolved while local city agents deliver their novel bids (solution proposals) for these new conditions. Finally, general manager agent makes a decision about the new solution. This study presents two different agent-based solution strategies for providing promising solutions to DTSP. One of these strategies is based on the competition of city agents in a greedy way and thereby city agents just search for randomly selected alternatives which are feasible for the new conditions. The second strategy covers competition of city agents by the use of great deluge algorithm as the search mechanism. Finally, both of those proposed strategies are compared against the solutions of reinvented models. Agent-based strategies start to produce better results as the problem size increases. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications 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.)

Let G be a directed graph associated with a weight w : E (G) → R + . For an edge-cut Q of G , the average weight of Q is denoted and defined as w ave (Q) = ∑ e ∈ Q w (e) | Q | . An optimal edge-cut with average weight is an edge-cut Q such that w ave (Q) is maximum among all edge-cuts (or minimum, symmetrically). In this paper, a polynomial algorithm for this problem is proposed for finding an optimal edge-cut in a rooted tree separating the root and the set of all leafs. This algorithm enables us to develop an automatic clustering method with more accurate detection of community output. [ABSTRACT FROM AUTHOR]

A model for energy trading in microgrids (MGs) is proposed in this paper. Imperialist competitive algorithm is used as a powerful method to determine the optimal schedule of all generation units in MG. The optimal scheduling is determined over a planning horizon considering all the constraints of the MG elements and the load demands. Scheduling of distributed generations (DGs) in the MG affects the risk of blackout in the power system. Therefore, a new objective function is presented to investigate the effect of DGs scheduling on the risk of partial or total blackout. DGs generate the great portion of energy in a MG. Generated power by some of DGs is strongly dependent on the weather and ambient conditions. Therefore, the power generation forecast is the major concern for constructing the model for MG energy trading. In this paper, artificial neural network (ANN) is used to predict hourly power outputs of DGs in the MG. Based on the ANN-based forecast module, the imperialist competitive algorithm is developed to determine the MG scheduling, by which the sources can be managed and an optimal operation can be achieved. [ABSTRACT FROM AUTHOR]

Our work is devoted to an inverse problem for three-dimensional parabolic partial differential equations. When the surface temperature data are given, the problem of reconstructing the heat flux and the source term is investigated. There are two main contributions of this paper. First, an adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional. Second, an improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm is studied. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Motivated by the behavioral phenomena that occur while human operators are carrying out tasks, we study multitasking scheduling problems with a rate-modifying activity. In the problems, the processing of a selected task suffers from interruptions by other tasks that are available but unfinished, and the human operators regularly engage rest breaks during work shifts allowing them to recover or mitigate some of the negative effects of fatigue. The objectives are to respectively minimize: makespan, total completion time, maximum lateness, and due-date assignment related cost by determining when to schedule the rate modifying activity and the optimal task sequence in the presence of multitasking. Scheduling models and algorithms are proposed to solve the problems. The numerical examples are presented to illustrate the theorems and algorithms. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel distributed differential evolution framework called distributed mixed variants (dynamic) differential evolution ( $$dmvD^{2}E)$$ . This novel framework is a heterogeneous mix of effective differential evolution ( DE) and dynamic differential evolution ( DDE) variants with diverse characteristics in a distributed framework to result in $$dmvD^{2}E$$ . The $$dmvD^{2}E$$ , discussed in this paper, constitute various proportions and combinations of DE/best/2/bin and DDE/best/2/bin as subpopulations with each variant evolving independently but also exchanging information amongst others to co-operatively enhance the efficacy of $$dmvD^{2}E$$ as whole. The $$dmvD^{2}E$$ variants have been run on 14 test problems of 30 dimensions to display their competitive performance over the distributed classical and dynamic versions of the constituent variants. The $$dmvD^{2}E$$ , when benchmarked on a different 13 test problems of 500 as well as 1,000 dimensions, scaled well and outperformed, on an average, five existing distributed differential evolution algorithms. [ABSTRACT FROM AUTHOR]

It is difficult for the robot to grasp objects of any pose by the independent grasping scheme without the help of human. And the independent grasping scheme is also the key technology to develop the AI robot. In order to solve the problem, this paper establishes the full 3D point cloud model of the target object in advance under the PCL point cloud library. The partial view model of the target object in the current working environment is extracted when dexterous hand grasps the target. After aligning the extracted partial view model, the best alignment homogeneous transformation matrix mapping the partial view model to the full 3D point cloud model is obtained. According to the inverse matrix of the obtained matrix, the 3D point cloud model of the target object in the current working environment, where dexterous hand grasps the target, is obtained through the homogeneous transformation. According to the characteristics of the dexterous hand, a grasping algorithm is proposed, which is suitable for the most objects. Finally, the algorithm is verified by the point cloud model of the target object, and finds out the grasping points and grasping pose accurately (the direction of the hand's force). It demonstrates that this algorithm is correct and useful. [ABSTRACT FROM AUTHOR]

