Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm

Traditional multiobjective evolutionary algorithms (MOEAs) consider multiple objectives as a whole when solving multiobjective optimization problems (MOPs). However, this consideration may cause difficulty to assign fitness to individuals because different objectives often conflict with each other. In order to avoid this difficulty, this paper proposes a novel coevolutionary technique named multiple populations for multiple objectives (MPMO) when developing MOEAs. The novelty of MPMO is that it provides a simple and straightforward way to solve MOPs by letting each population correspond with only one objective. This way, the fitness assignment problem can be addressed because the individuals' fitness in each population can be assigned by the corresponding objective. MPMO is a general technique that each population can use existing optimization algorithms. In this paper, particle swarm optimization (PSO) is adopted for each population, and coevolutionary multiswarm PSO (CMPSO) is developed based on the MPMO technique. Furthermore, CMPSO is novel and effective by using an external shared archive for different populations to exchange search information and by using two novel designs to enhance the performance. One design is to modify the velocity update equation to use the search information found by different populations to approximate the whole Pareto front (PF) fast. The other design is to use an elitist learning strategy for the archive update to bring in diversity to avoid local PFs. CMPSO is comprehensively tested on different sets of benchmark problems with different characteristics and is compared with some state-of-the-art algorithms. The results show that CMPSO has superior performance in solving these different sets of MOPs.

Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems

This work presents a multi-objective optimization method based on the artificial bee colony, called the MOABC, for optimizing problems with multiple objectives. The MOABC uses a grid-based approach to adaptively assess the Pareto front maintained in an external archive. The external archive is used to control the flying behaviours of the individuals and structuring the bee colony. The employed bees adjust their trajectories based on the non-dominated solutions maintained in the external archive. On the other hand, the onlooker bees select the food sources advertised by the employed bees to update their positions. The qualities of these food sources are computed based on the Pareto dominance notion. The scout bees are used by the MOABC to get rid of food sources with poor qualities. The proposed algorithm was evaluated on a set of standard test problems in comparison with other state-of-the-art algorithms. Experimental results indicate that the proposed approach is competitive compared to other algorithms considered in this work.

A multi-objective artificial bee colony algorithm

An important consideration of multiobjective optimization (MOO) is the quantitative metrics used for defining the optimality of different solution sets, which is also the basic principle for the design and evaluation of MOO algorithms. Although a plethora of performance metrics have been proposed in the MOO context, there has been a lack of insights on the relationships between metrics. In this paper, we first group the major MOO metrics proposed to date according to four core performance criteria considered in the literature, namely, capacity, convergence, diversity, and convergence-diversity. Then, a comprehensive study is conducted to investigate the relationships among representative group metrics, including generational distance, E-indicator (I
 1
 ∈+
), spread (Δ), generalized spread (Δ*), inverted generational distance, and hypervolume. Experimental results indicated that these six metrics show high consistencies when Pareto fronts (PFs) are convex, whereas they show certain contradictions on concave PFs.

Consistencies and contradictions of performance metrics in multiobjective optimization.

A new variant of particle swarm optimization (PSO), named phase angle-encoded and quantum-behaved particle swarm optimization (θ-QPSO), is proposed. Six versions of θ-QPSO using different mappings are presented and compared through their application to solve continuous function optimization problems. Several representative benchmark functions are selected as testing functions. The real-valued genetic algorithm (GA), differential evolution (DE), standard particle swarm optimization (PSO), phase angle-encoded particle swarm optimization ( θ-PSO), quantum-behaved particle swarm optimization (QPSO), and θ-QPSO are tested and compared with each other on the selected unimodal and multimodal functions. To corroborate the results obtained on the benchmark functions, a new route planner for unmanned aerial vehicle (UAV) is designed to generate a safe and flyable path in the presence of different threat environments based on the θ-QPSO algorithm. The PSO, θ-PSO, and QPSO are presented and compared with the θ-QPSO algorithm as well as GA and DE through the UAV path planning application. Each particle in swarm represents a potential path in search space. To prune the search space, constraints are incorporated into the pre-specified cost function, which is used to evaluate whether a particle is good or not. Experimental results demonstrated good performance of the θ-QPSO in planning a safe and flyable path for UAV when compared with the GA, DE, and three other PSO-based algorithms.

