With the rapid growth of the digital imaging, image processing techniques are widely involved in many industrial and medical applications. Image thresholding plays an essential role in image processing and computer vision applications. It has a vast domain of usage. Areas such document image analysis, scene or map processing, satellite imaging and material inspection in quality control tasks are examples of applications that employ image thresholding or segmentation to extract useful information from images. Medical image processing is another area that has extensively used image thresholding to help the experts to better interpret digital images for a more accurate diagnosis or to plan treatment procedures. Opposition-based computing, on the other hand, is a recently introduced model that can be employed to improve the performance of existing techniques. In this thesis, the idea of oppositional thresholding is explored to introduce new and better thresholding techniques. A recent method, called Opposite Fuzzy Thresholding (OFT), has involved fuzzy sets with opposition idea, and based on some preliminary experiments seems to be reasonably successful in thresholding some medical images. In this thesis, a Weighted Opposite Fuzzy Thresholding method (WOFT) will be presented that produces more accurate and reliable results compared to the parent algorithm. This claim has been verified with some experimental trials using both synthetic and real world images. Experimental evaluations were conducted on two sets of synthetic and medical images to validate the robustness of the proposed method in improving the accuracy of the thresholding process when fuzzy and oppositional ideas are combined.

With the rapid growth of the digital imaging, image processing techniques are widely involved in many industrial and medical applications. Image thresholding plays an essential role in image processing and computer vision applications. It has a vast domain of usage. Areas such document image analysis, scene or map processing, satellite imaging and material inspection in quality control tasks are examples of applications that employ image thresholding or segmentation to extract useful information from images. Medical image processing is another area that has extensively used image thresholding to help the experts to better interpret digital images for a more accurate diagnosis or to plan treatment procedures. Opposition-based computing, on the other hand, is a recently introduced model that can be employed to improve the performance of existing techniques. In this thesis, the idea of oppositional thresholding is explored to introduce new and better thresholding techniques. A recent method, called Opposite Fuzzy Thresholding (OFT), has involved fuzzy sets with opposition idea, and based on some preliminary experiments seems to be reasonably successful in thresholding some medical images. In this thesis, a Weighted Opposite Fuzzy Thresholding method (WOFT) will be presented that produces more accurate and reliable results compared to the parent algorithm. This claim has been verified with some experimental trials using both synthetic and real world images. Experimental evaluations were conducted on two sets of synthetic and medical images to validate the robustness of the proposed method in improving the accuracy of the thresholding process when fuzzy and oppositional ideas are combined.

In solving noise-free and noisy optimization problems, candidate initialization and sampling play a key role, but are not deeply investigated. It is of interest to know if the entire search space has the same quality for candidate-solutions during solving different type of optimization problems. In this thesis, a comprehensive investigation is conducted in order to clear those doubts, and to examine the effects of variant sampling methods on solving challenging optimization problems, such as large-scale, noisy, and multi-modal problems. As a result, the search space is segmented by using seven segmentation schemes, namely: Center-Point, Center-Based, Modula-Opposite, Quasi-Opposite, Quasi-Reflection, Supper- Opposite, and Opposite-Random. The introduced schemes are studied using Monte-Carlo simulation, on various types of noise-free optimization problems, and ultimately ranked based on their performance in terms of probability of closeness, average distance to unknown solution, number of solutions found, and diversity. Based on the results of the experiments, high-ranked schemes are selected and utilized on well-known metaheuristic algorithms, as case studies. Two categories of case studies are targeted; one for a singlesolution- based metaheuristic (S-metaheuristic) and another one for a population based metaheuristic (P-metaheuristic). A high-ranked single-solution-based scheme is utilized to accelerate Simulated Annealing (SA) algorithm, as a noise-free S-metaheuristic case study. Similarly, for noise-free P-metaheuristic case study, an effective population-based algorithm, Differential Evolution (DE), has been utilized. The experiments confirm that the new algorithms outperform the parent algorithm (DE) on large-scale problems. In the same direction, with regards to solving noisy problems more efficiently, a Shaking-based sampling method is introduced, in which the original noise is tackled by adding an additional noise into the search process. As a case study, the Shaking-based sampling is utilized on the DE algorithm, from which two variant algorithms have been developed and showed impressive performance in comparison to the classical DE, in tackling noisy largescale problems. This thesis has created an opportunity for a comprehensive investigation on search space segmentation schemes and proposed new sampling methods. The current study has provided a guide to use appropriate sampling schemes for a given types of problems such as noisy, large-scale and multi-modal optimization problems. Furthermore, this thesis questions the effectiveness of uniform-random sampling method, which is widely used in of S-Metaheuristic and P-Metaheuristic algorithms. / UOIT

