Showing papers on "Extremal optimization published in 2019"

Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems

Abstract: The connection weights parameters play important roles in adjusting the performance of PID neural network (PIDNN) for complex control systems. However, how to obtain an optimal set of initial values of these connection weight parameters in a multivariable PIDNN called MPIDNN is still an open issue for system designers and engineers. This paper formulates this issue as a typical constrained optimization problem firstly by minimizing the cumulative sum of the product of exponential time and the system errors, and a real-time penalty function for overshoots of the system outputs, and then proposes an adaptive population extremal optimization-based MPIDNN method called PEO-MPIDNN for the optimal control issue of multivariable nonlinear control systems. The simulation results for two typical multivariable nonlinear control systems have demonstrated the superiority of the proposed PEO-MPIDNN to real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO)-based MPIDNN, traditional MPIDNN with back propagation algorithm, and population extremal optimization-based multivariable PID control algorithm in terms of transient-state, steady-state, and robust control performance.

Combinatorial Optimization: Comparison of Heuristic Algorithms in Travelling Salesman Problem

Abstract: The Travelling Salesman Problem (TSP) is an NP-hard problem with high number of possible solutions. The complexity increases with the factorial of n nodes in each specific problem. Meta-heuristic algorithms are an optimization algorithm that able to solve TSP problem towards a satisfactory solution. To date, there are many meta-heuristic algorithms introduced in literatures which consist of different philosophies of intensification and diversification. This paper focuses on 6 heuristic algorithms: Nearest Neighbor, Genetic Algorithm, Simulated Annealing, Tabu Search, Ant Colony Optimization and Tree Physiology Optimization. The study in this paper includes comparison of computation, accuracy and convergence.

An improved artificial bee colony algorithm combined with extremal optimization and Boltzmann Selection probability

Abstract: Artificial Bee Colony (ABC) algorithm is an optimization algorithm based on a particular intelligent behavior of honeybee swarms. The standard ABC has been utilized to deal with a lot of optimization problems in real world. However, there are still some defects of the standard ABC such as weak local-search capability and low solution precision. In order to improve the performance of ABC, in this paper, we propose two improved versions of ABC-EO and IABC-EO presented in our previous work, called ABC-EO II and IABC-EO II, where Extremal Optimization (EO) is introduced to ABC and IABC in different ways. There are some advanced characteristics of our proposed algorithms: (1) Compared with ABC-EO and IABC-EO, the improved versions have lower computational costs by introducing EO in different ways; (2) An easier-operated mutation method is introduced which can increase the diversity of new offspring and helps our algorithms jump out of local optima; (3) The selection pressure can be dynamically adjusted in evolutionary process by means of Boltzmann selection probability; (4) A novel selection probability is used to select the worse solutions for the mutation operation by EO mechanism. The experimental results on three groups of benchmark functions indicate that the performance of the proposed algorithms is as good as or superior to those of 15 state-of-the-art optimization algorithms in terms of solution accuracy, convergence speed, successful rate and statistical tests. Finally, in order to testify the feasibilities of the proposed methods for solving the real life problems, our algorithms are applied to solving two kinds of parameters identification of photovoltaic models and four well-recognized evolutionary algorithms are selected as the competitors. The simulation results indicate that the proposed IABC-EO II algorithm has superior performance in comparison with other five algorithms, while the proposed ABC-EO II outperforms at least competitive with other four algorithms in term of solution accuracy and statistical tests. As a result, our algorithms may be good alternatives for solving complex unconstrained continuous optimization problems.

Experimental performance of graph neural networks on random instances of max-cut

Abstract: This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn functions on graphs -- and we apply them to the max-cut problem on random regular graphs. We focus on the max-cut problem on random regular graphs because it is a fundamental problem that has been widely studied. In particular, even though there is no known explicit solution to compare the output of our algorithm to, we can leverage the known asymptotics of the optimal max-cut value in order to evaluate the performance of the GNNs. In order to put the performance of the GNNs in context, we compare it with the classical semidefinite relaxation approach by Goemans and Williamson~(SDP), and with extremal optimization, which is a local optimization heuristic from the statistical physics literature. The numerical results we obtain indicate that, surprisingly, Graph Neural Networks attain comparable performance to the Goemans and Williamson SDP. We also observe that extremal optimization consistently outperforms the other two methods. Furthermore, the performances of the three methods present similar patterns, that is, for sparser, and for larger graphs, the size of the found cuts are closer to the asymptotic optimal max-cut value.

Fuzzy goal programming-based ant colony optimization algorithm for multi-objective topology design of distributed local area networks

Abstract: Topology design of a distributed local area network (DLAN) is a complex optimization problem and has been generally modelled as a single-objective optimization problem. Traditionally, iterative techniques such as genetic algorithms and simulated annealing have been used to solve the problem. In this paper, we formulated the DLAN topology design problem as a multi-objective optimization problem considering five design objectives. These objectives are network reliability, network availability, average link utilization, monetary cost, and average network delay. The multi-objective nature of the problem has been addressed by incorporating a fuzzy goal programming approach to combine the individual design objectives into a single-objective function. The objective function is then optimized using the ant colony algorithm adapted for the problem. The performance of the proposed fuzzy goal programming-based ant colony optimization algorithm (GPACO) is evaluated with respect to the algorithm control parameters, namely pheromone deposit and evaporation rate, colony size and heuristic values. A comparative study was also done using four other multi-objective optimization algorithms which are non-dominated sorting genetic algorithm II, archived multi-objective simulated annealing algorithm, lexicographic ant colony optimization, and Pareto-dominance ant colony optimization. Results revealed that, in general, GPACO was able to find solutions of higher quality as compared to the other four algorithms.

