Optimizing Decision Trees Using Multi-objective Particle Swarm Optimization

In this paper, a multi-objective particle swarm optimization algorithm based on the relative distance strategy is proposed to realize hydrodynamic coefficient identification, which can improve the accuracy of parameter identification without determining the weight manually. Firstly, single-objective particle swarm optimization (PSO) is used to identify the parameters of the model with a low coupling degree. Then, the parameters of the strongly coupled sway and yaw motion model are regarded as multi-objective, and a set of unbiased Pareto optimal solutions are obtained by the multi-objective particle swarm optimization (MOPSO) algorithm. Then the distance function of the Pareto solution is constructed to determine the parametric solution of the model. Finally, experimental identification is carried out by using the data set collected from the real ship. Experimental results show that the accuracy of model parameters obtained by this identification method is about 91.6%, and there is no need to set the weighting coefficient.

In this paper, a multi-objective hybrid firefly and particle swarm optimization (MOHFPSO) was proposed for different multi-objective optimal power flow (MOOPF) problems. Optimal power flow (OPF) was formulated as a non-linear problem with various objectives and constraints. Pareto optimal front was obtained by using non-dominated sorting and crowding distance methods. Finally, an optimal compromised solution was selected from the Pareto optimal set by applying an ideal distance minimization method. The efficiency of the proposed MOHFPSO technique was tested on standard IEEE 30-bus and IEEE 57-bus test systems with various conflicting objectives. Simulation results were also compared with non-dominated sorting based multi-objective particle swarm optimization (MOPSO) and different optimization algorithms reported in the current literature. The achieved results revealed the potential of the proposed algorithm for MOOPF problems.

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

An integrated optimization strategy based on Kriging model and multi-objective particle swarm optimization (PSO) algorithm was constructed. As a new surrogate model technology, Kriging model has better fitting precision for nonlinear problem. The Kriging model was adopted to replace computer aided engineering (CAE) simulation as fitness function of multi-objective PSO algorithm, and the computation cost can be reduced greatly. By introducing multi-objective handling mechanism of crowding distance and mutation operator to multi-objective PSO algorithm, the entire Pareto front can be approximated better. It is shown that the multi-objective optimization strategy can get higher solving accuracy and computation efficiency under small sample.

This paper addresses a multi-objective approach for simultaneous dynamic expansion planning of conventional sub-transmission grid and Regional Virtual Power Plant (RVPP). In such a feed-in tariff electricity market, it will assist RVVP’s stakeholders in deciding whether or not they should invest in new equipment’s installation. A Multi-Objective Particle Swarm Optimization (MOPSO) algorithm as a heuristic optimization method is proposed to eliminate the conventional centralized planning, which has led to competition between Regional Electric Company (REC) and RVPP for power delivery in sub-transmission system. Two objective functions are considered for simultaneous expansion planning of these two systems. The first one takes the minimum cost of the REC, as the sub-transmission grid operator, into account while the other one considers profit maximization for RVPP. To achieve the goals, MOPSO algorithm is employed to find the best expansion of REC and best location and capacity of RVPP’s resources. Having solved the proposed multi-objective optimization problem, a Pareto front is determined to show the trade-off between REC and RVPPs' contributions in joint optimal expansion planning of conventional sub-transmission grid and the RVPP. To demonstrate the applicability and effectiveness of the proposed approach, a realistic sub-transmission system in Guilan Province, Iran is used as a test system, and the results are evaluated accordingly.

Multi-objective particle swarm optimization model for conjunctive use of treated wastewater and groundwater

This paper is concerned with fuzzy tracking control optimized via multi-objective particle swarm optimization for stable walking of biped robots. To present an optimal control approach, multi-objective particle swarm optimization is used to design the parameters of the control method in comparison to three effectual multi-objective optimization algorithms in the literature. In particle swarm optimization, a dynamic elimination technique is utilized as a novel approach to prune the archive effectively. Moreover, a turbulence operator is used to skip the local optima and the personal best position of each particle is determined by making use of the Sigma method. Normalized summation of angles errors and normalized summation of control efforts are two conflicting objective functions addressed by dint of multi-objective optimization algorithms in the present investigation. By contrasting the Pareto front of multi-objective particle swarm optimization with the Pareto fronts of other methods, it is illustrated that multi-objective particle swarm optimization performs with high accuracy, convergence and diversity of solutions in the design of fuzzy tracking control for nonlinear dynamics of biped robots. Finally, the proper performance of the proposed controller is demonstrated by the results presenting an appropriate tracking system and optimal control inputs. Indeed, the appropriate tracking system and optimal control inputs prove the efficiency of optimal fuzzy tracking control in dealing with the nonlinear dynamics of biped robots.