Symmetry has been a very useful tool to researchers in various scientific fields. At its most basic, symmetry refers to the invariance of an object to some transformation, or set of transformations. Usually one searches for, and uses information concerning an existing symmetry within given data, structure or concept to somehow improve algorithm performance or compress the search space. This thesis examines the effects of imposing or inducing symmetry on a search space. That is, the question being asked is whether only existing symmetries can be useful, or whether changing reference to an intuition-based definition of symmetry over the evaluation function can also be of use. Within the context of optimization, symmetry induction as defined in this thesis will have the effect of equating the evaluation of a set of given objects. Group theory is employed to explore possible symmetrical structures inherent in a search space. Additionally, conditions when the search space can have a symmetry induced on it are examined. The idea of a neighborhood structure then leads to the idea of opposition-based computing which aims to induce a symmetry of the evaluation function. In this context, the search space can be seen as having a symmetry imposed on it. To be useful, it is shown that an opposite map must be defined such that it equates elements of the search space which have a relatively large difference in their respective evaluations. Using this idea a general framework for employing opposition-based ideas is proposed. To show the efficacy of these ideas, the framework is applied to popular computational intelligence algorithms within the areas of Monte Carlo optimization, estimation of distribution and neural network learning. The first example application focuses on simulated annealing, a popular Monte Carlo optimization algorithm. At a given iteration, symmetry is induced on the system by considering opposite neighbors. Using this technique, a temporary symmetry over the neighborhood region is induced. This simple algorithm is benchmarked using common real optimization problems and compared against traditional simulated annealing as well as a randomized version. The results highlight improvements in accuracy, reliability and convergence rate. An application to image thresholding further confirms the results. Another example application, population-based incremental learning, is rooted in estimation of distribution algorithms. A major problem with these techniques is a rapid loss of diversity within the samples after a relatively low number of iterations. The opposite sample is introduced as a remedy to this problem. After proving an increased diversity, a new probability update procedure is designed. This opposition-based version of the algorithm is benchmarked using common binary optimization problems which have characteristics of deceptivity and attractive basins characteristic of difficult real world problems. Experiments reveal improvements in diversity, accuracy, reliability and convergence rate over the traditional approach. Ten instances of the traveling salesman problem and six image thresholding problems are used to further highlight the improvements. Finally, gradient-based learning for feedforward neural networks is improved using opposition-based ideas. The opposite transfer function is presented as a simple adaptive neuron which easily allows for efficiently jumping in weight space. It is shown that each possible opposite network represents a unique input-output mapping, each having an associated effect on the numerical conditioning of the network. Experiments confirm the potential of opposite networks during pre- and early training stages. A heuristic for efficiently selecting one opposite network per epoch is presented. Benchmarking focuses on common classification problems and reveals improvements in accuracy, reliability, convergence rate and generalization ability over common backpropagation variants. To further show the potential, the heuristic is applied to resilient propagation where similar improvements are also found.

Symmetry has been a very useful tool to researchers in various scientific fields. At its most basic, symmetry refers to the invariance of an object to some transformation, or set of transformations. Usually one searches for, and uses information concerning an existing symmetry within given data, structure or concept to somehow improve algorithm performance or compress the search space. This thesis examines the effects of imposing or inducing symmetry on a search space. That is, the question being asked is whether only existing symmetries can be useful, or whether changing reference to an intuition-based definition of symmetry over the evaluation function can also be of use. Within the context of optimization, symmetry induction as defined in this thesis will have the effect of equating the evaluation of a set of given objects. Group theory is employed to explore possible symmetrical structures inherent in a search space. Additionally, conditions when the search space can have a symmetry induced on it are examined. The idea of a neighborhood structure then leads to the idea of opposition-based computing which aims to induce a symmetry of the evaluation function. In this context, the search space can be seen as having a symmetry imposed on it. To be useful, it is shown that an opposite map must be defined such that it equates elements of the search space which have a relatively large difference in their respective evaluations. Using this idea a general framework for employing opposition-based ideas is proposed. To show the efficacy of these ideas, the framework is applied to popular computational intelligence algorithms within the areas of Monte Carlo optimization, estimation of distribution and neural network learning. The first example application focuses on simulated annealing, a popular Monte Carlo optimization algorithm. At a given iteration, symmetry is induced on the system by considering opposite neighbors. Using this technique, a temporary symmetry over the neighborhood region is induced. This simple algorithm is benchmarked using common real optimization problems and compared against traditional simulated annealing as well as a randomized version. The results highlight improvements in accuracy, reliability and convergence rate. An application to image thresholding further confirms the results. Another example application, population-based incremental learning, is rooted in estimation of distribution algorithms. A major problem with these techniques is a rapid loss of diversity within the samples after a relatively low number of iterations. The opposite sample is introduced as a remedy to this problem. After proving an increased diversity, a new probability update procedure is designed. This opposition-based version of the algorithm is benchmarked using common binary optimization problems which have characteristics of deceptivity and attractive basins characteristic of difficult real world problems. Experiments reveal improvements in diversity, accuracy, reliability and convergence rate over the traditional approach. Ten instances of the traveling salesman problem and six image thresholding problems are used to further highlight the improvements. Finally, gradient-based learning for feedforward neural networks is improved using opposition-based ideas. The opposite transfer function is presented as a simple adaptive neuron which easily allows for efficiently jumping in weight space. It is shown that each possible opposite network represents a unique input-output mapping, each having an associated effect on the numerical conditioning of the network. Experiments confirm the potential of opposite networks during pre- and early training stages. A heuristic for efficiently selecting one opposite network per epoch is presented. Benchmarking focuses on common classification problems and reveals improvements in accuracy, reliability, convergence rate and generalization ability over common backpropagation variants. To further show the potential, the heuristic is applied to resilient propagation where similar improvements are also found.