A fast solution for bi-objective traffic minimization in geo-distributed data flows

Abstract: Geo-distributed analytics is becoming an increasingly common-place as IoT, fog computing and big data processing platforms are nowadays integrating with each other. In this work, we deal with a problem encountered when complex Spark workflows run on top of geographically dispersed nodes, either data centers or individual machines. There have been proposals that optimize the execution of such workflows in terms of the aggregate traffic generated or the latency (which is due to data transmission), or both metrics. However, the state-of-the-art solutions that target both objectives are either significantly sub-optimal or suffer from high optimization overhead. In this work, we address this limitation. The main solutions that we propose are both efficient and effective; based on either the extremal optimization or the greedy algorithm design paradigm, they can yield significant improvements having an optimization overhead of a few tens of seconds even for Spark workflows of 15 stages running on 15 distributed nodes. We also show the inadequacy of evolutionary optimization solutions, such as genetic algorithms, for our problem.

Experimental performance of graph neural networks on random instances of max-cut

Abstract: This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn functions on graphs -- and we apply them to the max-cut problem on random regular graphs. We focus on the max-cut problem on random regular graphs because it is a fundamental problem that has been widely studied. In particular, even though there is no known explicit solution to compare the output of our algorithm to, we can leverage the known asymptotics of the optimal max-cut value in order to evaluate the performance of the GNNs. In order to put the performance of the GNNs in context, we compare it with the classical semidefinite relaxation approach by Goemans and Williamson~(SDP), and with extremal optimization, which is a local optimization heuristic from the statistical physics literature. The numerical results we obtain indicate that, surprisingly, Graph Neural Networks attain comparable performance to the Goemans and Williamson SDP. We also observe that extremal optimization consistently outperforms the other two methods. Furthermore, the performances of the three methods present similar patterns, that is, for sparser, and for larger graphs, the size of the found cuts are closer to the asymptotic optimal max-cut value.

Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem

Abstract: We analyze the transformation of QUBO from its conventional Boolean presentation into an equivalent spin glass problem with coupled $\pm1$ spin variables exposed to a site-dependent external field. We find that in a widely used testbed for QUBO these fields tend to be rather large compared to the typical coupling and many spins in each optimal configurations simply align with the fields irrespective of their constraints. Thereby, the testbed instances tend to exhibit large redundancies - seemingly independent variables which contribute little to the hardness of the problem, however. We demonstrate various consequences of this insight, for QUBO solvers as well as for heuristics developed for finding spin glass ground states. To this end, we implement the Extremal Optimization (EO) heuristic, in a new adaptation for the QUBO problem. We also propose a novel way to assess the quality of heuristics for increasing problem sizes based on asymptotic scaling.

Research on Distribution Network Optimization with Distributed Generation

Abstract: Distributed generation access to distribution network will change its power flow and node voltage distribution, which may affect the safe and stable operation of distribution network. In this paper, the minimum active power loss is taken as the objective to model the distribution network with distributed generations, and the extremum optimization algorithm is introduced to improve it. Finally, an example is given to verify the superiority of the improved algorithm over other typical optimization algorithms.

Fuzzy Clusterization of Distorted by Missing Observations Data Sets Using Evolutionary Optimization

Abstract: The problem of probabilistic fuzzy clustering of data arrays, distorted by omissions under overlapping classes is considered. In contrast to the traditional approach (FCM of J. Bezdek), based on the nonlinear programming procedure using the uncertain Lagrange multipliers, it was proposed to solve a multi extremal optimization problems without restrictions using the partial distances. To solve this problem, it is proposed to use a modified evolutionary procedure - accelerated cat swarm optimization algorithm. A special feature of the proposed algorithm is uniting seeking and tracing modes within a multi step optimization procedure, having the properties of a gradient search, the “heavy ball” method, global random search and fuzzy J-means clustering algorithm.

Method of Deformed Stars for Multi-extremal Optimization. One- and Two-Dimensional Cases

Abstract: This paper describes the task of optimizing a multi-extremal function, which in general can be given analytically, tabularly or algorithmically. The method of deformed stars is developed, which belongs to the class of evolutionary methods and allows to take into account the relief of the investigated function. Its advantages are the speed of convergence and result accuracy in comparison with other evolutionary methods. The obtained results of experiments allow us to conclude that the proposed method is applicable to solving problems of finding optimal (suboptimal) values, including non-differentiated functions.

