Multidimensional Optimization Problem Research Articles

Extremal behavior of hitting a cone by correlated Brownian motion with drift

This paper derives an exact asymptotic expression for Pxu{∃t≥0X(t)−μt∈U},asu→∞,where X(t)=(X1(t),…,Xd(t))⊤,t≥0 is a correlated d-dimensional Brownian motion starting at the point xu=−αu with α∈Rd, μ∈Rd and U=∏i=1d[0,∞). The derived asymptotics depends on the solution of an underlying multidimensional quadratic optimization problem with constraints, which leads in some cases to dimension-reduction of the considered problem. Complementary, we study asymptotic distribution of the conditional first passage time to U, which depends on the dimension-reduction phenomena.

Multi-objective Optimization of Transmission Line Annual Maintenance Scheduling Based on Flower Pollination Algorithm

The optimization of the annual maintenance scheduling is a multidimensional and nonlinear integer optimization problem. In this paper, the annual maintenance scheduling model is established with the minimum cost of maintenance and the expected minimum power supply, and the pollination algorithm based on e constraint is proposed. By obtaining the Pareto optimal solutions and comparing the economic and reliability objectives of the optimization problem of the maintenance scheduling, the proposed algorithm can effectively improve the solution precision of the multi - objective optimization problem and the distribution of the optimal solution. Based on the annual inspection scheduling of 12 transmission lines in a region, this paper compares the proposed algorithm with the Differential Evolution Flower Pollination Algorithm with Time Variant Factor (TVDFPA) and the Simulated Annealing Pollination Algorithm (SFPA). Based on the result, e-constrained algorithm is superior to the other two in performance and calculation time.

The method for optimisation of gas compressors performance in gas storage systems

We present a computational method for achieving an optimal operation of compressor units used in industrial gas storage systems. The proposed method is capable to operate with a mix of compressor types (i.e., with different operational parameters, different power drives, and different types of construction, e.g., reciprocal and turbocompressors). The goal of the optimisation is to find an optimal compressors configuration and distribution of the compressor loads for each instance of time. The proposed method is based on conversion of a multidimensional discrete-continuous optimisation problem into a set of independent combinatorial and nonlinear optimisation problems. We derive the mathematical foundations of the algorithms. The exemplary results of the application are presented. [Received: May 4, 2016; Accepted: December 2, 2016]

A rapid solution adjustment strategy in solving Long-term scheduling of large cascade hydropower stations

Due to the great potential of large cascade hydropower stations on power generation, long-term scheduling of large cascade hydropower stations (LSLCHS) plays an important role in electrical power system. As more and more concentrations focused on the optimal operation of large cascade hydropower stations, the LSLCHS has been taken into a multi-dimensional, non-convex and non-linear optimization problem due to its complicated hydraulic connection relationships and varieties of complex constraints with considering its power generation, shipping and ecological characteristics. In order to solve this problem, a strategy of solution rapid adjustment regarding the principle of monotone principle is proposed accordingly. The simulation results show that the proposed method is an efficient for solving joint optimization dispatch model of cascade hydropower stations with fast convergent rate, strong robustness.

A Modified Artificial Bee Colony Algorithm for Parameter Estimation of Fractional-Order Nonlinear Systems

In this paper, a modified artificial bee colony (MABC) algorithm is proposed to estimate the unknown fractional-order nonlinear systems. First, the parameter estimation problem can be mathematically transformed into a multi-dimensional continuous function optimization problem, which is solved via the MABC algorithm. The proposed MABC algorithm well combines the original artificial bee colony algorithm (ABC) and the Nelder-Mead simplex method (NMS) in a very simple way, which takes full advantage of the exploration ability of the ABC algorithm and the exploitation ability of the NMS. And in the meanwhile, the proposed algorithm improves the speed of convergence. To evaluate the effectiveness of the proposed MABC algorithm, numerical simulations contain two typical uncertain fractional-order nonlinear systems. The results show that compared with the other population-based algorithm and ABC-variants, the proposed MABC for solving the problem of parameter estimation get the faster convergence speed and higher calculation accuracy.

On solution of a multidimensional tropical optimization problem using matrix sparsification

A complete solution is proposed for the problem of minimizing a function defined on vectors with elements in a tropical (idempotent) semifield. The tropical optimization problem under consideration arises, for example, when we need to find the best (in the sense of the Chebyshev metric) approximate solution to tropical vector equations and occurs in various applications, including scheduling, location, and decision-making problems. To solve the problem, the minimum value of the objective function is determined, the set of solutions is described by a system of inequalities, and one of the solutions is obtained. Thereafter, an extended set of solutions is constructed using the sparsification of the matrix of the problem, and then a complete solution in the form of a family of subsets is derived. Procedures that make it possible to reduce the number of subsets to be examined when constructing the complete solution are described. It is shown how the complete solution can be represented parametrically in a compact vector form. The solution obtained in this study generalizes known results, which are commonly reduced to deriving one solution and do not allow us to find the entire solution set. To illustrate the main results of the work, an example of numerically solving the problem in the set of three-dimensional vectors is given.

Parametric Design of Optimal in Average Fractional-Order PID Controller in Flight Control Problem

This paper considers a problem of fractional-order PID controller tuning to optimize it in average over a set of initial states of the plant–controller closed system and over a set of typical input signals. The problem is reduced to a multidimensional optimization problem. We suggest an approach to the solution, implementing it algorithmically. The approach is illustrated by a parametric design of an optimal in average fractional-order PID controller for pitch control of an aircraft.

Globalizer: A novel supercomputer software system for solving time-consuming global optimization problems

In this paper, we describe the Globalizer software system for solving the global optimization problems. The system is designed to maximize the use of computational potential of the modern high-performance computational systems in order to solve the most time-consuming optimization problems. The highly parallel computations are facilitated using various distinctive computational schemes: processing several optimization iterations simultaneously, reducing multidimensional optimization problems using multiple Peano space-filling curves, and multi-stage computing based on the nested block reduction schemes. These novelties provide for the use of the supercomputer system capabilities with shared and distributed memory and with large numbers of processors to solve the global optimization problems efficiently.

Parameter estimation for chaotic systems using improved bird swarm algorithm

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

Parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems via a hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm

Hyperchaos can be observed in fractional-order nonlinear systems with suitable orders. The knowledge about systematic parameters and fractional orders is important for control and synchronization of fractional-order hyperchaotic systems. In this article, parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems is investigated. Firstly, estimation of systematic parameters and fractional orders is formulated as a multi-dimensional optimization problem by treating the fractional orders as additional parameters. Secondly, a novel method called hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm is proposed to deal with this optimization problem. Finally, numerical simulations and comparisons with other typical algorithms are done to demonstrate the effectiveness of the proposed algorithm, which provides a promising tool for estimation of fractional-order arbitrary dimensional hyperchaotic systems as well as other numerical optimization problems in different fields.

Game Theory Based Radio Resource Management Algorithm for Packet Access Cellular Networks

Abstract The goal of Radio Resource Management (RRM) mechanisms is to allocate the transmission resources to the users such that the transmission requests are satisfied while several constraints are fulfilled. These constraints refer to low complexity and power consumption and high spectral efficiency and can be met by multidimensional optimization. This paper proposes a Game Theory (GT) based suboptimal solution to this multidimensional optimization problem. The results obtained by computer simulations show that the proposed RRM algorithm brings significant improvement in what concerns the average delay and the throughput, compared to other RRM algorithms, at the expense of somewhat increased complexity.

ON PROBLEM OF REGIONAL WAREHOUSE AND TRANSPORT INFRASTRUCTURE OPTIMIZATION

The article suggests an approach of solving the problem of warehouse and transport infrastructure optimization in a region. The task is to determine the optimal capacity and location of the support network of warehouses in the region, as well as power, composition and location of motor fleets. Optimization is carried out using mathematical models of a regional warehouse network and a network of motor fleets. These models are presented as mathematical programming problems with separable functions. The process of finding the optimal solution of problems is complicated due to high dimensionality, non-linearity of functions, and the fact that a part of variables are constrained to integer, and some variables can take values only from a discrete set. Given the mentioned above complications search for an exact solution was rejected. The article suggests an approximate approach to solving problems. This approach employs effective computational schemes for solving multidimensional optimization problems. We use the continuous relaxation of the original problem to obtain its approximate solution. An approximately optimal solution of continuous relaxation is taken as an approximate solution of the original problem. The suggested solution method implies linearization of the obtained continuous relaxation and use of the separable programming scheme and the scheme of branches and bounds. We describe the use of the simplex method for solving the linearized continuous relaxation of the original problem and the specific moments of the branches and bounds method implementation. The paper shows the finiteness of the algorithm and recommends how to accelerate process of finding a solution.

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.

CGRS — An advanced hybrid method for global optimization of continuous functions closely coupling extended random search and conjugate gradient method

A new hybrid method for global optimization of continuous functions is proposed. It is a combination of an extended random search method and a descent method. Random search is used as the global search strategy. A newly developed distribution-based region control makes use of already detected local minima to refine this search strategy. The approach resembles classical step size control in deterministic optimization. The descent method is embedded as a local search strategy for the detection of local minima. A special realization of this approach is presented in this paper and called CGRS. In CGRS the conjugate gradient method is utilized as descent method. The proof of global convergence in probability for CGRS is given and extended to other descent methods used in the hybrid optimization approach. In order to demonstrate the numerical properties of the approach test sets of multidimensional non-convex optimization problems are solved. The results are compared to well-established hybrid methods for global optimization. The new algorithm shows a high success rate with good and adjustable solution precision. Parameter tuning is not necessary, but of course possible. The new method proves to be efficient in terms of computational costs.