Evolutionary algorithms (EAs) are well-established techniques to approach those problems which for the classical optimization methods are difficult to solve. Tackling problems with mixed-type of variables, many local optima, undifferentiable or non-analytical functions are some examples to highlight the outstanding capabilities of the evolutionary algorithms. Among the various kinds of evolutionary algorithms, differential evolution (DE) is well known for its effectiveness and robustness. Many comparative studies confirm that the DE outperforms many other optimizers. Finding more accurate solution(s), in a shorter period of time for complex black-box problems, is still the main goal of all evolutionary algorithms. The opposition concept, on the other hand, has a very old history in philosophy, set theory, politics, sociology, and physics. But, there has not been any opposition-based contribution to optimization. In this thesis, firstly, the opposition-based optimization (OBO) is constituted. Secondly, its advantages are formally supported by establishing mathematical proofs. Thirdly, the opposition-based acceleration schemes, including opposition-based population initialization and generation jumping, are proposed. Fourthly, DE is selected as a parent algorithm to verify the acceleration effects of proposed schemes. Finally, a comprehensive set of well-known complex benchmark functions is employed to experimentally compare and analyze the algorithms. Results confirm that opposition-based DE (ODE) performs better than its parent (DE), in terms of both convergence speed and solution quality. The main claim of this thesis is not defeating DE, its numerous versions, or other optimizers, but to introduce a new notion into nonlinear continuous optimization via innovative metaheuristics, namely the notion of opposition. Although, ODE has been compared with six other optimizers and outperforms them overall. Furthermore, both presented experimental and mathematical results conform with each other and demonstrate that opposite points are more beneficial than pure random points for black-box problems; this fundamental knowledge can serve to accelerate other machine learning approaches as well (such as reinforcement learning and neural networks). And perhaps in future, it could replace the pure randomness with random-opposition model when there is no a priori knowledge about the solution/problem. Although, all conducted experiments utilize DE as a parent algorithm, the proposed schemes are defined at the population level and, hence, have an inherent potential to be utilized for acceleration of other DE extensions or even other population-based algorithms, such as genetic algorithms (GAs). Like many other newly introduced concepts, ODE and the proposed opposition-based schemes still require further studies to fully unravel their benefits, weaknesses, and limitations.

