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This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm. [ABSTRACT FROM AUTHOR]

Numerous studies on project scheduling only consider a single factor, which fails to reflect the actual environment of project operations. In light of this issue, the article synthesizes multiple perspectives and proposes a multi-skill resource-based multi-modal project scheduling problem (MRCMPSP). This problem is described, modeled, and solved using the resource capability matrix and other constraints to minimize the project duration. To effectively solve MRCMPSP and enrich scheduling algorithms, the paper selects the hybrid quantum algorithm (HQPSO) based on the quantum particle swarm algorithm (QPSO). The HQPSO introduces various improvements such as the JAYA optimization search to improve the algorithm's performance. In order to verify the generality, superiority, and effectiveness of the algorithm, independent operation comparison experiments and practical application experiments of the algorithm are designed based on different case sizes and resource quantities. The experimental results demonstrate that the proposed algorithm has superior convergence performance and solution accuracy and can provide an effective scheduling solution for real cases. Additionally, the article provides targeted management suggestions based on the research findings. Overall, this study contributes a novel mathematical model, solution algorithm, optimization strategies, and managerial insights, advancing the field of project management research. [ABSTRACT FROM AUTHOR]

There is a trend to deploy neural network on edge devices in recent years. While the mainstream of research often concerns with single edge device processing and edge-cloud two-layer neural network collaborative computing, in this paper, we propose partitioning multi-layer edge network for neural network collaborative computing. With the proposed method, sub-models of neural network are deployed on multi-layer edge devices along the communication path from end users to cloud. Firstly, we propose an optimal path selection method to form a neural network collaborative computing path with lowest communication overhead. Secondly, we establish a time-delay optimization mathematical model to evaluate the effects of different partitioning solutions. To find the optimal partition solution, an ordered elitist genetic algorithm (OEGA) is proposed. The experimental results show that, compared with traditional cloud computing, single-device edge computing and edge-cloud collaborative computing, the proposed multi-layer edge network collaborative computing has a smaller runtime delay with limited bandwidth resources, and because of the pipeline computing characteristics, the proposed method has a better response speed when processing large number of requests. Meanwhile, the OEGA algorithm has better performance than conventional methods, and the optimized partitioning method outperforms other methods like random and evenly partition. [ABSTRACT FROM AUTHOR]

The performance growth in processors has been continuing toward increasing the number of processing cores on the chip and scaling the feature size of transistors. However, in the nanoera, side effects of the scaling, such as induced heterogeneities in the performance, power, and soft error rate of identically designed cores, prevent the potential performance from being fully utilized. In this paper, we harness the mentioned side effects in shared-memory multicore processors with unknown workloads by a dynamic heuristic scheduling algorithm called HDSAP. HDSAP aims to maximize performance, i.e., the average response time, under power and reliability constraints in presence of induced heterogeneities. In this regard, we use a mathematical model to quantify task to core assignments based on performance variation. We also consider the variation in power to change selected cores when the power constraint is missed. To meet the reliability constraint, we use N-modular redundancy while being aware of the variation in the soft error rate of cores to prevent under/over reliability estimation. To evaluate HDSAP, we run SPLASH benchmark suite on Sniper and MACPat simulators. As a result, the response time of HDSAP reduces by 6%, 8%, and 25% in comparison with similar algorithms under the same power and reliability constraints. [ABSTRACT FROM AUTHOR]

Frequency response analysis (FRA) is considered as a reliable method for the diagnosis of the power transformer winding. Despite this popularity, interpretation of FRA signatures has challenges steel. This paper proposes an elegant and a robust decentralized computation methodology based on logistic chaotic JAYA algorithm (LCJAYA) to construct a high frequency mutually coupled equivalent circuit (HF-MCEC) of the transformer winding for diagnosis purposes. The decentralized HF-MCEC is firstly built from three frequency sub-bands (low, medium, and high frequency) separately. Afterwards, the synthesized LCJAYA algorithm with high efficiency and the mathematical model for HF-MCEC are elaborated. As well, the optimisation methods have difficulties in identifying the nearly unique equivalent circuit parameter in a large search space area. The proposed methodology uses two main strategies. At first, a logistic chaotic to enhance the population diversity and to improve the exploration search areas. Then, a chaotic mutation strategy to improve the exploration and the exploitation at different search process. The success of the proposed study can be imputed to a careful physical correlation between the inductances, capacitances, resistances parameters and their natural frequencies. FRA measurements has been conducted on transformer winding models. The performance of the proposed method is evaluated and compared under different cases. [ABSTRACT FROM AUTHOR]

