Problems encountered in fields like scheduling, assignment, vehicle routing are mostly NPhard. These problems need efficient solution procedures. If confronted with an NP-hard problem, one may have three ways to go: one chooses to apply an enumerative method that yields an optimum solution, or apply an approximation algorithm that runs in polynomial time, or one resorts to some type of heuristic technique without any a priori guarantee for quality of solution and time of computing (Aarts & Lenstra, 2003). Heuristics fall under the general heading of local search approaches. Hence, local search techniques are widely used to find “close-to-optimum” solutions to these problems in a “reasonable” amount of time. Tabu search (TS) is one of the most efficient heuristic techniques in the sense that it finds quality solutions in relatively short running time. This chapter will provide a basic description of TS giving insights for novice readers as well as introduce application areas and provide comparisons of TS to other meta-heuristic procedures for the readers with more experience on local search procedures. The chapter will be organized as follows: The second section is going to introduce the basic terminology. For example, definitions for global optimization, local search, heuristics, and meta-heuristics will be provided. The section will also provide brief descriptions of TS as well as the following meta-heuristics to which TS will be compared: simulated annealing (SA), genetic algorithms (GA), ant colony optimization (ACO), greedy randomized adaptive search procedure (GRASP), and particle swarm optimization (PSO). Second section is intended to give the readers a good overall view of the “local search” area and let them know that TS will be compared to several other meta-heuristic procedures. In the third section, basic steps of TS, SA, GA, ACO, GRASP and PSO will be described. As the mechanisms of these procedures are explained, differences and similarities between TS and each of the other procedures will be pointed out. Section three will familiarize the readers with the various meta-heuristic procedures that will be discussed throughout the chapter. The fourth section will be dedicated to identifying the different problems for which TS was used to generate solutions. For example; TS has been used to solve scheduling problems, routing problems, and assignment problems. We will try to generate a comprehensive list of the problems to which TS has been applied. This section will provide the reader with an understanding of how TS has been used. In the fifth section, efficiency and effectiveness of TS will be compared to other metaheuristic procedures. Reasons why TS is more efficient and/or effective than some of the O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

/pdf/tabu-search-a-comparative-study-3wypbvwmqj.pdf

Tabu Search: A Comparative Study

In many diagnostic imaging settings, including positron emission tomography (PET), images are typically used for multiple tasks such as detecting disease and quantifying disease. Unlike conventional image reconstruction that optimizes a single objective, this work proposes a multi-objective optimization algorithm for PET image reconstruction to identify a set of images that are optimal for more than one task. This work is reliant on a genetic algorithm to evolve a set of solutions that satisfies two distinct objectives. In this paper, we defined the objectives as the commonly used Poisson log-likelihood function, typically reflective of quantitative accuracy, and a variant of the generalized scan-statistic model, to reflect detection performance. The genetic algorithm uses new mutation and crossover operations at each iteration. After each iteration, the child population is selected with non-dominated sorting to identify the set of solutions along the dominant front or fronts. After multiple iterations, these fronts approach a single non-dominated optimal front, defined as the set of PET images for which none the objective function values can be improved without reducing the opposing objective function. This method was applied to simulated 2D PET data of the heart and liver with hot features. We compared this approach to conventional, single-objective approaches for trading off performance: maximum likelihood estimation with increasing explicit regularization and maximum a posteriori estimation with varying penalty strength. Results demonstrate that the proposed method generates solutions with comparable to improved objective function values compared to the conventional approaches for trading off performance amongst different tasks. In addition, this approach identifies a diverse set of solutions in the multi-objective function space which can be challenging to estimate with single-objective formulations.