Machine intelligence techniques contribute to solving real-world problems. Reinforcement learning (RL) is one of the machine intelligence techniques with several characteristics that make it suitable for the applications, for which the model of the environment is not available to the agent. In real-world applications, intelligent agents generally face a very large state space which limits the usability of reinforcement learning. The condition for convergence of reinforcement learning implies that each state-action pair must be visited infinite times, a condition which can be considered impossible to be satisfied in many practical situations. The goal of this work is to propose a class of new techniques to overcome this problem for off-policy, step-by-step (incremental) and model-free reinforcement learning with discrete state and action space. The focus of this research is using the design characteristics of RL agent to improve its performance regarding the running time while maintaining an acceptable level of accuracy. One way of improving the performance of the intelligent agents is using the model of environment. In this work, a special type of knowledge about the agent actions is employed to improve its performance because in many applications the model of environment may only be known partially or not at all. The concept of opposition is employed in the framework of reinforcement learning to achieve this goal. One of the components of RL agent is the action. For each action we define its associate opposite action. The actions and opposite actions are implemented in the framework of reinforcement learning to update the value function resulting in a faster convergence. At the beginning of this research the concept of opposition is incorporated in the components of reinforcement learning, states, actions, and reinforcement signal which results in introduction of the oppositional target domain estimation algorithm, OTE. OTE reduces the search and navigation area and accelerates the speed of search for a target. The OTE algorithm is limited to the applications, in which the model of the environment is provided for the agent. Hence, further investigation is conducted to extend the concept of opposition to the model-free reinforcement learning algorithms. This extension contributes to the generating of several algorithms based on using the concept of opposition for Q(lambda) technique. The design of reinforcement learning agent depends on the application. The emphasize of this research is on the characteristics of the actions. Hence, the primary challenge of this work is design and incorporation of the opposite actions in the framework of RL agents. In this research, three different applications, namely grid navigation, elevator control problem, and image thresholding are implemented to address this challenge in context of different applications. The design challenges and some solutions to overcome the problems and improve the algorithms are also investigated. The opposition-based Q(lambda) algorithms are tested for the applications mentioned earlier. The general idea behind the opposition-based Q(lambda) algorithms is that in Q-value updating, the agent updates the value of an action in a given state. Hence, if the agent knows the value of opposite action then instead of one value, the agent can update two Q-values at the same time without taking its corresponding opposite action causing an explicit transition to opposite state. If the agent knows both values of action and its opposite action for a given state, then it can update two Q-values. This accelerates the learning process in general and the exploration phase in particular. Several algorithms are outlined in this work. The OQ(lambda) will be introduced to accelerate Q(lambda) algorithm in discrete state spaces. The NOQ(lambda) method is an extension of OQ(lambda) to operate in a broader range of non-deterministic environments. The update of the opposition trace in OQ(lambda) depends on the next state of the opposite action (which generally is not taken by the agent). This limits the usability of this technique to the deterministic environments because the next state should be known to the agent. NOQ(lambda) will be presented to update the opposition trace independent of knowing the next state for the opposite action. The results show the improvement of the performance in terms of running time for the proposed algorithms comparing to the standard Q(lambda) technique.

Evolutionary algorithms (EAs) are well-established techniques to approach those problems which for the classical optimization methods are difficult to solve. Tackling problems with mixed-type of variables, many local optima, undifferentiable or non-analytical functions are some examples to highlight the outstanding capabilities of the evolutionary algorithms. Among the various kinds of evolutionary algorithms, differential evolution (DE) is well known for its effectiveness and robustness. Many comparative studies confirm that the DE outperforms many other optimizers. Finding more accurate solution(s), in a shorter period of time for complex black-box problems, is still the main goal of all evolutionary algorithms. The opposition concept, on the other hand, has a very old history in philosophy, set theory, politics, sociology, and physics. But, there has not been any opposition-based contribution to optimization. In this thesis, firstly, the opposition-based optimization (OBO) is constituted. Secondly, its advantages are formally supported by establishing mathematical proofs. Thirdly, the opposition-based acceleration schemes, including opposition-based population initialization and generation jumping, are proposed. Fourthly, DE is selected as a parent algorithm to verify the acceleration effects of proposed schemes. Finally, a comprehensive set of well-known complex benchmark functions is employed to experimentally compare and analyze the algorithms. Results confirm that opposition-based DE (ODE) performs better than its parent (DE), in terms of both convergence speed and solution quality. The main claim of this thesis is not defeating DE, its numerous versions, or other optimizers, but to introduce a new notion into nonlinear continuous optimization via innovative metaheuristics, namely the notion of opposition. Although, ODE has been compared with six other optimizers and outperforms them overall. Furthermore, both presented experimental and mathematical results conform with each other and demonstrate that opposite points are more beneficial than pure random points for black-box problems; this fundamental knowledge can serve to accelerate other machine learning approaches as well (such as reinforcement learning and neural networks). And perhaps in future, it could replace the pure randomness with random-opposition model when there is no a priori knowledge about the solution/problem. Although, all conducted experiments utilize DE as a parent algorithm, the proposed schemes are defined at the population level and, hence, have an inherent potential to be utilized for acceleration of other DE extensions or even other population-based algorithms, such as genetic algorithms (GAs). Like many other newly introduced concepts, ODE and the proposed opposition-based schemes still require further studies to fully unravel their benefits, weaknesses, and limitations.