Infinite horizon optimization (IHO) problems present a number of challenges for their solution, most notably, the inclusion of an infinite data set. This hurdle is often circumvented by approximating its solution by solving increasingly longer finite horizon truncations of the original infinite horizon problem. In this paper, we adopt a novel transformation that reduces the infinite dimensional IHO problem into an equivalent one dimensional optimization problem, i.e., minimizing a Hölder continuous objective function with known parameters over a closed and bounded interval of the real line. We exploit the characteristics of the transformed problem in one dimension and introduce an algorithm with a graphical implementation for solving the underlying infinite dimensional optimization problem. [ABSTRACT FROM AUTHOR]

In this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed. [ABSTRACT FROM AUTHOR]

Steiner tree problem and its derivations are widely employed to optimize the design of transportation, communication networks, biological engineering and the QoS multicast routing problem. It is one of well-defined open issues which have attracted many research efforts. Different from the existing works, this paper develops a new method of solving Steiner tree problem by using the improved estimation of distribution algorithms (EDA). Further, the performance of developed method is validated by applying on multicast routing optimization. The developed method randomly initializes n trees which contain the source node and the destination nodes. And some individuals select the crossover operation randomly to add the population diversity and avoid the algorithm premature convergence. The algorithm constructs a probabilistic model according to the selected elites, which is capable of estimating the probability distribution of the solution. The probabilistic model is updated according to the new population. New trees are generated based on the probabilistic model. This process iterated until designated termination criteria are met. The improved EDA algorithm gradually evolves trees to obtain a better solution. Simulation validations suggest that the developed method leads to better performance. In particular, the complexity in terms of the converging speed improves significantly compared to other algorithms. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give an uncertainty distribution of the least cost of shipment of a commodity through a network with uncertain capacities. Uncertainty theory is used to deal with uncertain capacities, and an $$\alpha $$ -minimum cost flow problem model is proposed. After defining the $$\alpha $$ -minimum cost flow, the properties of the model are analyzed, and then an algorithm for uncertain minimum cost flow problem is developed. The algorithm can be considered as a general solution to the uncertain minimum cost flow problem. To demonstrate the efficiency of the proposed algorithm, a numerical example is illustrated. [ABSTRACT FROM AUTHOR]

In a recent paper by Fattahi et al. (Int J Adv Manuf Technol 65:787-802, ), a mathematical model is presented for a two-stage assembly scheduling problem containing a hybrid flow shop and an assembly stage. Some constraints in the model are not valid. This note shows that some new constraints are proposed for the mathematical model. An example is proposed to present and prove this new model by executing mathematical software. [ABSTRACT FROM AUTHOR]

In this paper we introduce an extension of the proximal point algorithm proposed by Güler for solving convex minimization problems. This extension is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic entropy-like distances, called f-divergences. A study of the convergence rate of this new proximal point method under mild assumptions is given, and further it is shown that this estimate rate is better than the available one of proximal-like methods. Some applications are given concerning general convex minimizations, linearly constrained convex programs and variationnal inequalities. [ABSTRACT FROM AUTHOR]

Merged processes (MPs) are a recently proposed condensed representation of a Petri net's behaviour similar to branching processes (unfoldings), which copes well not only with concurrency but also with other sources of state space explosion like sequences of choices. They are by orders of magnitude more compact than traditional unfoldings, and yet can be used for efficient model checking. However, constructing complete MPs is difficult, and the only known algorithm is based on building a (potentially much larger) complete unfolding prefix of a Petri net, whose nodes are then merged. Obviously, this significantly reduces their appeal as a representation that can be used for practical model checking. In this paper, we develop an algorithm that avoids constructing the intermediate unfolding prefix and builds a complete merged process directly from a safe Petri net. In particular, a challenging problem of truncating a merged process is solved. [ABSTRACT FROM AUTHOR]

Finitely presented algebraic systems, such as groups and semigroups, are of foundational interest in algebra and computation. Finitely presented algebraic systems necessarily have a computably enumerable (c.e. for short) word equality problem and these systems are finitely generated. Call finitely generated algebraic systems with a c.e. word equality problem computably enumerable. Computably enumerable finitely generated algebraic systems are not necessarily finitely presented. This paper is concerned with finding finitely presented expansions of finitely generated c.e. algebraic systems. The method of expansions of algebraic systems, such as turning groups into rings or distinguishing elements in the underlying algebraic systems, is an important method used in algebra, model theory, and in various areas of theoretical computer science. Bergstra and Tucker proved that all c.e. algebraic systems with decidable word problem possess finitely presented expansions. Then they, and, independently, Goncharov asked if every finitely generated c.e. algebraic system has a finitely presented expansion. In this paper we build examples of finitely generated c.e. semigroups, groups, and algebras that fail to possess finitely presented expansions, thus answering the question of Bergstra- Tucker and Goncharov for the classes of semigroups, groups and algebras. We also construct an example of a residually finite, infinite, and algorithmically finite group, thus answering the question of Miasnikov and Osin. Our constructions are based on the interplay between key concepts and known results from computability theory (such as simple and immune sets) and algebra (such as residual finiteness and the theorem of Golod-Shafaverevich). [ABSTRACT FROM AUTHOR]