Multi-Objective Evolutionary Algorithm for PET Image Reconstruction: Concept

A fast and robust method to detect and recognize scaled and skewed road signs is proposed in this paper. In the detection stage, the input color image is first quantized in HSV color model. Border tracing those regions with the same colors as road signs is adopted to find the regions of interest (ROI). The ROIs are then automatically adjusted to fit road sign shape models so as to facilitate detection verification even for scaled and skewed road signs in complicated scenes. Moreover, the ROI adjustment and verification are both performed only on border pixels; thus, the proposed road sign detector is fast. In the recognition stage, the detected road sign is normalized first. Histogram matching based on polar mesh is then adopted to measure the similarity between the scene and model road signs to accomplish recognition. Since histogram matching is fast and has high tolerance to distortion and deformation while contextual information can still be incorporated into it in a natural and elegant way, our method has high recognition accuracy and fast execution speed. Experiment results show that the detection rate and recognition accuracy of our method can achieve 94.2p and 91.7p, respectively. On an average, it takes only 4–50 and 10 ms for detection and recognition, respectively. Thus, the proposed method is effective, yet efficient. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 28–39, 2007

Scale and skew-invariant road sign recognition

It is well-known that the problem of MEG source localization can be cast as an optimization problem. So far, there have been many works in which various optimization methods were adopted for source localization. In this paper, we compare the performance of three typical and widely used optimization techniques for a specific MEG source localization problem. We first introduce a hybrid algorithm by combining genetic and local search strategies to overcome disadvantages of conventional genetic algorithms. Second, we apply the tabu search, a widely used optimization method in combinational optimization and discrete mathematics, to source localization. To the best of our knowledge, this is the first attempt in the literature to apply tabu search to MEG/EEG source localization. Third, in order to further compare the performance of the above algorithms, simulated annealing is also applied to MEG source localization problem. The computer simulation results show that our local genetic algorithm is the most effective approach to dipole localization, and the tabu search method is also a very good strategy for this problem.

https://www.mat.univie.ac.at/~neum/glopt/mss/JiaLL03.pdf

A comparative study of global optimization approaches to meg source localization

Various fitness functions have been evaluated for image reconstruction using binary genetic algorithm (BGA) based parallel ray transmission tomography. The population initialization is carried out using the filtered backprojection (FBP) technique. Various fitness functions used for image reconstruction include: root mean squared error (RMSE), mean squared error (MSE), mean absolute error (MAE), relative squared error (RSE), root relative squared error (RRSE) and relative absolute error (RAE). RMSE and MAE outperformed for small as well as large size images with different shape complexities. Mixed selection scheme with two variations of crossover operators, namely image-row and block crossover operators have been used for crossover. Binary mutation operator has been used for creating diversity in local search scope. For 64 times 64 head and lung phantoms, BGA has resulted in PSNR values with RMSE 19.26 and 16.49 respectively and 27.20 and 29.65 dB with MAE

/pdf/fitness-function-evaluation-for-image-reconstruction-using-1y1ls9vaey.pdf

Fitness Function Evaluation for Image Reconstruction using Binary Genetic Algorithm for Parallel Ray Transmission Tomography

Image reconstruction from projections is a key problem in medical image analysis. In this paper, we cast image reconstruction from projections as a multi-objective problem. It is essential to choose some proper objective functions of the problem. We choose the square error, smoothness of the reconstructed image, and the maximum entropy as our objective functions of the problem. Then we introduce a hybrid algorithm comprising of multi-objective genetic and local search algorithms to reconstruct the image. Our algorithm has remarkable global performance. Our experiments show that we can get different results when we give different weights to different objective functions. We can also control the noise by giving different weights on different objective function. At the same time, we can adjust the parameter to let it have good local performance. Though the computation demands of the hybrid algorithm tends to be larger because of the random search of the GA, it is really a common feature of the global optimization method. Our results show that the hybrid algorithm is a more effective than the conventional method. We think our method is very promising for the medical imaging held.

Medical image reconstruction using a multi-objective genetic local search algorithm

The authors compare the performance of three typical and widely used optimization techniques for a specific MEG source localization problem. Firstly, they introduce a hybrid algorithm by combining genetic and local search strategies to overcome disadvantages of conventional genetic algorithms. Secondly, they apply the tabu search: a widely used optimization methods in combinational optimization and discrete mathematics, to source localization. To the best of the authors' knowledge, this is the first attempt in the literature to apply tabu search to MEG/EEG source localization. Thirdly, in order to further comparison of the performance of above algorithms, simulated annealing is also applied to MEG source localization problem. The computer simulation results show that the authors' local genetic algorithm is the most effective approach to dipole location.

Global optimization approaches to MEG source localization

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A comparative study of global optimization approaches to meg source localization

Medical image reconstruction using a multi-objective genetic local search algorithm

Global optimization approaches to MEG source localization