To reveal the complete limits of a flow network, this paper proposes the concept of critical flow. Firstly, it is found that a flow network is in a critical state when it reaches its maximum flow, and the network cannot afford any flow increase. In fact, not only maximum flow but many other network flows, i.e., blocking flows, indicate the critical states of a flow network. From a new viewpoint, the concept of critical flow is proposed, which unifies the maximum flow and the blocking flow. Secondly, the mathematical model, solution algorithms, and visualization method for critical flow are proposed. An analytical algorithm and a numerical algorithm are proposed to calculate the complete critical flows. In addition, a critical flow curve is designed to visualize the complete limits of a network, with the top point being the maximum flow. Finally, case studies are conducted to illustrate the critical flow and its typical applications in flow networks and real networks. It is concluded that the complete limits of a flow network are the range of critical flows, not a single maximum flow value. The proposed critical flows describe the complete limits of a flow network for the first time. Critical flow can be used for network monitoring and network planning. In monitoring, it reflects the margin of the flow network more accurately than maximum flow. In planning, it evaluates the flow transmission capability more accurately than maximum flow. [ABSTRACT FROM AUTHOR]

The objective of a fixed-cost transportation problem (FCTP) is to minimize the total transportation cost (or to maximize the total profit). FCTPs become more complex due to the presence of uncertain factors like suppliers' capacity, customers' demand, fixed cost and amount of goods transported. In order to deal with its complexity, three mathematical models, namely the expected value, chance-constrained and measure chance models, are basically available in the literature. This paper aims to solve the crisp equivalent models of an uncertain two-echelon FCTP by employing a robust hybrid evolutionary algorithm. The framework of the designed algorithm comprises of parameter-free Jaya algorithm and the efficient quadratic approximation operator. Initially, its efficiency is validated on the 24 constrained benchmark functions from CEC 2006 (Liang et al. in Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization, 2006) and 30 unconstrained benchmark functions (Rao in Int J Ind Eng Comput 7:19–34, 2016). Friedman rank test and Iman–Davenport test are conducted for both constrained and unconstrained test instances. Additionally, five real-life engineering design problems are solved to further analyze the flexibility of the proposed algorithm. The computational results and convergence graphs justify the robustness of the designed algorithm over state-of-the-art algorithms. Finally, its application is demonstrated on chance-constrained and measure chance two-echelon FCTP models. Near-optimal results are contradicted by genetic algorithm and particle swarm optimization in solving both these models. Further, a few large-scale instances of FCTP are solved by the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper aims to verify a new automatic berthing system using a path following algorithm. Berthing operation is one of the most burdensome tasks for crews among several ship operations. The maneuverability of a ship at low speed during berthing operation deteriorates and becomes more vulnerable to disturbances such as wind. Therefore, it is necessary to support and automate operations that require advanced skills such as berthing operation. Previous studies on automatic berthing have investigated various methods to handle the nonlinearity of ship maneuvering motion and determine the optimal control variable. There is a trade-off between accuracy and real-time performance of berthing control from these studies. The algorithms must have sufficiently real-time performance while maintaining the accuracy of control. For these purposes, we propose the automatic berthing system applied a path following algorithm for a ship with one propeller and one rudder in this paper. We show the mathematical model for numerical simulation of berthing control and carried out system identification of the subject ship. In full-scale experiments, the proposed system performed automatic berthing control in both calm wind conditions around 2 m/s and strong wind conditions around 6 m/s. [ABSTRACT FROM AUTHOR]

This paper presents a novel meta-heuristic algorithm called Ali Baba and the forty thieves (AFT) for solving global optimization problems. Recall the famous tale of Ali Baba and the forty thieves, where Ali Baba once saw a gang of forty thieves enter a strange cave filled with all kinds of treasures. The strategies pursued by the forty thieves in the search for Ali Baba inspired us to design ideas and underlie the basic concepts to put forward the mathematical models and implement the exploration and exploitation processes of the proposed algorithm. The performance of the AFT algorithm was assessed on a set of basic benchmark test functions and two more challenging benchmarks called IEEE CEC-2017 and IEEE CEC-C06 2019 benchmark test functions. These benchmarks cover simple and complex test functions with various dimensions and levels of complexity. An extensive comparative study was performed between the AFT algorithm and other well-studied algorithms, and the significance of the results was proved by statistical test methods. To study the potential performance of AFT, its further development is discussed and carried out from five aspects. Finally, the applicability of the AFT algorithm was subsequently demonstrated in solving five engineering design problems. The results in both benchmark functions and engineering problems show that the AFT algorithm has stronger performance than other competitors' algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we present a new structure of the n-dimensional trigonometric cubic B-spline collocation algorithm, which we show in three different formats: one-, two-, and three-dimensional. These constructs are critical for solving mathematical models in different fields. We illustrate the efficiency and accuracy of the proposed method by its application to a few two- and three-dimensional test problems. We use other numerical methods available in the literature to make comparisons. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model for intermodal chains with seaborne transport, in which the optimization of a multi-objective model enables conflicting objectives to be handled simultaneously. Through the assessment of 'door-to-door' transport in terms of costs, time, and environmental impact, the most suitable maritime route and the optimized fleet are jointly proposed to maximize the opportunities for success of intermodal chains versus trucking. The NSGA-II algorithm is applied to resolve the model. The Pareto fronts obtained not only permit decision-making in the short-term but also enable long-term strategies to be defined according to the behaviour of these frontiers when sensitivity analysis is undertaken. A real-life case in Chile is studied to test the usefulness of the model. Aside from identifying the most suitable Motorway of the Sea with its optimized fleet for Chile, the application case has provided several significant findings to promote the intermodal option regardless of its location. [ABSTRACT FROM AUTHOR]