Inverse analysis using particle swarm optimization for detecting corrosion profile of rebar in concrete structure

The steam turbine control system is strongly non-linear in all operating conditions. Proportional-Integral-Derivative (PID) controller that is currently used in control systems of many types of equipment is not considered highly precision for turbine speed control system. A fine tuning of the PID controller by some optimization technique is a desired objective to maintain the precise speed of the turbine in a wide range of operating conditions. This Paper evaluates the feasibility of the use of Particle Swarm Optimization (PSO) method for determining the optimal Proportional-Integral-Derivative (PID) controller parameters for steam turbine control. The turbine speed control is modelled in SimulinkTM with PID controller and the PSO algorithm is implemented in MATLAB to optimize the PID function. The PSO optimization technique is also compared with Genetic Algorithm (GA) and it is validated that PSO based controller is more efficient in reducing the steady-states error; settling time, rise time, and overshoot limit in speed control of the steam turbine control.

Nature is a wonderful source of inspiration for building models and techniques for solving difficult problems in design, optimisation, and control. More specifically, the study of evolution, the human immune system, and the collective behaviour of insects/birds have guided the origin of evolutionary algorithms, artificial immune systems, and optimisation techniques based on swarm intelligence, respectively. In this chapter, we present the use of particle swarm optimisation (PSO) and the Taguchi method for the identification of optimised fuzzy models from the available data. PSO is a member of the broad category of swarm intelligence (SI) techniques based on the metaphor of social interaction. It has been used for finding promising solutions in complex search spaces through the interaction of particles in a swarm, and is especially useful when dealingwith a high number of dimensions and situations where problem-specific information is not available. However, caution needs to be exercised in selecting PSO, as the performance of PSO largely depends on their values. In this chapter, a systematic reasoning approach based on the Taguchi method is also presented to quickly identify PSO parameters. The Taguchi method is a robust design approach that helps in optimisation, and which requires relatively few experiments. Although we focus here on the use of PSO and the Taguchi method for fuzzy model identification, these techniques have much broader use and application. In order to validate our approach, data from the rapid Nickel-Cadmium (Ni-Cd) battery charger developed by the authors were used. The results are based on real data and illustrate the viability and efficiency of the approach.Request access from your librarian to read this chapter's full text.

The optimal placement of Thyristor Controlled Series Compensators (TCSCs) in transmission systems is formulated as a multi-objective optimization problem with the objective of maximizing transmission system loadability, minimizing transmission loss and minimizing the cost of TCSCs. The thermal limits of transmission lines and voltage limits of load buses are considered as security constraints. Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Comprehensive Learning Particle Swarm Optimizer (MOCLPSO) are applied to solve this problem. The proposed approach has been successfully tested on IEEE 14 bus system and IEEE 118 bus system. From the results it is inferred that MOCLPSO can obtain an evenly distributed pareto front. A multi-criterion decision-making tool, known as TOPSIS, has been employed to arrive at the best trade-off solution.

State-of-the-art decision tree methods apply heuristics recursively to create each split in isolation, which may not capture well the underlying characteristics of the dataset. The optimal decision tree problem attempts to resolve this by creating the entire decision tree at once to achieve global optimality. In the last 25?years, algorithmic advances in integer optimization coupled with hardware improvements have resulted in an astonishing 800 billion factor speedup in mixed-integer optimization (MIO). Motivated by this speedup, we present optimal classification trees, a novel formulation of the decision tree problem using modern MIO techniques that yields the optimal decision tree for axes-aligned splits. We also show the richness of this MIO formulation by adapting it to give optimal classification trees with hyperplanes that generates optimal decision trees with multivariate splits. Synthetic tests demonstrate that these methods recover the true decision tree more closely than heuristics, refuting the notion that optimal methods overfit the training data. We comprehensively benchmark these methods on a sample of 53 datasets from the UCI machine learning repository. We establish that these MIO methods are practically solvable on real-world datasets with sizes in the 1000s, and give average absolute improvements in out-of-sample accuracy over CART of 1---2 and 3---5% for the univariate and multivariate cases, respectively. Furthermore, we identify that optimal classification trees are likely to outperform CART by 1.2---1.3% in situations where the CART accuracy is high and we have sufficient training data, while the multivariate version outperforms CART by 4---7% when the CART accuracy or dimension of the dataset is low.

To overcome the defect of wide-ranged exploration for particle swarm optimization, a kind of multi-objective particle swarm optimization algorithm with disturbance operation(MPSOD) is proposed. It employs particle swarm optimization and disturbance operation to generate new population in order to enhance the wide-ranged exploration for particle swarm optimization algorithm. Numerical experiments are compared with NSGA-II, SPEA2 and MOPSO on six benchmark problems. The numerical results show the effectiveness of the proposed MPSOD algorithm.Keywordsmulti-objective optimizationparticle swarm optimizationdisturbance operation

Particle Swarm Optimization for the design of H∞ static output feedbacks

A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification