Global optimization of signomial geometric programming using linear relaxation

In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P).

The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder–Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.

A Riemannian metric for geometry-aware singularity avoidance by articulated robots

An algorithm based on a Hopfield network for solving the hierarchical graph visualization problem is presented. It simultaneously minimizes the number of crossings and total path length to produce two-dimensional drawings easily interpreted by human observers. Traditional heuristics often follow a more local optimization approach where "readability" criteria are sequentially applied, such as applying the barycentric heuristic followed by the priority layout heuristic. As a result of the more global approach, the neural network achieved comparable crossing minimization to the barycentric heuristic while simultaneously reducing total path length up to 50% over the priority layout heuristic for the benchmarks tested.

Simulation and optimization of multi effect desalination coupled to a gas turbine plant with HRSG consideration

"Antibody of Unknown Significance" (AUS): The Issue of Interpreting Antibody Test Results.

It is difficult to get the correct segmentation results for the intensity inhomogeneity images,and the segmentation results are very sensitive to the initial contours.Thus,a fast and stable approach was proposed to overcome these disadvantages.First,an Adaptive Distance Preserving Level Set(ADPLS) method was utilized to get a better initial contour.Second,the Local Binary Fitting(LBF) model was used for a further segmentation.The experimental results show that the improved model can achieve good performance and is better to solve the contradiction among the segmentation speed,accuracy and stability.

We have proposed a misfit function based on adaptive matching filtering (AMF) to tackle challenges associated with cycle skipping and local minima in full-waveform inversion (FWI). This AMF is designed to measure time-varying phase differences between observations and predictions. Compared with classical least-squares waveform differences, our misfit function behaves as a smooth, quadratic function with a broad basin of attraction. These characters are important because local gradient-based optimization approaches used in most FWI schemes cannot guarantee convergence toward true models if misfit functions include local minima or if the starting model is far away from the global minimum. The 1D and 2D synthetic experiments illustrate the advantages of the proposed misfit function compared with the classical least-squares waveform misfit. Furthermore, we have derived adjoint sources associated with the proposed misfit function and applied them in several 2D time-domain acoustic FWI experiments. Numerical results found that the proposed misfit function can provide good starting models for FWI, particularly when low-frequency signals are absent in recorded data.

Connecting wind power to the power grid has recently become more common. To better manage and use wind power, its strength must be predicted precisely, which is of great safety and economic significance. In this paper, the short-term power prediction of wind power is based on self-adaptive niche particle swarm optimization (NPSO) in a neural net. Improved PSO adopts the rules of classification and elimination of a niche using a self-adaptive nonlinear mutation operator. Compared with the traditional method of maximum gradient, NPSO can skip a local optimal solution and approach the global optimal solution more easily in practice. Compared with the basic PSO, the number of iterations is reduced when the global optimal solution is obtained. The method proposed in this paper is experimentally shown to be capable of efficient prediction and useful for short-term power prediction.

A multi–objective geometric programming problem contains more than one objective that needs to be achieved simultaneously. Such problems arise in many applications where two or more, sometimes conflicting objective functions have to be minimised concurrently. In this paper a new adaptive strategy called hybrid method proposed to find Pareto optimal solutions of the multi–objective geometric programming problem. Using geometric programming technique, a global best optimal solution is obtained from a set of Pareto optimal solution having a great impact on convergence of solution. The discussed hybrid method having a goal to enhance the optimisers over all performance by combining different optimisation techniques. In the proposed method we have combined e–constraint and weighted mean method and finally the result so obtained compared with the result obtained by fuzzy programming method. The solution procedure of the proposed hybrid method is illustrated by the numerical examples.

Multi-objective geometric programming (MOGP) is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Generally, the parameters of a multi-objective geometric programming (MOGP) models are assumed to be deterministic and fixed. However, the values observed for the parameters in real-world MOGP problems are often imprecise and subject to fluctuations. Therefore, we use MOGP within an uncertainty based framework and propose a MOGP model whose coefficients are uncertain in nature. We assume the uncertain variables (UVs) to have linear, normal or zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained multi-objective geometric programming (UCCMOGP) problems can be transformed into conventional MOGP problems to calculate the objective values. The paper develops a procedure to solve a UCCMOGP problem using an MOGP technique based on a weighted-sum method. The efficacy of this procedure is demonstrated by some numerical examples.

This paper revisits an efficient procedure for solving posynomial geometric programming (GP) problems, which was initially developed by Avriel et al. The procedure, which used the concept of conden...

Degree of difficulty is an important concept in the classicalGeometric Programming (GP) theory.The dual problem is often infeasible when the degree of difficulty is negative and very little subjects have been published on this topic.This paper presents the basic concepts and principles of multiple-objective geometric programming model, and developed a numerical procedure to solve multi-objective Geometric Programming Problems (GPP) having a negative degree of difficulty using weighted method to obtain the non-inferior solution and using Brickers simple technique to ensure the dual feasibility; namely the addition of a constant term to the primal objective function.

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

Beyond the 2 × 2 -contingency table: A primer on entropies and mutual information in various scenarios involving m diagnostic categories and n categories of diagnostic tests