In this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid iterative method to approximate a common solution of split monotone variational inclusion problem and hierarchical fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. We prove that sequences generated by the proposed hybrid iterative method converge strongly to a common solution of these problems. Further, we discuss some applications of the main result. We also discuss a numerical example to demonstrate the applicability of the iterative method. The method and results presented in this paper extend and unify the corresponding known results in this area. [ABSTRACT FROM AUTHOR]

The distance vector-hop (DV-hop) is a typical localization algorithm. It estimates sensor nodes location through detecting the hop count between nodes. To enhance the positional precision, the weight is used to estimate position, and the conventional wisdom is that the more hop counts are, the smaller value of weight will be. However, there has been no clear mathematical model among positioning error, hop count, and weight. This paper constructs a mathematical model between the weights and hops and analyzes the convergence of this model. Finally, the genetic algorithm is used to solve this mathematical weighted DV-hop (MW-GADV-hop) positioning model, the simulation results illustrate that the model construction is logical, and the positioning error of the model converges to 1/4R. [ABSTRACT FROM AUTHOR]

This paper studies a telecommunication network design problem. In this network, users must be connected to capacitated hubs. Then, hubs that concentrate users must be connected to each other and possibly to other hubs with no users. The connections in the network must lead to a tree topology. Hence, connection between hubs can be considered as looking for forming a Steiner tree. This problem is modeled as a bi-objective mathematical programming problem. One objective function minimizes user's latency with respect to the information packages flowing through the capacitated hubs, and the other objective function aims the minimization of the total network's connection cost. To approximate the Pareto front of this bi-objective problem, a co-evolutionary algorithm is developed. In the proposed algorithm, two populations are considered. Each population is associated with one objective function. The co-evolutionary operator consists of an information exchange between both populations that occurs after the genetic operators have been applied. As a result of this co-evolutionary operator, the non-dominated solutions are identified. Computational experimentation shows that the approximated Pareto fronts are representative despite their non-convexity, and they contain a sufficient number of non-dominated solutions over the tested instances. Also, the kth distance among non-dominated solutions is relatively small, which indicates that the approximated Pareto fronts are dense. Furthermore, the required computational time is very small for a problem with the characteristics herein considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function f(x), obtained from stochastic observations of the function or its gradient. Our method also utilizes estimates of function values to gauge progress that is being made. The convergence analysis relies on requirements that these models and these estimates are sufficiently accurate with high enough, but fixed, probability. Beyond these conditions, no assumptions are made on how these models and estimates are generated. Under these general conditions we show an almost sure global convergence of the method to a first order stationary point. In the second part of the paper, we present examples of generating sufficiently accurate random models under biased or unbiased noise assumptions. Lastly, we present some computational results showing the benefits of the proposed method compared to existing approaches that are based on sample averaging or stochastic gradients. [ABSTRACT FROM AUTHOR]

The trabecular bone adapts its form to mechanical loads and is able to form structures that are both lightweight but very stiff. In this sense, it is a problem (for the Nature or living entities) similar to the structural optimization, especially the topology optimization. The structural optimization system developed by the authors previously was based directly on the bio-mechanical models. The paper aims to clarify the approach of using the bio-mechanical models of the trabecular bone remodelling phenomenon as a base for the structural optimization. The justified algorithm for shape optimization mimics the natural phenomenon to satisfy the condition of constant value of the strain energy density on the structural surface, issuing from the considerations in the area of mechanics. The main body of the paper contains the analysis of the stiffness optimization problem in the framework of speed method approach to shape optimization. The given numerical example (cantilever beam in bending) includes the influence of the structural surface curvature on the optimization procedure. The presented in the paper approach can be used as a method of structural optimization unrelated already to trabecular bone remodelling phenomenon. [ABSTRACT FROM AUTHOR]

