Large Optimization Problems Research Articles

Optimization of Reactive Power in BenXi Steel Distribution Feeders Based on RARW-GA

Optimal allocation of reactive power compensation plays an important role in power system planning and design. However, as a non-linear, large scale combinatorial optimization problem, Conventional methods are not normally appropriate for it . A mathematical model is firstly presented in this paper for comprehensive optimal configuration in distribution feeders based on the analysis of engineering factors of reactive power compensation, whose objective is to minimize the annual expenditure involving the devices investment and the income of energy saving, and satisfy all sorts of operation，fixing and maintenance constrains. The control variables include the capacitor banks’ number and capacity of various compensation schemes. RARW-GA algorithm is adopted to solve this problem. The result of calculation and analysis of BenXi Steel group corporation power system shows that the proposed method is feasible and effective.

Assessing the performance of an optimization-based multilevel method

Many large nonlinear optimization problems are based upon a hierarchy of models, corresponding to levels of discretization or detail in the problem. Optimization-based multilevel methods – that is, multilevel methods based on solving coarser versions of an optimization problem – are designed to solve such multilevel problems efficiently by taking explicit advantage of the hierarchy of models. The methods are generalizations of multigrid methods for solving partial differential equations. These multilevel methods are a powerful tool, but they will not lead to improved performance over traditional algorithms for all optimization problems. We develop techniques whereby a particular multilevel method can assess the properties of the optimization problem, with the goal of automatically determining whether it is well suited for the multilevel algorithm. We also show that our diagnostic tests are sufficient to measure the properties of the optimization problem relevant to the performance of the multilevel method.

An efficient stochastic optimization framework for studying the impact of seasonal variation on the minimum water consumption of pulverized coal (PC) power plants

Coal-fired power plants use water in large amounts second only to agricultural irrigation. Water restrictions become more influential when water-expensive carbon capture technologies are added to the process. Therefore, national efforts to study the reduction of water withdrawal and consumption in existing and future plants have been intensified. Water consumption in these plants is strongly associated with the dry bulb temperature and humidity of air. There is significant variability in these parameters. In this work, we characterized the uncertainty and variability in these parameters in terms of probability distributions. These distributions change with seasons. We obtained optimal operating conditions for each season in the face of uncertainties using water minimization as the objective. It has been found that the water consumption is reduced from 3.2 to 15.4% depending on the season. In order to solve this large scale real world optimization problem, we had to resort to an efficient stochastic nonlinear programming (SNLP) algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). It has been found that BONUS reduces the computationally intensity of this problem by 98.7%, making it possible to obtain optimal operating conditions in reasonable computational time.

Teaching–Learning-Based Optimization: An optimization method for continuous non-linear large scale problems

An efficient optimization method called ‘Teaching–Learning-Based Optimization (TLBO)’ is proposed in this paper for large scale non-linear optimization problems for finding the global solutions. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The effectiveness of the method is tested on many benchmark problems with different characteristics and the results are compared with other population based methods.

Linear Dynamic Programs for Resource Management

Sustainable resource management in many domains presents large continuous stochastic optimization problems, which can often be modeled as Markov decision processes (MDPs). To solve such large MDPs, we identify and leverage linearity in state and action sets that is common in resource management. In particular, we introduce linear dynamic programs (LDPs) that generalize resource management problems and partially observable MDPs (POMDPs). We show that the LDP framework makes it possible to adapt point-based methods--the state of the art in solving POMDPs--to solving LDPs. The experimental results demonstrate the efficiency of this approach in managing the water level of a river reservoir. Finally, we discuss the relationship with dual dynamic programming, a method used to optimize hydroelectric systems.

An efficient algorithm for stochastic capacity portfolio planning problems

This study investigates capacity portfolio planning problems under demand, price, and yield uncertainties. We model this capacity portfolio planning problem as a Markov decision process. In this research, we consider two types of capacity: dedicated and flexible capacity. Among these capacity types, flexible capacity costs higher but provides flexibility for producing different products. To maximize expected profit, decision makers have to choose the optimal capacity level and expansion timing for both capacity types. Since large stochastic optimization problems are intractable, a new heuristic search algorithm (HSA) is developed to reduce computational complexity. Compare to other algorithms in literature, HSA reduces computational time by at least 30% in large capacity optimization problems. In addition, HSA yields optimal solution in all numerical examples that we have examined.

A new descent memory gradient method and its global convergence

In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties: 1) The search direction is always a sufficiently descent direction at every iteration without the line search used; 2) The search direction always satisfies the angle property, which is independent of the convexity of the objective function. Under mild conditions, the authors prove that the proposed method has global convergence, and its convergence rate is also investigated. The numerical results show that the new descent memory method is efficient for the given test problems.

Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems

We introduce a gradient descent algorithm for solving large scale unconstrained nonlinear optimization problems. The computation of the initial trial steplength is based on the usage of both the quasi-Newton property and the Hessian inverse approximation by an appropriate scalar matrix. The nonmonotone line search technique for the steplength calculation is applied later. The computational and storage complexity of the new method is equal to the computational and storage complexity of the Barzilai and Borwein method. On the other hand, the reported numerical results indicate improvements in favor of the new method with respect to the well known global Barzilai and Borwein method.