Constrained transmit beampattern design for colocated MIMO radar

This paper considers the constrained waveform design for Multiple-Input Multiple-Output (MIMO) radar to synthesize a desired beampattern. Specifically, resorting to SemiDefinite Programming (SDP) related technique, we first minimize Integration Sidelobe Level (ISL) to optimize the waveform covariance matrix enforcing a uniform elemental power restriction as well as a 3dB bandwidth constraint. Then, based on Least Square (LS) approach, we present the existing Cyclic Algorithm (CA) and a new Sequential Iterative Algorithm (SIA) to devise the waveform under a constant modulus constraint, and a similarity constraint to allow the designed waveform sharing the similarity feature with a given reference waveform. In particular, the proposed SIA directly optimizes the objective function and its each iteration turns the multidimensional optimization problem into multiple one-dimensional optimization problems with closed-form solutions. Finally, we assess the effectiveness of the proposed technique through numerical simulations in comparison with CA.

PGMA: An algorithmic approach for multi-objective hardware software partitioning

Designing embedded systems efficiently has always been of significant interest. This has been tremendously scaled-up for contemporary and high-end applications with their increasing complexity and the need to satisfy multiple conflicting constraints. This paper presents a high-speed Hardware Software Partitioning technique for the design of such systems. The partitioning problem has been modeled as a multi-dimensional optimization problem with the aim of minimizing the area utilization, power dissipation, time of execution and system memory requirement of the implementation. A two-phased algorithm (Phased Greedy Metaheuristic Algorithm or PGMA) has been proposed which also takes into consideration the communication costs between hardware and software Processing-Engines (PEs) while partitioning. Subsequently, a detailed empirical analysis of the proposed algorithm is presented to ascertain its efficiency, quality and speed. The execution time is as low as 18 ms for partitioning an algorithm consisting of 1000 blocks. Thereafter, the proposed algorithm is applied to a real-life embedded system, the Joint Photographic Expert-Group (JPEG) Encoder, to demonstrate its effectiveness. For a power constraint of 600 mW, an area utilization of 58.28% has been achieved, which is the maximum amongst all the reported works till date, to the best of our knowledge. This allowed for a decreased offloading of tasks to software, resulting in a memory usage of only 14 KB and execution time of 20 ms.

Parameter Estimation for Chaotic Fractional Systems by Using the Locust Search Algorithm

Due to its multiple applications, parameteridentification for fractional-order chaotic systems hasattracted the interests of several research communities.In the identification, the parameter estimation processis transformed into a multidimensional optimizationproblem where fractional orders, as well as functionalparameters of the chaotic system are considered thedecision variables. Under this approach, the complexityof fractional-order chaotic systems tends to producemultimodal error surfaces for which their cost functionsare significantly difficult to minimize. Several algorithmsbased on evolutionary computation principles havebeen successfully applied to identify the parameters offractional-order chaotic systems. However, most ofthem maintain an important limitation; they frequentlyobtain sub-optimal results as a consequence of aninappropriate balance between exploration andexploitation in their search strategies. This paperpresents an algorithm for parameter identification offractional-order chaotic systems. In order to determinethe parameters, the proposed method uses theevolutionary method called Locust Search (LS), whichis based on the behavior of swarms of locusts. Differentto the most of existent evolutionary algorithms, itexplicitly avoids the concentration of individuals in thebest positions, eliminating critical flaws such as thepremature convergence to sub-optimal solutions andthe limited exploration-exploitation balance. Numericalsimulations have been conducted on the fractional-Order Van der Pol oscillator to show the effectivenessof the proposed scheme.

Stochastic mesh method for optimal stopping problems

Abstract A Monte Carlo method for solving the multi-dimensional optimal stopping problem is considered. Consistent estimators for a general jump-diffusion are pointed out. It is shown that the variance of estimators is inverse proportional to the number of points in each layer of the mesh.

From Prediction to Action: Improving User Experience With Data-Driven Resource Allocation

Driven by the desire for a better user experience and enabled by improved data storage and processing, much of the recent work has studied user experience prediction in cellular networks. In this paper, moving beyond the prediction-only approach, we propose a data-driven resource allocation framework that uses data-generated prediction models to explicitly guide resource allocation for user experience improvement. In a closed-loop fashion, it further leverages and verifies the causal relation that often exists between certain feature values (e.g., bandwidth) and user experience in computer networks. As a case study, we consider how to reduce the number of user complaints in cellular networks. Our approach consists of three components: we train a logistic regression classifier to predict user experience, utilize the trained likelihood as the objective function to allocate network resource, and then evaluate user experience with allocated resource to (in)validate and adjust the original model. We design a DualHet algorithm to tackle the problem of multi-dimensional resource optimization with heterogeneous users. Numerical simulations based on both synthetic and real network data sets demonstrate the effectiveness of the proposed algorithms. In particular, the simulations based on real data demonstrate up to $2\times $ performance improvement compared with the baseline algorithm.

Constrained radar waveform design algorithm for spectral coexistence

The design problem of radar waveform to enhance target delectability while ensuring spectral compatibility is considered. Precisely, an iterative sequential optimisation algorithm is developed to jointly optimise signal-to-interference-plus-noise ratio and stopband frequency energy. In each iteration of the proposed algorithm, the multidimensional optimisation problem is turned into multiple one-dimensional optimisation problems with closed-form solutions. Finally, the computational cost and objective value of the proposed algorithm in comparison with the existing method is assessed.