Although researchers have successfully incorporated metamodels in evolutionary algorithms to solve computational-expensive optimization problems, they have scarcely performed comparisons among different metamodeling techniques. This paper presents an in-depth comparison study over four of the most popular metamodeling techniques: polynomial response surface, Kriging, radial basis function neural network (RBF), and support vector regression. We adopted six well-known scalable test functions and performed experiments to evaluate their suitability to be coupled with an evolutionary algorithm and the appropriateness to surrogate problems by regions (instead of surrogating the entire problem). Notwithstanding that most researchers have undertaken accuracy as the main measure to discern among metamodels, this paper shows that the precision, measured with the ranking preservation indicator, gives a more valuable information for selecting purposes. Additionally, nonetheless each model has its own peculiarities; our results concur that RBF fulfills most of our interests. Furthermore, the readers can also benefit from this study if their problem at hand has certain characteristics such as a low budget of computational time or a low-dimension problem since they can assess specific results of our experimentation. [ABSTRACT FROM AUTHOR]

Increasing the cutter size to enhance its stiffness is of great significance for improving the machining efficiency and precision of deep and narrow channel parts. In this paper, the concept of cutter size critical sphere (CSCS) is presented, which is a specified sphere and tangent to several geometric constraints of tool accessible regions. With this concept, the complex multi-constraints of the workpiece can be transformed into several simple but precise geometric conditions to optimize the size and tool orientation of a conical cutter. The conical cutter generated by CSCS can reach a critical state with multi-constraints simultaneously. Firstly, the mathematical principle of the conical cutter generated by a cylindrical cutter is deduced based on the motion envelope theory. Secondly, the concept of CSCS is proposed based on the deduced mathematical principle and the calculation method of the CSCS with the general situation is provided. Thirdly, the CSCS with special situations is discussed and the calculation method is proposed. Fourthly, the mathematical model and solving algorithm for the max-size CSCS is given. The solving algorithm is designed based on the 3D Medial Axis Transformation (3D MAT) theory. Finally, the proposed method is verified by three simulation experiments and a comparison experiment. The results show that the proposed method can efficiently and accurately calculate the max size and tool orientation of the conical cutter simultaneously. The optimized conical cutter can be tangent to the multi-constraints of the workpiece but do no interfer with them. [ABSTRACT FROM AUTHOR]

Pulse-coupled neural network (PCNN) is a powerful unsupervised learning model with many parameters to be determined empirically. In particular, the weight matrix is invariable in the iterative process, which is inconsistent with the actual biological system. Based on the existing research foundation of biology and neural network, we propose a spike-synchronization-dependent plasticity (SSDP) rule. In this paper, the mathematical model and algorithm of SSDP are presented. Furthermore, a novel memristor-based circuit model of SSDP is designed. Finally, experimental results demonstrate that SSDP has greatly improved the image processing capabilities of PCNN. [ABSTRACT FROM AUTHOR]

This paper proposes an improved meta-heuristic algorithm called multivector particle swarm optimization (MVPSO) for solving single-objective optimization problems. MVPSO improves particle swarm optimization (PSO) algorithm by creating more possible solutions for each particle during the optimization process. It proposes a mathematical model and new position vectors for each particle that enhance the particle movement toward the global best value. This improvement emphasizes the exploration and exploitation of the particles in the search space during the optimization process. To test the performance of MVPSO, the algorithm is then benchmarked on 23 well-known test functions including unimodal, multimodal and fixed multimodal functions at different dimensions. These benchmark functions test the exploration, exploitation, local optima avoidance and convergence features of MVPSO. MVPSO has been compared to the state-of-the-art swarm optimization algorithms as well as PSO algorithm. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, MVPSO is better than original PSO algorithm, especially as the dimension increases. Further, it shows that a MVPSO based on the multivector mathematical model is competitive with the state-of-the-art swarm optimization algorithms. Moreover, the results of the tested benchmark functions, statistical analysis and performance metrics prove that the proposed algorithm is able to explore more solutions and regions in the search space, avoiding local optima points. [ABSTRACT FROM AUTHOR]

Disasters such as earthquake or tsunami can easily take the lives of thousands of people and millions worth of property in a fleeting moment. A successful emergency evacuation plan is critical in response to disasters. In this paper, we seek to investigate the multi-source, multi-destination evacuation problem. First, we construct a mixed integer linear programming model. Second, based on K shortest paths and user equilibrium, we propose a novel algorithm (hereafter KPUE), whose complexity is polynomial in the numbers of nodes and evacuees. Finally, we demonstrate the effectiveness of algorithm KPUE by a real evacuation network in Shanghai, China. The numerical examples show that the average computation time of the proposed algorithm is 95% less than that of IBM ILOG CPLEX solver and the optimality gap is no more than 5%. [ABSTRACT FROM AUTHOR]