Accelerating floating-point fitness functions in evolutionary algorithms: a FPGA-CPU-GPU performance comparison

Many large combinatorial optimization problems tackled with evolutionary algorithms often require very high computational times, usually due to the fitness evaluation. This fact forces programmers to use clusters of computers, a computational solution very useful for running applications of intensive calculus but having a high acquisition price and operation cost, mainly due to the Central Processing Unit (CPU) power consumption and refrigeration devices. A low-cost and high-performance alternative comes from reconfigurable computing, a hardware technology based on Field Programmable Gate Array devices (FPGAs). The main objective of the work presented in this paper is to compare implementations on FPGAs and CPUs of different fitness functions in evolutionary algorithms in order to study the performance of the floating-point arithmetic in FPGAs and CPUs that is often present in the optimization problems tackled by these algorithms. We have taken advantage of the parallelism at chip-level of FPGAs pursuing the acceleration of the fitness functions (and consequently, of the evolutionary algorithms) and showing the parallel scalability to reach low cost, low power and high performance computational solutions based on FPGA. Finally, the recent popularity of GPUs as computational units has moved us to introduce these devices in our performance comparisons. We analyze performance in terms of computation times and economic cost.

Gene silencing—A genetic operator for constrained optimization

Genetic algorithms (GA) are generally considered to be suitable for solving large optimization problems. Even then, constrained optimization through GA is considered to be a challenging task because, GAs do not provide a direct methodology to solve such problems. For such types of problems, some modifications of the existing process of evolution have to be done or some special operators have to be used to satisfy the additional constraints. This paper proposes a bio inspired gene silencing operator that solves the problem of constrained optimization efficiently through simple and natural means. Two types of gene silencing operators have been realized and tested on the 0/1 knapsack problem. The results are compared with standard GA and a variant of GA, designed and implemented according to the strategies suggested in the literature for constraint optimization problems.

Real-Time Power Management of Integrated Power Systems in All Electric Ships Leveraging Multi Time Scale Property

All-electric ships (AES), enabled by integrated power systems (IPS), have been pursued for both commercial and military applications to meet the increasing ship-board power demand and environmental sustainability initiatives. They necessitate real-time power management (PM) for dynamic reconfiguration to support system critical operations in the event of dynamic load change or IPS component failures. The nonlinear, large scale trajectory optimization problem associated with IPS, along with the non-analytical nature of IPS model, makes many existing methods inadequate in meeting the real-time requirements. In this paper, we develop a methodology that exploits time scale separation, a characteristic associated with IPS dynamics, to achieve real-time optimization. In parallel, a dynamic model of the IPS with gas turbine and fuel cell as power plants is developed that captures the relevant dynamics but is simple enough for real-time optimization. The tradeoffs between the computational efficiency and optimization accuracy are analyzed. The optimization results for IPS PM on a real-time simulator are reported, which illustrate the real-time feasibility of the proposed optimization strategy.

A Modified Super-linear QN-Algorithm for Unconstrained Optimization

In this paper, we have proposed a modified QN-algorithm for solving a self-scaling large scale unconstrained optimization problems based on a new QN-update. The performance of the proposed algorithm is better than that used by Wei, Li, Yuan algorithm. Our numerical tests show that the new proposed algorithm seems to converge faster as compared with a standard similar algorithm in many situations .

A DSS generator for multiobjective optimisation of spreadsheet-based models

Water management practice has benefited from the development of model-driven Decision Support Systems (DSS), and in particular those that combine simulation with single or multiple-objective optimisation tools. However, there are many performance, acceptance and adoption problems with these decision support tools caused mainly by misunderstandings between the communities of system developers and users. This paper presents a general-purpose decision-support system generator, GANetXL, for developing specific applications that require multiobjective optimisation of spreadsheet-based models. The system is developed as an Excel add-in that provides easy access to evolutionary multiobjective optimisation algorithms to non-specialists by incorporating an intuitive interactive graphical user interface that allows easy creation of specific decision-support applications. GANetXL’s utility is demonstrated on two examples from water engineering practice, a simple water supply reservoir operation model with two objectives and a large combinatorial optimisation problem of pump scheduling in water distribution systems. The two examples show how GANetXL goes a long way toward closing the gap between the achievements in optimisation technology and the successful use of DSS in practice.

Parallelizing a Modified Particle Swarm Optimizer (PSO)

Recently, a modified Particle Swarm Optimizer (MLPSO) has been succeeded in solving truss topological optimization problems and competitive results are obtained. Since this optimizer belongs to evolutionary algorithm and plagued by high computational cost as measured by execution time, in order to reduce its execution time for solving large complex optimization problem, a parallel version for this optimizer is studied in this paper. This paper first gives an overview of PSO algorithm as well as the modified PSO, and then a design and an implementation of parallel PSO is proposed. The performance of the proposed algorithm is tested by two examples and promising speed-up rate is obtained. Final part is conclusion and outlook.

Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains

Nowadays, large scale optimisation problems arise as a very interesting field of research, because they appear in many real-world problems (bio-computing, data mining, etc.). Thus, scalability becomes an essential requirement for modern optimisation algorithms. In a previous work, we presented memetic algorithms based on local search chains. Local search chain concerns the idea that, at one stage, the local search operator may continue the operation of a previous invocation, starting from the final configuration reached by this one. Using this technique, it was presented a memetic algorithm, MA-CMA-Chains, using the CMA-ES algorithm as its local search component. This proposal obtained very good results for continuous optimisation problems, in particular with medium-size (with up to dimension 50). Unfortunately, CMA-ES scalability is restricted by several costly operations, thus MA-CMA-Chains could not be successfully applied to large scale problems. In this article we study the scalability of memetic algorithms based on local search chains, creating memetic algorithms with different local search methods and comparing them, considering both the error values and the processing cost. We also propose a variation of Solis Wets method, that we call Subgrouping Solis Wets algorithm. This local search method explores, at each step of the algorithm, only a random subset of the variables. This subset changes after a certain number of evaluations. Finally, we propose a new memetic algorithm based on local search chains for high dimensionality, MA-SSW-Chains, using the Subgrouping Solis Wets’ algorithm as its local search method. This algorithm is compared with MA-CMA-Chains and different reference algorithms, and it is shown that the proposal is fairly scalable and it is statistically very competitive for high-dimensional problems.

Self-adaptive differential evolution algorithm using population size reduction and three strategies

Many real-world optimization problems are large-scale in nature. In order to solve these problems, an optimization algorithm is required that is able to apply a global search regardless of the problems’ particularities. This paper proposes a self-adaptive differential evolution algorithm, called jDElscop, for solving large-scale optimization problems with continuous variables. The proposed algorithm employs three strategies and a population size reduction mechanism. The performance of the jDElscop algorithm is evaluated on a set of benchmark problems provided for the Special Issue on the Scalability of Evolutionary Algorithms and other Metaheuristics for Large Scale Continuous Optimization Problems. Non-parametric statistical procedures were performed for multiple comparisons between the proposed algorithm and three well-known algorithms from literature. The results show that the jDElscop algorithm can deal with large-scale continuous optimization effectively. It also behaves significantly better than other three algorithms used in the comparison, in most cases.

A New Method for Unconstrained Optimization Problem

This paper presents a new memory gradient method for unconstrained optimization problems. This method makes use of the current and previous multi-step iteration information to generate a new iteration and add the freedom of some parameters. Therefore it is suitable to solve large scale unconstrained optimization problems. The global convergence is proved under some mild conditions. Numerical experiments show the algorithm is efficient in many situations.

Restart particle swarm optimization with velocity modulation: a scalability test

Large scale continuous optimization problems are more relevant in current benchmarks since they are more representative of real-world problems (bioinformatics, data mining, etc.). Unfortunately, the performance of most of the available optimization algorithms deteriorates rapidly as the dimensionality of the search space increases. In particular, particle swarm optimization is a very simple and effective method for continuous optimization. Nevertheless, this algorithm usually suffers from unsuccessful performance on large dimension problems. In this work, we incorporate two new mechanisms into the particle swarm optimization with the aim of enhancing its scalability. First, a velocity modulation method is applied in the movement of particles in order to guide them within the region of interest. Second, a restarting mechanism avoids the early convergence and redirects the particles to promising areas in the search space. Experiments are carried out within the scope of this Special Issue to test scalability. The results obtained show that our proposal is scalable in all functions of the benchmark used, as well as numerically very competitive with regards to other compared optimizers.

A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test

Continuous optimization is one of the areas with more activity in the field of heuristic optimization. Many algorithms have been proposed and compared on several benchmarks of functions, with different performance depending on the problems. For this reason, the combination of different search strategies seems desirable to obtain the best performance of each of these approaches. This contribution explores the use of a hybrid memetic algorithm based on the multiple offspring framework. The proposed algorithm combines the explorative/exploitative strength of two heuristic search methods that separately obtain very competitive results. This algorithm has been tested with the benchmark problems and conditions defined for the special issue of the Soft Computing Journal on Scalability of Evolutionary Algorithms and other Metaheuristics for Large Scale Continuous Optimization Problems. The proposed algorithm obtained the best results compared with both its composing algorithms and a set of reference algorithms that were proposed for the special issue.

Modified nonmonotone Armijo line search for descent method

Nonmonotone line search approach is a new technique for solving optimization problems. It relaxes the line search range and finds a larger step-size at each iteration, so as to possibly avoid local minimizer and run away from narrow curved valley. It is helpful to find the global minimizer of optimization problems. In this paper we develop a new modification of matrix-free nonmonotone Armijo line search and analyze the global convergence and convergence rate of the resulting method. We also address several approaches to estimate the Lipschitz constant of the gradient of objective functions that would be used in line search algorithms. Numerical results show that this new modification of Armijo line search is efficient for solving large scale unconstrained optimization problems.