Approximate Global Optimal Solution Research Articles

An integration method of a hybrid genetic algorithm and the Levenberg–Marquardt algorithm for ultrasonic testing

The accurate measurement of time-of-flight (TOF) is essential in ultrasonic testing. Further, noise interference is the key factor affecting the measurement accuracy. Therefore, to develop a reliable computational method of TOF for test pieces working in noisy environments, an integration method of a hybrid genetic algorithm and the Levenberg–Marquardt algorithm (GA–LM) for ultrasonic thickness measurement is proposed in the present research. A Gaussian model is first established for an echo signal. Further, the model-based parameter estimation is converted into a nonlinear optimization problem by applying the least square method. As the parameter estimation methods are easily affected by the initial value, an integrating innovation of the GA–LM algorithm is proposed. The initial values of the model parameters are selected by GA to obtain an approximate global optimal solution. Subsequently, this approximate solution is used as the initial value for the LM algorithm to perform iterations. The accurate global optimal solution of the Gaussian model is obtained through these iterations. Finally, the measuring accuracy and robustness of the GA–LM algorithm for TOF computation are verified by both numerical simulation and experiment data

Physician scheduling problem in Mobile Cabin Hospitals of China during Covid-19 outbreak.

In this paper, we investigate a novel physician scheduling problem in the Mobile Cabin Hospitals (MCH) which are constructed in Wuhan, China during the outbreak of the Covid-19 pandemic. The shortage of physicians and the surge of patients brought great challenges for physicians scheduling in MCH. The purpose of the studied problem is to get an approximately optimal schedule that reaches the minimum workload for physicians on the premise of satisfying the service requirements of patients as much as possible. We propose a novel hybrid algorithm integrating particle swarm optimization (PSO) and variable neighborhood descent (VND) (named as PSO-VND) to find the approximate global optimal solution. A self-adaptive mechanism is developed to choose the updating operators dynamically during the procedures. Based on the special features of the problem, three neighborhood structures are designed and searched in VND to improve the solution. The experimental comparisons show that the proposed PSO-VND has a significant performance increase than the other competitors.

Global Simultaneous Optimization of Oil, Hysteretic and Inertial Dampers Using Real-Valued Genetic Algorithm and Local Search

A method for global simultaneous optimization of oil, hysteretic and inertial dampers is proposed for building structures using a real-valued genetic algorithm and local search. Oil dampers has the property that they can reduce both displacement and acceleration without significant change of natural frequencies and hysteretic dampers possess the characteristic that they can absorb energy efficiently and reduce displacement effectively in compensation for the increase of acceleration. On the other hand, inertial dampers can change (prolong) the natural periods with negative stiffness and reduce the effective input and the maximum acceleration in compensation for the increase of deformation. By using the proposed simultaneous optimization method, structural designers can select the best choice of these three dampers from the viewpoints of cost and performance indices (displacement, acceleration). For attaining the global optimal solution which cannot be attained by the conventional sensitivity-based approach, a method including a real-valued genetic algorithm and local search is devised. In the first stage, a real-valued genetic algorithm is used for searching an approximate global optimal solution. Then a local search procedure is activated for enhancing the optimal character of the solutions by reducing the total quantity of three types of dampers. It is demonstrated that a better design from the viewpoint of global optimality can be obtained by the proposed method and the preference of damper selection strongly depends on the design target (displacement, acceleration). Finally, a multi-objective optimization for the minimum deformation and acceleration is investigated.

Single node failure repair method for distributed storage system based on genetic algorithm and MSR code

In view of the minimum storage regeneration (MSR) single fault node repair plan, design a kind of new single repair fault node topology. Consider link bandwidth available and the node processing power of heterogeneity, the repair delay and repair traffic node of combinatorial optimization. Topology can be converted to Steiner tree model with constraints, and design the corresponding hybrid genetic algorithm to solve the approximate global optimal solution. Finally, a compromise between the two optimization objectives is achieved. Simulation results show that under the same MSR code size, the repair delay of this topology is only 60%-80% of that of the traditional tree topology and 30%-40% of that of the traditional star topology. While the repair traffic for this topology is 9% to 65% higher than for the traditional star topology, the repair traffic is only 40% to 55% higher than for the traditional tree topology.