Income tax systems with "pass-through" entities transfer a firm's income to shareholders, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual given the complex network of corporations and companies, usually including cycles between them. In this paper, we show the mathematical conceptualization and the solution to the problem, proving that there is only one way to distribute income to taxpayers. Using the theory of absorbing Markov chains, we define a mathematical model for computing the taxable income of each taxpayer, and we propose a decomposition algorithm for this problem. This approach allows us to compute the solution accurately and to efficiently use computational resources. Finally, we present some characteristics of Chilean taxpayers' network and the computational results of the algorithm using this network. [ABSTRACT FROM AUTHOR]

Electroencephalogram (EEG) analysis has been widely used in the diagnosis of stroke diseases for its low cost and noninvasive characteristics. In order to classify the EEG signals of stroke patients with cerebral infarction and cerebral hemorrhage, this paper proposes a novel EEG stroke signal classification method. This method has two highlights. The first is that a multi-feature fusion method is given by combining wavelet packet energy, fuzzy entropy and hierarchical theory. The second highlight is that a suitable classification model based on ensemble classifier is constructed for perfectly classification stroke signals. Entropy is an accessible way to measure information and uncertainty of time series. Many entropy-based methods have been developed these years. By comparing with the performances of permutation entropy, sample entropy, approximate entropy in measuring the characteristic of stroke patient's EEG signals, it can be found that fuzzy entropy has best performance in characterization stroke EEG signal. By combining hierarchical theory, wavelet packet energy and fuzzy entropy, a multi-feature fusion method is proposed. The method first calculates wavelet packet energy of EEG stroke signal, then extracts hierarchical fuzzy entropy feature by combining hierarchical theory and fuzzy entropy. The experimental results show that, compared with the fuzzy entropy feature, the classification accuracy based on the fusion feature of wavelet packet energy and hierarchical fuzzy entropy is much higher than benchmark methods. It means that the proposed multi-feature fusion method based on stroke EEG signal is an efficient measure in classifying ischemic and hemorrhagic stroke. Support vector machine (SVM), decision tree and random forest are further used as the stroke signal classification models for classifying ischemic stroke and hemorrhagic stroke. Experimental results show that, based on the proposed multi-feature fusion method, the ensemble method of random forest can get the best classification performance in accuracy among three models. [ABSTRACT FROM AUTHOR]

Physarum polycephalum is an amoeba-like organism and is able to find the shortest path in a labyrinth. Inspired by P. polycephalum, recently, a mathematical model and an algorithm (Physarum Solver) was developed. There are, however, only sequential implementations of this algorithm. In this paper, a fast and efficient parallel Physarum Solver is proposed. The proposed algorithm requires the solution of linear systems whose coefficient matrix is a symmetric M-matrix. The solution of the linear system is the most time consuming step of the Physarum Solver which is classically handled by direct solvers without taking advantage of the fact that the coefficient matrix is an M-matrix. However, direct solvers are infeasible for solving large real-world problems. In the proposed parallel Physarum Solver, an effective parallel iterative linear solver with a parallel preconditioner for M-matrices is used. The parallel scalability, solution time, and accuracy of the proposed algorithm are presented and compared to a state-of-the-art parallel implementation of Δ -stepping shortest path algorithm in the Parallel Boost Graph Library. Our implementation exhibits a remarkable parallel speedup with comparable accuracy for synthetic and real world applications. [ABSTRACT FROM AUTHOR]

This paper introduces interval union arithmetic, a new concept which extends the traditional interval arithmetic. Interval unions allow to manipulate sets of disjoint intervals and provide a natural way to represent the extended interval division. Considering interval unions lead to simplifications of the interval Newton method as well as of other algorithms for solving interval linear systems. This paper does not aim at describing the complete theory of interval union analysis, but rather at giving basic definitions and some fundamental properties, as well as showing theoretical and practical usefulness of interval unions in a few selected areas. [ABSTRACT FROM AUTHOR]

In this paper, we improve the convergence theorem in the paper by Yang (Journal of Industrial and Management Optimization 1, 211-217, 2005), and propose a new modified convergence theorem. The theorem and the proof presented in the present paper are interesting improvements on the convergence theorem of Yang. [ABSTRACT FROM AUTHOR]