Phase Angle-Encoded and Quantum-Behaved Particle Swarm Optimization Applied to Three-Dimensional Route Planning for UAV

A multiple-swarm multiobjective particle swarm optimization (PSO) algorithm, named dynamic multiple swarms in multiobjective PSO, is proposed in which the number of swarms is adaptively adjusted throughout the search process via the proposed dynamic swarm strategy. The strategy allocates an appropriate number of swarms as required to support convergence and diversity criteria among the swarms. Additional novel designs include a PSO updating mechanism to better manage the communication within a swarm and among swarms and an objective space compression and expansion strategy to progressively exploit the objective space during the search process. Comparative study shows that the performance of the proposed algorithm is competitive in comparison to the selected algorithms on standard benchmark problems. In particular, when dealing with test problems with multiple local Pareto fronts, the proposed algorithm is much less computationally demanding. Sensitivity analysis indicates that the proposed algorithm is insensitive to most of the user-specified design parameters.

Dynamic Multiple Swarms in Multiobjective Particle Swarm Optimization

Fault classification based upon vibration measurements is an essential building block of a conditional based health usage monitoring system. Multiple sensors are incorporated to assure the redundancy and to achieve the desired reliability and accuracy. The shortcoming of using multiple sensors is the need to deal with a high dimensional feature set, a computationally expensive task in classification. It is vital to reduce the feature dimension via an effective feature extraction and feature selection algorithm. A simple wavelet based feature selection scheme is proposed herein, uniquely built by local discriminant bases and genetic optimization. This scheme overcomes the disadvantages faced by the existing feature selection methods by producing a generic feature set, reducing the dimensionality of features, and requiring no prior information of the problem domain. The proposed feature selection scheme is based upon the strategy of "divide and conquer" that significantly reduce the computation time without compromising the classification performance. The simulation results show the proposed feature selection scheme provides at least 65% reduction of the total number of features at no cost of the classification accuracy.

Fault classification on vibration data with wavelet based feature selection scheme.

In this article, the authors propose a particle swarm optimization PSO for constrained optimization. The proposed PSO adopts a multiobjective approach to constraint handling. Procedures to update the feasible and infeasible personal best are designed to encourage finding feasible regions and convergence toward the Pareto front. In addition, the infeasible nondominated solutions are stored in the global best archive to exploit the hidden information for guiding the particles toward feasible regions. Furthermore, the number of feasible personal best in the personal best memory and the scalar constraint violations of personal best and global best are used to adapt the acceleration constants in the PSO flight equations. The purpose is to find more feasible particles and search for better solutions during the process. The mutation procedure is applied to encourage global and fine-tune local searches. The simulation results indicate that the proposed constrained PSO is highly competitive, achieving promising performance.

Constraint Handling in Particle Swarm Optimization

In this paper, the proposed constrained multiobejctive particle swarm optimization (MOPSO) adopts the multiobjective constraint handling framework and includes the following design features: An infeasible global best archive to guide the infeasible particles towards feasible region(s); procedures to update the personal best archive are designed to encourage finding feasible regions and convergence towards the Pareto front; acceleration constants in the particle swarm optimization equation are adjusted during the search process to encourage finding more feasible particles or to search for better solutions; and mutation operators are adopted to encourage global and local searches. The simulation results indicate that the proposed algorithm is highly competitive in solving the benchmark problems.

Constraint handling procedure for multiobjective particle swarm optimization

Generally, constraint-handling techniques are designed for evolutionary algorithms to solve Constrained Multiobjective Optimization Problems (CMOPs). Most Multiojective Particle Swarm Optimization (MOPSO) designs adopt these existing constraint-handling techniques to deal with CMOPs. In this chapter, the authors present a constrained MOPSO in which the information related to particles’ infeasibility and feasibility status is utilized effectively to guide the particles to search for feasible solutions and to improve the quality of the optimal solution found. The updating of personal best archive is based on the particles’ Pareto ranks and their constraint violations. The infeasible global best archive is adopted to store infeasible nondominated solutions. The acceleration constants are adjusted depending on the personal bests’ and selected global bests’ infeasibility and feasibility statuses. The personal bests’ feasibility statuses are integrated to estimate the mutation rate in the mutation procedure. The simulation results indicate that the proposed constrained MOPSO is highly competitive in solving selected benchmark problems.

Wen Fung Leong

Papers

Dynamic Multiple Swarms in Multiobjective Particle Swarm Optimization

Fault classification on vibration data with wavelet based feature selection scheme.

Constraint Handling in Particle Swarm Optimization

Constraint handling procedure for multiobjective particle swarm optimization

A Particle Swarm Optimizer for Constrained Multiobjective Optimization