A Variable-Length Chromosome Genetic Algorithm for Time-Based Sensor Network Schedule Optimization.

Scheduling sensor nodes has an important role in real monitoring applications using sensor networks, lowering the power consumption and maximizing the network lifetime, while maintaining the satisfaction to application requirements. Nevertheless, this problem is usually very complex and not easily resolved by analytical methods. In a different manner, genetic algorithms (GAs) are heuristic search strategies that help to find the exact or approximate global optimal solution efficiently with a stochastic approach. Genetic algorithms are advantageous for their robustness to discrete and noisy objective functions, as they are only evaluated at independent points without requirements of continuity or differentiability. However, as explained in this paper, a time-based sensor network schedule cannot be represented by a chromosome with fixed length that is required in traditional genetic algorithms. Therefore, an extended genetic algorithm is introduced with variable-length chromosome (VLC) along with mutation and crossover operations in order to address this problem. Simulation results show that, with help of carefully defined fitness functions, the proposed scheme is able to evolve the individuals in the population effectively and consistently from generation to generation towards optimal ones, and the obtained network schedules are better optimized in comparison with the result of algorithms employing a fixed-length chromosome.

Trade-off between spectral efficiency and normalized energy in Ad-hoc wireless networks

With the ever-increasing deployment of wireless communication technologies, effective management of scarce power and radio spectrum resources is of primary concern. The available bandwidth spectrum should be utilized in the most efficient and controlled way for practical economic growth of industries in conformity with the evolving demand of energy for powering wireless devices. In the proposed optimization scheme, energy management and limited spectrum sharing are distributively implemented for handling quality of service provisioning and potential resource allocation across multiple nodes with inherent operational capability deficiencies. We employ cross-layer information exchange and convex optimization techniques to simultaneously achieve more efficient radio spectrum usage and optimal energy consumption in ad-hoc wireless networks with distributed scenarios. We consider the time-invariant additive white Gaussian noise channel and the time-varying Rayleigh fading channel to study the trade-off between the two network design objectives of achieving improved spectrum efficiency and minimizing the energy overhead in data routing paradigm. The original problem is transformed into an equivalent convex optimization problem through logarithmic processing to obtain the approximate global optimal solution. Moreover, the robustness and efficiency of the proposed framework is evaluated in large-scale set ups to provide the scalability analysis on both the employed performance objectives. The developed optimization scheme is compared with the machine learning models previously proposed in literature by employing the computational and/or time complexity metrics. Finally, the effectiveness of the proposed optimization model is substantiated through the simulation comparison results with the existing schemes in terms of various key performance parameters such as throughput, energy efficiency, and average bit errors.

Fetal Electrocardiography Extraction Based on Improved Fast Independent Components Analysis Algorithm.

Aiming at the problem that the fast independent components analysis (ICA) algorithm is sensitive to the initial value and easy to fall into local optimization, an improved fast ICA method is proposed for the extraction of fetal echocardiography (FECG) by combining the Simpson-Newton iterative and chaotic optimization algorithm to replace the traditional Newton iterative method. First, the Simpson formula is used to modify the traditional Newton method and a Simpson-Newton iterative algorithm is constructed. It shows that the Simpson-Newton iterative algorithm can significantly reduce the sensitivity of initial value selection, and has faster convergence speed. Then, combined with the Simpson-Newton method, the chaos optimization algorithm can obtain the approximate global optimal solution, which solves the problem that the traditional Newton iterative method tends to fall into local optimal and improves the separation performance of the fast ICA algorithm. Finally, based on chaos optimization, the proposed Simpson-Newton iterative fast ICA algorithm is applied to the extraction of FECG signals, and the extraction effect is evaluated by visual waveform and quantitative indicators. Furthermore, the algorithm is verified by different clinical signals. The experimental results show that the improved fast ICA algorithm can extract clear fetal heart signals, and there are almost no mixed maternal ECG signals in the extracted FECG signals. The extraction effect of the proposed method is thus optimal than that of the traditional fast ICA method.