Gene expression programming (GEP) is a mathematical model that can be used to optimize complex systems. It has not only limited to specific problems, but also has good robustness in solving various problems, which has been applied in many disciplines such as biochemistry, physics, and mathematics. In this paper, the IGEP algorithm was proposed based on the optimization of GEP algorithm, and the algorithm for solving the inverse problem of parameter identification of partial differential equations based on this algorithm was studied. The structure and steps of GEP algorithm were analyzed firstly, and the GEP (IGEP) based on improved mutation operator was proposed. The algorithm advantage of IGEP for solving the inverse problem of partial differential equations was discussed. In addition, the simulation experiments were carried out to prove the feasibility and superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Inventory routing problem (IRP) is one of the most important logistics problems; in this type of problems, decision maker usually has the option to use several types of vehicles to form a fleet with appropriate size and composition in order to minimize both inventory and transportation costs. Meanwhile, the increasing fuel consumption and its economic and environmental impacts mean that this issue must also be incorporated into the routing problems. This paper proposes a new bi-objective model for green inventory routing problem with the heterogeneous fleet. The objectives of the proposed model are (I) to reduce the emissions and (II) to minimize the fleet size, vehicle type, routing, and inventory costs. Given the NP-hard nature of the assessed problem, a bi-objective meta-heuristic algorithm based on the quantum evolutionary algorithm is proposed to achieve these objectives. To evaluate the performance of the proposed algorithm, its results are compared with the results of the exact method and Non-dominated Sorting Genetic Algorithm II (NSGAII). The results of these comparisons indicate the better performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper describes the package sppmix for the statistical environment R. The sppmix package implements classes and methods for modeling spatial point patterns using inhomogeneous Poisson point processes, where the intensity surface is assumed to be a multiple of a finite additive mixture of normal components and the number of components is a finite, fixed or random integer. Extensions to the marked inhomogeneous Poisson point processes case are also presented. We provide an extensive suite of R functions that can be used to simulate, visualize and model point patterns, estimate the parameters of the models, assess convergence of the algorithms and perform model selection and checking in the proposed modeling context. In addition, several approaches have been implemented in order to handle the standard label switching issue which arises in any modeling approach involving mixture models. We adapt a hierarchical Bayesian framework in order to model the intensity surfaces and have implemented two major algorithms in order to estimate the parameters of the mixture models involved: the data augmentation and the birth-death Markov chain Monte Carlo (DAMCMC and BDMCMC). We used C++ (via the Rcpp package) in order to implement the most computationally intensive algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study a very general type of online network design problem, and generalize two different previous algorithms, one for an online network design problem due to Berman and Coulston (Proceedings of the 29th annual ACM symposium on theory of computing, pp 344-353, 1997) and one for (offline) general network design problems due to Goemans and Williamson (SIAM J Comput 24:296-317, 1995); we give an O(logk)-competitive algorithm, where k is the number of nodes that must be connected. We also consider a further generalization of the problem that allows us to pay penalties in exchange for violating connectivity constraints; we give an online O(logk)-competitive algorithm for this case as well. [ABSTRACT FROM AUTHOR]

Cooperative matching games (Shapley and Shubik) and Network bargaining games (Kleinberg and Tardos) are games described by an undirected graph, where the vertices represent players. An important role in such games is played by stable graphs, that are graphs whose set of inessential vertices (those that are exposed by at least one maximum matching) are pairwise non adjacent. In fact, stable graphs characterize instances of such games that admit the existence of stable outcomes. In this paper, we focus on stabilizing instances of the above games by blocking as few players as possible. Formally, given a graph G we want to find a minimum cardinality set of vertices such that its removal from G yields a stable graph. We give a combinatorial polynomial-time algorithm for this problem, and develop approximation algorithms for some NP-hard weighted variants, where each vertex has an associated non-negative weight. Our approximation algorithms are LP-based, and we show that our analysis are almost tight by giving suitable lower bounds on the integrality gap of the used LP relaxations. [ABSTRACT FROM AUTHOR]

The results of testing formula simplification tools are presented in the first part of this paper. In the second part, an algorithm for constructing canonical forms of linear semi-algebraic formulas is described. The main result of the study is the definition of the canonical form of a linear semi-algebraic formula that has the property of uniqueness and other useful properties. An algorithm for constructing such a formula is described. [ABSTRACT FROM AUTHOR]