A hybrid variable selection algorithm for multi-layer perceptron with nonnegative garrote and extremal optimization

Abstract: In the paper, a new hybrid variable selection algorithm for nonlinear regression multi-layer perceptron (MLP) is proposed. The proposed algorithm applies nonnegative garrote (NNG) to compress the input weights of the MLP. The zero input weights dependent variables will be removed from the initial dataset. Next, a further variable selection is carried out by extremal optimization (EO) algorithm. The new variable selection algorithm integrates powerful global selection ability of NNG and accurate local search ability of EO. Finally, two examples of artificial data sets and an industrial application for a debutanizer column are implemented to demonstrate the performance of the new algorithm. The simulation result demonstrates that the developed algorithm presents d better model performance along with less input variable selected than other state-of-art variable selection methods.

Distributed Processor Load Balancing Based on Multi-objective Extremal Optimization

Abstract: The paper proposes and discusses distributed processor load balancing algorithms which are based on nature inspired approach of multi-objective Extremal Optimization. Extremal Optimization is used for defining task migration aiming at processor load balancing in execution of graph-represented distributed programs. The analysed multi-objective algorithms are based on three or four criteria selected from the following four choices: the balance of computational loads of processors in the system, the minimal total volume of application data transfers between processors, the number of task migrations during program execution and the influence of task migrations on computational load imbalance and the communication volume. The quality of the resulting load balancing is assessed by simulation of the execution of the distributed program macro data flow graphs, including all steps of the load balancing algorithm. It is done following the event-driven model in a simulator of a message passing multiprocessor system. The experimental comparison of the multi-objective load balancing to the single objective algorithms demonstrated the superiority of the multi-objective approach.

Microwave imaging based on two hybrid particle swarm optimization approaches

Abstract: In this paper, the solution of the inverse scattering problem for determining the shape and location of perfectly conducting scatterers by making use of electromagnetic scattered fields is presented. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization one. Then, two evolutionary algorithms are used to solve the inverse scattering problem. To further clarify, our contribution is to test two well-known algorithms in the literature to the problem of microwave imaging. The hybrid approaches combine the standard particle swarm optimization (PSO) with the ideas of the simulated annealing and extremal optimization algorithms, respectively. Both of them are shown to be more efficient than original PSO technique. Reconstruction results by using the two presented schemes are compared with exact shapes of some conducting cylinders; and good agreements with the original shapes are observed.

Shapley Value and Extremal Optimization for the Network Influence Maximization Problem

Abstract: The problem of Network Influence Maximization is approached by an Extremal Optimization algorithm called Shapley value Extremal Optimization (SvEO). The influence maximization problem for the independent cascade model is considered as a cooperative game. In this cooperative game players seek to choose seeder nodes to maximize the value of the game computed as the size of the influence set of their cascade model by maximizing their average marginal contribution to all possible player coalitions (i.e. subsets of the seeder set). SvEO is compared with other influence maximization algorithms by means of numerical experiments, with promising results. Possible implications of the use of the Shapley value are discussed using a network constructed from highly cited publication data in the field of computer science.

3D IC optimal layout design. A parallel and distributed topological approach.

Abstract: The task of 3D ICs layout design involves the assembly of millions of components taking into account many different requirements and constraints such as topological, wiring or manufacturability ones. It is a NP-hard problem that requires new non-deterministic and heuristic algorithms. Considering the time complexity, the commonly applied Fiduccia-Mattheyses partitioning algorithm is superior to any other local search method. Nevertheless, it can often miss to reach a quasi-optimal solution in 3D spaces. The presented approach uses an original 3D layout graph partitioning heuristics implemented with use of the extremal optimization method. The goal is to minimize the total wire-length in the chip. In order to improve the time complexity a parallel and distributed Java implementation is applied. Inside one Java Virtual Machine separate optimization algorithms are executed by independent threads. The work may also be shared among different machines by means of The Java Remote Method Invocation system.

An Electric Load Forecasting Model Based on BP Neural Network and Improved Bat Algorithm Hybridized with Extremal Optimization

Abstract: Electric load forecasting is a vital role in obtaining effective management of modern power systems. The accuracy forecasting results will lead to the improvement of the energy efficiency and reduction of production cost. This paper presents a novel electric load forecasting model by using BP neural network and improved bat algorithm with extremal optimization called IBA-EO-BP model. First, to enhance the global search ability and diversity of original bat algorithm (BA), we propose IBA-EO by improving original BA and combining with extremal optimization. Then, considering traditional BP is more likely converge to local optimal values, the IBA-EO is employed to find out the optimal connection weight parameters in BP. Two datasets from energy market operation in Australia are selected as case study. The simulation results demonstrate that the proposed IBA-EO-BP model is much more accurate than the traditional BP forecasting model and persistence model in terms of three widely used performance indices and two statistical tests.

Influence Maximization and Extremal Optimization

Abstract: Influence Extremal Optimization (InfEO) is an algorithm based on Extremal Optimization, adapted for the influence maximization problem for the independent cascade model. InfEO maximizes the marginal contribution of a node to the influence set of the model. Numerical experiments are used to compare InfEO with other influence maximization methods, indicating the potential of this approach. Practical results are discussed on a network constructed from publication data in the field of computer science.