For variants of the single-mode resource-constrained project scheduling problem, state-of-the-art exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming and Boolean Satisfiability Solving. In our paper, we propose new exact approaches extending the above principles to the multi-mode RCPSP (MRCPSP) with generalized precedence relations (GPRs). More precisely, we implemented two constraint handlers cumulativemm and gprecedencemm for the optimization framework SCIP. With the latter, one can model renewable resource constraints and GPRs in the context of multi-mode activities, respectively. Moreover, they integrate domain propagation and explanation generation techniques for the above problem characteristics. We formulate three SCIP-models for the MRCPSP with GPRs, two without and one with our constraint handler gprecedencemm. Our computational results on instances from the literature with 30, 50 and 100 activities show that the addition of this constraint handler significantly strengthens the SCIP-model. Moreover, we outperform the state-of-the-art exact approach on instances with 50 activities when imposing time limits of 27 s. In addition, we close (find the optimal solution and prove its optimality for) 289 open instances and improve the best known makespan for 271 instances from the literature. [ABSTRACT FROM AUTHOR]

In this paper we emphasize a similarity between the logarithmic type image processing (LTIP) model and the Naka-Rushton model of the human visual system (HVS). LTIP is a derivation of logarithmic image processing (LIP), which further replaces the logarithmic function with a ratio of polynomial functions. Based on this similarity, we show that it is possible to present a unifying framework for the high dynamic range (HDR) imaging problem, namely, that performing exposure merging under the LTIP model is equivalent to standard irradiance map fusion. The resulting HDR algorithm is shown to provide high quality in both subjective and objective evaluations. [ABSTRACT FROM AUTHOR]

This paper combines two rival preference modeling techniques in a new approach to multi-attribute decision making. Currently existing multi-attribute procedures use either global or local preference modeling. In the global modeling technique, a single preference function is constructed in the large; its maximum is the optimal alternative. In the local procedure, sequential approximations of the preference function are constructed in the small. Each approximation generates a trial solution. Under suitable conditions, each trial solution is preferred to its predecessor, so the trial sequence eventually reaches the optimum. Each technique has advantages and disadvantages; this paper combines the desirable features of both techniques in a new improved method. This new method, called the proxy approach, uses the advantages of one technique to overcome the disadvantages of the other. This paper first develops the theoretical aspects of the proxy approach and then compares it to existing procedures. Finally, the proxy algorithm is applied to a curriculum planning problem and numerous insights are gained. [ABSTRACT FROM AUTHOR]

Logistics plays an important role in the field of global economy, and the storage and retrieval of tasks in a warehouse which has symmetry is the most important part of logistics. Generally, the shelves of a warehouse have a certain degree of symmetry and similarity in their structure. The storage and retrieval efficiency directly affects the efficiency of logistics. The efficiency of the traditional storage and retrieval mode has become increasingly inconsistent with the needs of the industry. In order to solve this problem, this paper proposes a greedy algorithm based on cost matrix to solve the path planning problem of the automatic storage and retrieval system (AS/RS). Firstly, aiming at the path planning mathematical model of AS/RS, this paper proposes the concept of cost matrix, which transforms the traditional storage and retrieval problem into the element combination problem of cost matrix. Then, a more efficient backtracking algorithm is proposed based on the exhaustive method. After analyzing the performance of the backtracking algorithm, combined with some rules, a greedy algorithm which can further improve efficiency is proposed; the convergence of the improved greedy algorithm is also proven. Finally, through simulation, the time consumption of the greedy algorithm is only 0.59% of the exhaustive method, and compared with the traditional genetic algorithm, the time consumption of the greedy algorithm is about 50% of the genetic algorithm, and it can still maintain its advantage in time consumption, which proves that the greedy algorithm based on cost matrix has a certain feasibility and practicability in solving the path planning of the automatic storage and retrieval system. [ABSTRACT FROM AUTHOR]

The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1 + ϵ) -approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j − 1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O ((1891 e k ϵ 2) 8 k / ϵ n d) , and outputs a collection of size O ((1891 e k ϵ 2) 8 k / ϵ n) of candidate sets including approximation centers. [ABSTRACT FROM AUTHOR]

The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied. For getting the optimized solution of the inverse problem the differential evolution algorithm is paralleled to 32 kernels. Numerical results for different technological levels and errors in measured data are presented and discussed. [ABSTRACT FROM AUTHOR]