Bounded lower subdifferentiability optimization techniques : applications

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have "flat parts". We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an algorithm to mathematical programming problems inwhich the objective function is derived from economic systems and location problems are described. Computational results are presented.

Sample subset optimization for classifying imbalanced biological data

Data in many biological problems are often compounded by imbalanced class distribution. That is, the positive examples may largely outnumbered by the negative examples. Many classification algorithms such as support vector machine (SVM) are sensitive to data with imbalanced class distribution, and result in a suboptimal classification. It is desirable to compensate the imbalance effect in model training for more accurate classification. In this study, we propose a sample subset optimization technique for classifying biological data with moderate and extremely high imbalanced class distributions. By using this optimization technique with an ensemble of SVMs, we build multiple roughly balanced SVM base classifiers, each trained on an optimized sample subset. The experimental results demonstrate that the ensemble of SVMs created by our sample subset optimization technique can achieve higher area under the ROC curve (AUC) value than popular sampling approaches such as random over-/under-sampling; SMOTE sampling, and those in widely used ensemble approaches such as bagging and boosting.

A GA-PSO layered encoding evolutionary approach to 0/1 knapsack optimization

This paper presents a layered encoding cascade evolutionary approach to solve a 0/1 knapsack optimization problem. A layered encoding structure is proposed and developed based on the schema theorem and the concepts of cascade correlation and multi-population evolutionary algorithms. Genetic algorithm (GA) and particle swarm optimization (PSO) are combined with the proposed layered encoding structure to form a generic optimization model denoted as LGAPSO. In order to enhance the finding of both local and global optimum in the evolutionary search, the model adopts hill climbing evaluation criteria, feature of strength Pareto evolutionary approach (SPEA) as well as nondominated spread lengthen criteria. Four different sizes benchmark knapsack problems are studied using the proposed LGAPSO model. The performance of LGAPSO is compared to that of the ordinary multi-objective optimizers such as VEGA, NSGA, NPGA and SPEA. The proposed LGAPSO model is shown to be efficient in improving the search of knapsack’s optimum, capable of gaining better Pareto trade-off front.

Building monotonicity-preserving fuzzy inference models with optimization-based similarity reasoning and a monotonicity index

In this paper, a novel approach to building a Fuzzy Inference System (FIS) that preserves the monotonicity property is proposed. A new fuzzy re-labeling technique to re-label the consequents of fuzzy rules in the database (before the Similarity Reasoning process) and a monotonicity index for use in FIS modeling are introduced. The proposed approach is able to overcome several restrictions in our previous work that uses mathematical conditions in building monotonicity-preserving FIS models. Here, we show that the proposed approach is applicable to different FIS models, which include the zero-order Sugeno FIS and Mamdani models. Besides, the proposed approach can be extended to undertake problems related to the local monotonicity property of FIS models. A number of examples to demonstrate the usefulness of the proposed approach are presented. The results indicate the usefulness of the proposed approach in constructing monotonicity-preserving FIS models.

A cascade genetic algorithm and particle swarm approach for solving unit commitment and economic dispatch problems

Positive Unit commitment and economic dispatch are two important decisions in thermal power generation scheduling. The tasks involve determination and allocation of power generation to thermal units that minimize the total power generation cost and satisfy the production constraints.This paper presents a cascade Genetic Algorithm and Particle Swarm Optimization (GA-PSO) approach for solving thermal power generation scheduling based on a layered matrix encoding structure.The proposed hybrid method is compared to layered matrix encoding GA using the thermal power generation problem given in Williams [1] to demonstrate its effectiveness in generating an optimal, cost-effective power generation schedule.The results showed that cascade GA-PSO outperformed the layered matrix encoding GA in minimizing the total power production cost for unit commitment and power dispatch problems.

Pseudoconvex proximal splitting for L∞problems in multiview geometry

In this paper we study optimization methods for minimizing large-scale pseudoconvex L∞problems in multiview geometry. We present a novel algorithm for solving this class of problem based on proximal splitting methods. We provide a brief derivation of the proposed method along with a general convergence analysis. The resulting meta-algorithm requires very little effort in terms of implementation and instead makes use of existing advanced solvers for non-linear optimization. Preliminary experiments on a number of real image datasets indicate that the proposed method experimentally matches or outperforms current state-of-the-art solvers for this class of problems.

An accelerated particle swarm optimization based levenberg marquardt back propagation algorithm

The Levenberg Marquardt (LM) algorithm is one of the most effective algorithms in speeding up the convergence rate of the Artificial Neural Networks (ANN) with Multilayer Perceptron (MLP) architectures. However, the LM algorithm suffers the problem of local minimum entrapment. Therefore, we introduce several improvements to the Levenberg Marquardt algorithm by training the ANNs with meta-heuristic nature inspired algorithm. This paper proposes a hybrid technique Accelerated Particle Swarm Optimization using Levenberg Marquardt (APSO_LM) to achieve faster convergence rate and to avoid local minima problem. These techniques are chosen since they provide faster training for solving pattern recognition problems using the numerical optimization technique.The performances of the proposed algorithm is evaluated using some bench mark of classification’s datasets. The results are compared with Artificial Bee Colony (ABC) Algorithm using Back Propagation Neural Network (BPNN) algorithm and other hybrid variants. Based on the experimental result, the proposed algorithms APSO_LM successfully demonstrated better performance as compared to other existing algorithms in terms of convergence speed and Mean Squared Error (MSE) by introducing the error and accuracy in network convergence.

A new physarum-based hybrid optimization algorithm for solving 0/1 knapsack problem

As a typical NP-complete problem, 0/1 Knapsack Problem (KP), has been widely applied in many domains for solving practical problems. Although ant colony optimization (ACO) algorithms can obtain approximate solutions to 0/1 KP, there exist some shortcomings such as the low convergence rate, premature convergence and weak robustness. In order to get rid of the above-mentioned shortcomings, this paper proposes a new kind of Physarum-based hybrid optimization algorithm, denoted as PM-ACO, based on the critical paths reserved by Physarum-inspired mathematical (PM) model. By releasing additional pheromone to items that are on the important pipelines of PM model, PM-ACO algorithms can enhance item pheromone matrix and realize a positive feedback process of updating item pheromone. The experimental results in two different datasets show that PM-ACO algorithms have a stronger robustness and a higher convergence rate compared with traditional ACO algorithms.

Linear optimization for ecological indices based on aggregation functions

We consider an optimization problem in ecology where our objective is to maximize biodiversity with respect to different land-use allocations. As it turns out, the main problem can be framed as learning the weights of a weighted arithmetic mean where the objective is the geometric mean of its outputs. We propose methods for approximating solutions to this and similar problems, which are non-linear by nature, using linear and bilevel techniques.