Buckling surrogate-based optimization framework for hierarchical stiffened composite shells by enhanced variance reduction method

The surrogate-based optimization of hierarchical stiffened composite shells against buckling is a typical multimodal and multivariables optimization problem. To improve the computational efficiency and global optimizing ability of the surrogate-based optimization of hierarchical stiffened composite shells, an enhanced variance reduction method based on Latinized partially stratified sampling and multifidelity analysis methods is proposed in this paper and then integrated into the surrogate-based optimization framework. In the offline step of the optimization framework, candidate pairing strategies of design variables are generated by Latinized partially stratified sampling and compared by performing priori optimizations based on the low-fidelity analysis method, and the optimal pairing strategy is therefore determined. On the basis of the optimal pairing strategy, the surrogate-based optimization is carried out using the high-fidelity analysis method in the online step. With less computational cost in the offline step, the proposed enhanced variance reduction method overcomes the limitation of Latinized partially stratified sampling that the optimal pairing strategy is not obvious in complex problems. Then, extensive optimization examples are carried out to verify the efficiency and effectiveness of the proposed optimization framework. Given an approximate computational cost, the optimal buckling result of the proposed framework using enhanced variance reduction method increases by 18.2% than that of the traditional framework based on Latin hypercube sampling. In particular, the advantage of enhanced variance reduction method in the space-filling ability is highlighted in comparison to Latin hypercube sampling. When achieving an approximate global optimal solution, the proposed framework reduces the total computational cost by 76.3% than the traditional framework. Finally, the numerical implementation of asymptotic homogenization method is used herein for the accurate prediction of effective stiffness coefficients of the initial design and optimal results. Through comparison, it is concluded that the high axial stiffness and bending stiffness are the main mechanism for the high load-carrying capacity of optimal results.

Application of Fuzzy Controller Based on Chaos Optimal Design

It is difficult to tune parameters of fuzzy controller (FC), and control rules and membership functions of FC are hard to obtain optimization too.Therefore, the control results show strong overshoot and oscillation often.The authors propose a chaos optimal design method based on annealing strategy.According to random and ergodic features of chaos dynamics, the chaotic variables are applied to searching for parameters of FC, the optimal variables are transformed into chaotic variables by carrier-wave, the global search process is done using ergodic features of chaotic motion, and then an approximate global optimal solution is obtained. After that, the chaos local searching and optimization based on annealing strategy is cited, the parameters are optimized again within the limits of the approximate global optimal solution, which is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value.Finally, simulations of third order and nonlinear system show that control result of the method is good.

Fuzzy linearization strategy for multiple objective linear fractional programming with binary utility functions

This paper integrates fuzzy linearization strategy, goal programming, a membership function and conditional control mechanisms to produce a novel method to deal with the binary behavior of multiple objective fractional programming problems and multiple objective fractional programming problems with a utility function. The major contributions of the proposed method are twofold. (1) The binary behavior of multiple objective fractional programming problems can easily be converted into a linearized program using the proposed fuzzy linearization strategy. The linearized program can easily be solved, using commercial linear programming packages, yielding an approximate global optimal solution, and (2) The utility function is also used to ensure that the qualification requirements for a multiple objective fractional programming problem are met, in contrast to most past mathematical approaches, which only use quantitative approaches to deal with such a problem. In addition, an illustrative example and a practical real case are provided to demonstrate the usefulness of the proposed model. The discussion of the practical problem will help decision makers to realize the usefulness of a utility function and the binary behavior in multiple objective fractional programming problems.