Machine intelligence techniques contribute to solving real-world problems. Reinforcement learning (RL) is one of the machine intelligence techniques with several characteristics that make it suitable for the applications, for which the model of the environment is not available to the agent. In real-world applications, intelligent agents generally face a very large state space which limits the usability of reinforcement learning. The condition for convergence of reinforcement learning implies that each state-action pair must be visited infinite times, a condition which can be considered impossible to be satisfied in many practical situations. The goal of this work is to propose a class of new techniques to overcome this problem for off-policy, step-by-step (incremental) and model-free reinforcement learning with discrete state and action space. The focus of this research is using the design characteristics of RL agent to improve its performance regarding the running time while maintaining an acceptable level of accuracy. One way of improving the performance of the intelligent agents is using the model of environment. In this work, a special type of knowledge about the agent actions is employed to improve its performance because in many applications the model of environment may only be known partially or not at all. The concept of opposition is employed in the framework of reinforcement learning to achieve this goal. One of the components of RL agent is the action. For each action we define its associate opposite action. The actions and opposite actions are implemented in the framework of reinforcement learning to update the value function resulting in a faster convergence. At the beginning of this research the concept of opposition is incorporated in the components of reinforcement learning, states, actions, and reinforcement signal which results in introduction of the oppositional target domain estimation algorithm, OTE. OTE reduces the search and navigation area and accelerates the speed of search for a target. The OTE algorithm is limited to the applications, in which the model of the environment is provided for the agent. Hence, further investigation is conducted to extend the concept of opposition to the model-free reinforcement learning algorithms. This extension contributes to the generating of several algorithms based on using the concept of opposition for Q(lambda) technique. The design of reinforcement learning agent depends on the application. The emphasize of this research is on the characteristics of the actions. Hence, the primary challenge of this work is design and incorporation of the opposite actions in the framework of RL agents. In this research, three different applications, namely grid navigation, elevator control problem, and image thresholding are implemented to address this challenge in context of different applications. The design challenges and some solutions to overcome the problems and improve the algorithms are also investigated. The opposition-based Q(lambda) algorithms are tested for the applications mentioned earlier. The general idea behind the opposition-based Q(lambda) algorithms is that in Q-value updating, the agent updates the value of an action in a given state. Hence, if the agent knows the value of opposite action then instead of one value, the agent can update two Q-values at the same time without taking its corresponding opposite action causing an explicit transition to opposite state. If the agent knows both values of action and its opposite action for a given state, then it can update two Q-values. This accelerates the learning process in general and the exploration phase in particular. Several algorithms are outlined in this work. The OQ(lambda) will be introduced to accelerate Q(lambda) algorithm in discrete state spaces. The NOQ(lambda) method is an extension of OQ(lambda) to operate in a broader range of non-deterministic environments. The update of the opposition trace in OQ(lambda) depends on the next state of the opposite action (which generally is not taken by the agent). This limits the usability of this technique to the deterministic environments because the next state should be known to the agent. NOQ(lambda) will be presented to update the opposition trace independent of knowing the next state for the opposite action. The results show the improvement of the performance in terms of running time for the proposed algorithms comparing to the standard Q(lambda) technique.

Opposition-based learning (OBL) was recently proposed to extend di erent machine learning algorithms. The main idea of OBL is to consider opposite estimates, actions or states as an attempt to increase the coverage of the solution space and to reduce exploration time. OBL has already been applied to reinforcement learning, neural networks and genetic algorithms. This thesis explores the application of OBL to ant algorithms. Ant algorithms are based on the trail laying and following behaviour of ants. They have been successfully applied to many complex optimization problems. However, like any other technique, they can benefit from performance improvements. Thus, this work was motivated by the idea of developing more complex pheromone and path selection behaviour for the algorithm using the concept of opposition. This work proposes opposition-based extensions to the construction and update phases of the ant algorithm. The modifications that focus on the solution construction include three direct and two indirect methods. The three direct methods work by pairing the ants and synchronizing their path selection. The two other approaches modify the decisions of the ants by using opposite-pheromone content. The extension of the update phase lead to an approach that performs additional pheromone updates using opposite decisions. Experimental validation was done using two versions of the ant algorithm: the Ant System and the Ant Colony System. The di erent OBL extensions were applied to the Travelling Salesman Problem (TSP) and to the Grid World Problem (GWP). Results demonstrate that the concept of opposition is not easily applied to the ant algorithm. One pheromone-based method showed performance improvements that were statistically significant for the TSP. The quality of the solutions increased and more optimal solutions were found. The extension to the update phase showed some improvements for the TSP and led to accuracy improvements and a significant speed-up for the GWP. The other extensions showed no clear improvement. The proposed methods for applying opposition to the ant algorithm have potential, but more investigations are required before ant colony optimization can fully benefit from opposition. Most importantly, fundamental theoretical work with graphs, specifically, clearly defining opposite paths or opposite path components, is needed. Overall, the results indicate that OBL ideas can be beneficial for ant algorithms.