Conjugate Gradient Methods Memoryless BFGS Preconditioned

The minimization of the molecular potential energy function is one of the most important real-life problems which can help to predict the 3D structure of the protein by knowing the steady (ground) state of the molecules of the protein. In this paper, we propose a new hybrid algorithm between the social spider algorithm and the genetic algorithm in order to minimize a simplified model of the energy function of the molecule. We call the proposed algorithm by hybrid social spider optimization and genetic algorithm (HSSOGA). The HSSOGA comprises of three main steps. In the first step, we apply the social spider optimization algorithm to balance between the exploration and the exploitation processes in the proposed algorithm. In the second step, we use the dimensionality reduction process and the population partitioning process by dividing the population into subpopulations and applying the arithmetical crossover operator for each subpopulation order to increase the diversity of the search in the algorithm. In the last steps, we use the genetic mutation operator in the whole population to avoid the premature convergence and avoid trapping in local minima. The combination of three steps helps the proposed algorithm to solve the molecular potential energy function with different molecules size, especially when the problem dimension $$D>100$$D>100 with powerful performance. We test it on 13 large-scale unconstrained global optimization problems to investigate its performance on these functions. In order to investigate the efficiency of the proposed HSSOGA, we compare HSSOGA against eight benchmark algorithms when we minimize the potential energy function problem. The numerical experiment results show that the proposed algorithm is a promising and efficient algorithm and can obtain the global minimum or near global minimum of the large-scale optimization problems up to 1000 dimension and the molecular potential energy function of the simplified model with up to 200 degrees of freedom faster than the other comparative algorithms.

<p>The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.</p>

Buildings contribute to more than 70% of overall U.S. electricity usage and greenhouse gas emissions. The future building control optimizes more connected devices and renewable energy equipment, which requires a rapid and accurate response. It also poses the challenge of solving non-linear problems with discrete variables in real time. In one study, we developed a novel optimization using quantum annealing for MPC of rooftop units in buildings. Our approach demonstrated significant improvements in computational speed from hours to seconds by considering day-ahead demand response signals. Our findings highlight the potential of quantum computing in solving large-scale non-linear discrete optimization problems for building energy systems. The other research presented a new framework for building-to-grid integration. We developed MPC for a commercial distribution grid for cost reduction. With similar solutions to traditional algorithms, quantum computing reduced computational time to less than 1.1%. We proved its potential to solve large-scale discrete optimization problems for urban energy systems

In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or inefficient for each class are examined.Keywordsinterior-point methodslarge-scale optimizationnonlinear programming

Conjugate gradient methods are a class of very effective iterative methods for large-scale unconstrained optimization. In this paper, a new Dai-Liao conjugate gradient method for solving large-scale unconstrained optimization problem is proposed. Based on the approximately optimal stepsize for the gradient method, we derive three new choices for the important parameters tk in Dai-Liao conjugate gradient method. The search direction satisfies the sufficient descent condition, and the global convergences of the proposed method for uniformly convex and general functions are proved under some mild conditions. Numerical experiments on a set of test problems from the CUTEst library show that the proposed method is superior to some well-known conjugate gradient methods.

Although there are many studies on large-scale unconstrained optimization (e.g., with 100 to 1000 variables) and small-scale constrained optimization (e.g., with 10 to 30 variables) using nature-inspired algorithms (e.g., evolutionary algorithms and swarm intelligence algorithms), no publicly available nature-inspired algorithm is developed for large-scale constrained optimization. In this paper, we combine a cooperative coevolutionary particle swarm optimization (CCPSO) algorithm with the e constrained method to solve large-scale real-valued constrained optimization problems. The eCCPSO framework is proposed, and three different algorithms based on the framework, i.e., eCCPSOd, eCCPSOw and eCCPSOw2, are developed. The proposed algorithms compare favorably to the state-of-the-art constrained optimization algorithm eDEag on large-scale problems. The experimental results further suggest that eCCPSOw2 with adaptive improvement detection technique is highly competitive compared with the other algorithms considered in this work for solving large-scale real-valued constrained optimization problems.

Genetic algorithms are able to search very large, variable complex spaces and locate the global optimum. However, there exist many difficulties in applying GA to large-scale nonlinear system optimization or "GA hard" problems. This paper presents an improved GA based on domain evolution model and fuzzy environment factor. Simulation study shows that it is a powerful search technique which can avoid premature convergence and locate the real global optimum. An example is given to show how this new algorithm can be successfully applied to solve large-scale industrial chemical separation process optimization problem.

ABSTRACTThis paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden–Fletcher–Goldfarb–Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under appropriate assumptions, the method is proven to possess global convergence for nonconvex smooth functions, and R-linear convergence for strongly convex functions. Preliminary numerical results and related comparisons show the efficiency of the proposed method in practical computation.

The growing penetration of renewable energy sources (RES) has boosted the necessity of cost-effective and flexible power system operations. Battery Energy Storage Systems (BESS) provide a real-world solution by improving grid reliability, facilitating flexible dispatch, and renewable integration. This paper models the Economic Dispatch (ED) problem with BESS integration, with an objective to minimize overall generation cost subject to operation constraints of thermal units and BESS. Two optimization methods are compared: (i) fmincon, a gradient-based constrained nonlinear solver, and (ii) the JAYA algorithm, a parameter-free metaheuristic that repeatedly pushes solutions towards best and away from worst. Simulation studies on a 6-bus system with six thermal units show that integration with BESS highly enhances operation flexibility and lowers costs. The total generation cost was reduced from Rs.23.74 million to Rs.21.21 million, corresponding to a saving of Rs.2.53 million (10.66%) using FMINCON whereas using JAYA algorithm the tota generation cost was reduced from Rs.23.68 million to Rs.20.83 million, corresponding to a saving of Rs.2.85 million (12.06%). The Jaya algorithm performs better consistently compared to fmincon in both cost minimization and the speed of convergence, showing its suitability for solving large-scale nonlinear power system optimization problems.

A techno-economic multi-objective model for hybrid harmonic filter planning considering uncertainty in non-linear loads

Short-term scheduling and recipe optimization of blending processes

An accelerated descent CG algorithm with clustering the eigenvalues for large-scale nonconvex unconstrained optimization and its application in image restoration problems

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

A Liu-Storey-type conjugate gradient method for unconstrained minimization problem with application in motion control

In large-scale unconstrained optimization problems, preconditioned conjugate gradient techniques are often used to solve the Newton equations approximately. In certain applications, “natural” sparse preconditioners can be derived from the structure of the problem and can accelerate convergence significantly. Since these preconditioners are not necessarily positive definite, modified Cholesky (MC) factorizations can be applied to construct related positive definite preconditioners. This paper describes such an adaptation of two MC techniques–GMW (Gill–Murray–Wright) and SE (Schnabel–Eskow)–in a truncated Newton minimization method. This paper then analyzes their effects on three interesting test problems of moderate size. The preliminary results suggest that the two MC algorithms perform quite differently in practice. Trends can be noted for sparse problems that differ from the dense case. Differences in the size of the modifications and in their variances throughout the minimization are observed and relat...