Optimal Load Shedding in Electricity Grids with Renewable Sources via Message Passing

The increased penetration of volatile and intermittent renewable energy sources challenges existing power-distribution methods as current dispatch methods were not designed to consider high levels of volatility. We suggest a principled algorithm called message passing, which complements existing techniques. It is based on statistical physics methodology and passes probabilistic messages locally to find the approximate global optimal solution for a given objective function. The computational complexity of the algorithm increases linearly with the system size, allowing one to solve large-scale problems. We show how message passing considers fluctuations effectively and prioritise consumers in the event of insufficient resource. We demonstrate the efficacy of the algorithm in managing load-shedding and power-distribution on synthetic benchmark IEEE data and discuss the role of weights in the trade-off between minimising load-shedding and transmission costs.

An improved particle swarm-ant colony hybrid algorithm for HMM training

The traditional parameter estimation methods of Hidden Markov Models (HMM) are easy to fall into local optimum, have higher requirements for initial parameter values and might result in over-coupling phenomena. In order to improve the robustness and identification performance of the model, a novel HMM parameter training method based on an improved particle swarm-ant colony algorithm (IPSAA) is presented. First, extremum disturbance is added into particle swarm optimisation algorithm (PSO) and parameters of ant colony algorithm (ACA) such as stimulating factor, volatilisation coefficients and pheromone are all improved adaptively. Second, the fitness function values of particles' history optimal solutions after PSO coarse search are used to adjust the initial pheromone distribution in fine search of ACA. Finally, Baum-Welch algorithm (B-W) is adopted to locally modify the approximate global optimal solution. The new algorithm not only solves the BW dependency on initial values and the trapped local optimum problem, but also makes full use of the global search ability of IPSAA and local development ability of B-W. The experimental results show that the system using the new algorithm is more efficient, more stable, and has better classification performance than that of traditional HMM training algorithm.

Emission path planning based on dynamic abatement cost curve

Global climate change is one of the most serious environmental problems that has attracted an unprecedented global attention. The scientific community has recognized that human activity is mostly responsible for global climate warming. Therefore, states participating in the United Nations Framework Convention on Climate Change (UNFCCC) have initiated a series of negotiations on how to develop their own emission reduction targets. However, the realization of these targets is at the expense of economic development to a great extent. Therefore, an abatement plan is necessary to decide how and when to implement emission reduction targets. A marginal abatement cost curve (MACC), often used as an important quantitative tool to estimate abatement burden or evaluate abatement performance, should be considered carefully. In this paper, we enrich the traditional MACC by introducing the concept of an “immediate unit marginal abatement cost” to describe its intrinsic incremental abatement difficulty. This cost is proved to be agreed with the actual situation in many ways, and is therefore very suitable for practical use. Two-factor learning curve are considered in the model, which can go some way in improving the performance of the revised MACC. Using a parameterization method, the original problem can be converted into a tractable nonlinear programming problem. We use an algorithm to search for the approximate global optimal solution. The effectiveness and the efficiency of the algorithm are discussed respectively. In the results, we find that the abatement path distinguishes largely under different abatement targets. Some plausible reasons and policy advices are given.

Optimal Control for a Cooperative Rendezvous Between Two Spacecraft from Determined Orbits

The mathematical model of a far-distance cooperative rendezvous between two spacecraft in a non-Keplerian orbit was established. Approximate global optimization was performed by a type of hybrid algorithm consisting of particle swarm optimization and differential evolution. In this process, the double-fitness function was established according to the objective function and the constraints; the double-fitness function was used to enable a better choice between the solutions obtained by the two algorithms at every iteration. In addition, the costate variables obtained were set as the initial values of the sequential quadratic programming to greatly increase the possibility of finding the approximate global optimal solution. After performing the calculations and simulations, it was concluded that the fuel required for orbiting was not influenced by the initial positions of the two spacecraft if the initial orbits of the two spacecraft were determined. However, the time consumption is strongly influenced in this situation.