In this paper, we consider the perturbation of the orthogonal projection and the generalized inverse for an n × n matrix A and present some perturbation bounds for the orthogonal projections on the rang spaces of A and A∗, respectively. A combined bound for the orthogonal projection on the rang spaces of A and A∗ is also given. The proposed bounds are sharper than the existing ones. From the combined bounds of the orthogonal projection on the rang spaces of A and A∗, we derived new perturbation bounds for the generalized inverse, which always improve the existing ones. The combined perturbation bound for the orthogonal projection and the generalized inverse is also given. Some numerical examples are given to show the advantage of the new bounds. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an algorithm as combination between the subgradient extragradient method and inertial method for solving variational inequality problems in Hilbert spaces. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. The proposed algorithm can be considered as an improvement of the previously known inertial extragradient method over each computational step. The performance of the proposed algorithm is also illustrated by several preliminary numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a piecewise constant time-stepping discontinuous Galerkin method combined with a piecewise linear finite element method is applied to solve control constrained optimal control problem governed by time fractional diffusion equation. The control variable is approximated by variational discretization approach. The discrete first-order optimality condition is derived based on the first discretize then optimize approach. We demonstrate the commutativity of discretization and optimization for the time-stepping discontinuous Galerkin discretization. Since the state variable and the adjoint state variable in general have weak singularity near t = 0and t = T, a time adaptive algorithm is developed based on step doubling technique, which can be used to guide the time mesh refinement. Numerical examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

If A has no eigenvalues on the closed negative real axis, and B is arbitrary square complex, the matrix-matrix exponentiation is defined as AB := elog(A)B. It arises, for instance, in Von Newmann’s quantum-mechanical entropy, which in turn finds applications in other areas of science and engineering. In this paper, we revisit this function and derive new related results. Particular emphasis is devoted to its Fréchet derivative and conditioning. We propose a new definition of bivariate matrix function and derive some general results on their Fréchet derivatives, which hold, not only to the matrix-matrix exponentiation but also to other known functions, such as means of two matrices, second order Fréchet derivatives and some iteration functions arising in matrix iterative methods. The numerical computation of the Fréchet derivative is discussed and an algorithm for computing the relative condition number of ABis proposed. Some numerical experiments are included. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive a numerical scheme for solving stochastic differential equations (SDEs) via Wong-Zakai approximation. One of the most important methods for solving SDEs is Milstein method, but this method is not so popular because the cost of simulating the double stochastic integrals is high. For overcoming this complexity, we present an implicit Milstein scheme based on Wong-Zakai approximation by approximating the Brownian motion with its truncated Haar expansion. The main advantages of this method lie in the fact that it preserves the convergence order and also stability region of the Milstein method while its simulation is much easier than Milstein scheme. We show the convergence rate of the method by some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we prove that for a linearly ordered skewfield the groups of quotients of the semigroup Gn(픻) coincides with the group GLn(픻) for n ≥ 3. [ABSTRACT FROM AUTHOR]

Since the large amount of surface-related multiple existed in the marine data would influence the results of data processing and interpretation seriously, many researchers had attempted to develop effective methods to remove them. The most successful surface-related multiple elimination method was proposed based on data-driven theory. However, the elimination effect was unsatisfactory due to the existence of amplitude and phase errors. Although the subsequent curvelet-domain multiple-primary separation method achieved better results, poor computational efficiency prevented its application. In this paper, we adopt the cubic B-spline function to improve the traditional curvelet multiple matching method. First, select a little number of unknowns as the basis points of the matching coefficient; second, apply the cubic B-spline function on these basis points to reconstruct the matching array; third, build constraint solving equation based on the relationships of predicted multiple, matching coefficients, and actual data; finally, use the BFGS algorithm to iterate and realize the fast-solving sparse constraint of multiple matching algorithm. Moreover, the soft-threshold method is used to make the method perform better. With the cubic B-spline function, the differences between predicted multiple and original data diminish, which results in less processing time to obtain optimal solutions and fewer iterative loops in the solving procedure based on the L1 norm constraint. The applications to synthetic and field-derived data both validate the practicability and validity of the method. [ABSTRACT FROM AUTHOR]

In this paper, I present an interpretation of the use of constructions in both the problems and theorems of Elements I-VI, in light of the concept of given as developed in the Data, that makes a distinction between the way that constructions are used in problems, problem-constructions, and the way that they are used in theorems and in the proofs of problems, proof-constructions. I begin by showing that the general structure of a problem is slightly different from that stated by Proclus in his commentary on the Elements. I then give a reading of all five postulates, Elem. I.post.1-5, in terms of the concept of given. This is followed by a detailed exhibition of the syntax of problem-constructions, which shows that these are not practical instructions for using a straightedge and compass, but rather demonstrations of the existence of an effective procedure for introducing geometric objects, which procedure is reducible to operations of the postulates but not directly stated in terms of the postulates. Finally, I argue that theorems and the proofs of problems employ a wider range of constructive and semi- and non-constructive assumptions that those made possible by problems. [ABSTRACT FROM AUTHOR]

This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work. [ABSTRACT FROM AUTHOR]