Optimal distribution in smart grids with volatile renewable sources using a message passing algorithm

The design of future electricity grids will allow for renewable energy generators to be effectively incorporated into the network. Current methods of economic dispatch were not designed to accommodate the level of volatility and uncertain nature of sources such as wind and solar; here we demonstrate how an optimisation algorithm called message passing, which is based on principled statistical physics methodologies and is inherently probabilistic, could be an alternative way of considering source volatility efficiently and reliably. The algorithm iteratively passes probabilistic messages in order to find an approximate global optimal solution with moderate computational complexity and inherently consider source volatility. We demonstrate the capabilities of message passing as a distribution algorithm in the presence of uncertainty on synthetic benchmark IEEE networks and show how the volatility increase effects distribution costs

A criterion for an approximation global optimal solution based on the filled functions

In this paper, a new definition of the filled function is given. Based on the new definition, a new class of filled functions is constructed, and the properties of the new filled functions are analysed and discussed. Moreover, according to the new class of filled functions, a criterion is given to decide whether the point we have obtained is an approximate global optimal solution. Finally, a global optimization algorithm based on the new class of filled functions is presented. The implementation of the algorithm on several test problems is reported with numerical results.

Neural fuzzy inference systems with knowledge-based cultural differential evolution for nonlinear system control

This study proposes a knowledge-based cultural differential evolution (KCDE) method for neural fuzzy inference systems (NFIS). Cultural algorithms acquire the belief space from the evolving population space and then exploit that information to guide the search. The proposed KCDE method adopts the mutation strategies of differential evolution as knowledge sources to influence the population space. The proposed KCDE method uses these knowledge sources, including normative knowledge, situational knowledge, domain knowledge, history knowledge, and topographic knowledge, to optimize the parameters of the NFIS model to avoid falling in a local optimal solution and to ensure the searching capacity of approximate global optimal solution. Experimental results demonstrate that the proposed NFIS-KCDE method performs well in nonlinear system control problems.

A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model

In order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a compensatory DEA model for ranking all units, point out the existing problem for solving the model, and present an improved algorithm for which an approximate global optimal solution of the model can be obtained by solving a sequence of linear programming. Then, we applied the key idea of the compensatory DEA model to develop the MOP model in which the objectives are to simultaneously maximize all common weights under constraints that the sum of efficiency values of all DMUs is equal to unity and the sum of all common weights is also equal to unity. In order to solve the MOP model, we transform it into a single objective programming (SOP) model using a fuzzy programming method and solve the SOP model using the proposed approximation algorithm. To illustrate the ranking method using the proposed method, two numerical examples are solved.

Optimal switching between autonomous subsystems

A novel scheme is presented for solving the problem of optimal switching with nonlinear autonomous subsystems. This scheme determines the approximate global optimal solution for different initial conditions in a feedback form. Restrictions, including the need to enforce a mode sequence and/or a number of switching, do not exist for the developed method. Performance is evaluated in several examples with different complexities and the numerical simulation shows great promises for the controller.

Hybrid Feature Selection Based on Improved GA for the Intrusion Detection System

High dimensionality is one of the most troublesome difficulties encountered in intrusion detection system analysis and application. For high dimension data, feature selection not only can improve the accuracy and efficiency of classification, but also discover informative subset. Combining Filter type and Wrapper type characteristics, this paper proposes a hybrid type method for feature selection using a improved genetic algorithm contained reward and punishment mechanism. The mechanism can guarantee this algorithm rapid convergence on approximate global optimal solution. According to the experimental results, this algorithm performs well and it's time complexity is low. Keywords: intrusion detection system; genetic algorithm(GA); Feature selection; Mutual information; hybrid type