In the current research papers on multi-agent (multi-person) scheduling, a person's objective function is always considered as a cost function on scheduling, whereas a cooperative profit function is defined to serve as his objective one in this paper. In the two-person scheduling problem addressed in this paper, the two persons jointly order a common operational time interval of a single machine. Each person needs to process a set of his own jobs in that time window. The same objective function of each person still relies on the sequence of all the jobs of both persons since each part of the function is determined by some given parameters except one part assumed to be a given multiple of the total completion time of his own jobs. The two persons have to negotiate a job sequence and determine the (related) final solution on cooperative profit allocation. Such a two-person scheduling problem is essentially a cooperative game. An algorithm is designed to yield the cooperative-profit-based Pareto efficient solution set acting as the first game-based solution concept in this paper. The parallelized version of the algorithm is also developed. The second game-based solution concept is the Shapley value appropriate for the above cooperative-game situation on two-person scheduling. Several instances are presented and analyzed to reveal the necessity to employ the two solution concepts together. [ABSTRACT FROM AUTHOR]

Slicing is an important step for all layer-based additive manufacturing (AM) processes. This paper proposes an improved and robust slicing algorithm with efficient contour construction to reduce the slicing time and be able to slice a complex STereoLithography (STL) model with millions of triangles (resulting from high-accuracy STL files). Also, another important feature of the proposed method is it can identify outer and inner contours automatically. Test results to demonstrate the improvements in execution time and comparisons with results from published papers have been given to illustrate the algorithm efficiency. The robustness of this slicing algorithm is demonstrated by several complex models with large numbers of nested contours on each slice. [ABSTRACT FROM AUTHOR]

In many fault detection problems, we want to identify all defective items from a sample set of items using the minimum number of tests. Group testing is for the scenario where each test is performed on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number of defective items in the sample set is usually unknown. In this paper, we investigate new algorithms for the group testing problem with unknown number of defective items. We consider the scenario where the performance of a group testing algorithm is measured by two criteria: the primary criterion is the number of tests performed, which measures the total cost spent; and the secondary criterion is the number of stages the algorithm works in, which is referred to as the sequentiality of the algorithm in this paper and measures the minimum amount of time required by using the algorithm to identify all the defective items. We present a new algorithm Recursive Binary Splitting (RBS) for the above group testing problem with unknown number of defective items, and prove an upper bound on the number of tests required by RBS. The computational results show that RBS exhibits very good practical performance, measured in terms of both the above two criteria. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a solution of the convex minimization problem (CMP) with constraints of several problems: finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and the fixed point problem of a strictly pseudocontractive mapping. In the meantime, we also prove the strong convergence of the proposed algorithm to the unique solution of a hierarchical variational inequality problem (over the fixed point set of a strictly pseudocontractive mapping) with constraints of finitely many GMEPs, finitely many variational inclusions and the CMP. The results presented in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, global optimization model is designed for grid computing system. It is provided as a promising model for grid resource scheduling algorithm. It aims at solving the problem of optimally allocating services on the grid to optimize the grid service reliability, deadline and cost. In this paper, the problem of optimizing the reliability of grid systems has been modeled as a multi-objective optimization problem where apart from the grid system reliability; the system cost, deadline and redundancy are also considered as its constraints. The algorithm considers failure rate of computational and network resources to do the reliability analysis of the grid system. Based on the service reliability of the grid system, the proposed RORS algorithm selects the set of optimal resources among the candidate resources based on reliability, application execution time and cost that achieves optimal performance using a genetic algorithm. The proposed algorithm has been demonstrated using Java-based GridSim tool. [ABSTRACT FROM AUTHOR]

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]

This paper proposes an improved memetic algorithm relying on ring neighborhood topology for constrained optimization problems based on our previous work in Cai et al. (Soft Comput (in press), ). The main motivation of using ring neighborhood topology is to provide a good balance between effective exploration and efficient exploitation, which is a very important design issue for memetic algorithms. More specifically, a novel variant of invasive weed optimization (IWO) as the local refinement procedure is proposed in this paper. The proposed IWO variant adopts a neighborhood-based dispersal operator to achieve more fine-grained local search through the estimation of neighborhood fitness information relying on the ring neighborhood topology. Furthermore, a modified version of differential evolution (DE), known as 'DE/current-to-best/1', is integrated into the improved memetic algorithm with the aim of providing a more effective exploration. Performance of the improved memetic algorithm has been comprehensively tested on 13 well-known benchmark test functions and four engineering constrained optimization problems. The experimental results show that the improved memetic algorithm obtains greater competitiveness when compared with the original memetic approach Cai et al. in (Soft Comput (in press), ) and other state-of-the-art algorithms. The effectiveness of the modification of each component in the proposed approach is also discussed in the paper. [ABSTRACT FROM AUTHOR]