Solution of Combined Economic Emission Dispatch Problem with Valve-Point Effect Using Hybrid NSGA II-MOPSO

This chapter formulates a multi-objective optimization problem to simultaneously minimize the objectives of fuel cost and emissions from the power plants to meet the power demand subject to linear and nonlinear system constraints. These conflicting objectives are formulated as a combined economic emission dispatch (CEED) problem. Various meta-heuristic optimization algorithms have been developed and successfully implemented to solve this complex, highly nonlinear, non-convex problem. To overcome the shortcomings of the evolutionary multi-objective algorithms like slow convergence to Pareto-optimal front, premature convergence, local trapping, it is very natural to think of integrating various algorithms to overcome the shortcomings. This chapter proposes a hybrid evolutionary multi-objective optimization framework using Non-Dominated Sorting Genetic Algorithm II and Multi-Objective Particle Swarm Optimization to solve the CEED problem. The hybrid method along with the proposed constraint handling mechanism is able to balance the exploration and exploitation tasks. This hybrid method is tested on IEEE 30 bus system with quadratic cost function considering transmission loss and valve point effect. The Pareto front obtained using hybrid approach demonstrates that the approach converges to the true Pareto front, finds the diverse set of solutions along the Pareto front and confirms its potential to solve the CEED problem

Diversifying Multi-Objective Gradient Techniques and their Role in Hybrid Multi-Objective Evolutionary Algorithms for Deformable Medical Image Registration

Gradient methods and their value in single-objective, real-valued optimization are well-established. As such, they play a key role in tackling real-world, hard optimization problems such as deformable image registration (DIR). A key question is to which extent gradient techniques can also play a role in a multi-objective approach to DIR. We therefore aim to exploit gradient information within an evolutionary-algorithm-based multi-objective optimization framework for DIR. Although an analytical description of the multi-objective gradient (the set of all Pareto-optimal improving directions) is available, it is nontrivial how to best choose the most appropriate direction per solution because these directions are not necessarily uniformly distributed in objective space. To address this, we employ a Monte-Carlo method to obtain a discrete, spatially-uniformly distributed approximation of the set of Pareto-optimal improving directions. We then apply a diversification technique in which each solution is associated with a unique direction from this set based on its multi- as well as single-objective rank. To assess its utility, we compare a state-of-the-art multi-objective evolutionary algorithm with three different hybrid versions thereof on several benchmark problems and two medical DIR problems. Results show that the diversification strategy successfully leads to unbiased improvement, helping an adaptive hybrid scheme solve all problems, but the evolutionary algorithm remains the most powerful optimization method, providing the best balance between proximity and diversity

On the usefulness of gradient information in multi-objective deformable image registration using a B-spline-based dual-dynamic transformation model: comparison of three optimization algorithms

The use of gradient information is well-known to be highly useful in single-objective optimization-based image registration methods. However, its usefulness has not yet been investigated for deformable image registration from a multi-objective optimization perspective. To this end, within a previously introduced multi-objective optimization framework, we use a smooth B-spline-based dual-dynamic transformation model that allows us to derive gradient information analytically, while still being able to account for large deformations. Within the multi-objective framework, we previously employed a powerful evolutionary algorithm (EA) that computes and advances multiple outcomes at once, resulting in a set of solutions (a so-called Pareto front) that represents efficient trade-offs between the objectives. With the addition of the B-spline-based transformation model, we studied the usefulness of gradient information in multiobjective deformable image registration using three different optimization algorithms: the (gradient-less) EA, a gradientonly algorithm, and a hybridization of these two. We evaluated the algorithms to register highly deformed images: 2D MRI slices of the breast in prone and supine positions. Results demonstrate that gradient-based multi-objective optimization significantly speeds up optimization in the initial stages of optimization. However, allowing sufficient computational resources, better results could still be obtained with the EA. Ultimately, the hybrid EA found the best overall approximation of the optimal Pareto front, further indicating that adding gradient-based optimization for multiobjective optimization-based deformable image registration can indeed be beneficial

Evolving Combinational Logic Circuits Using a Hybrid Quantum Evolution and Particle Swarm Inspired Algorithm

An algorithm inspired from quantum evolution and particle swarm optimization is used to evolve combinational logic circuits. This algorithm uses the framework of the local version of particle swarm optimizations with quantum evolutionary algorithms, and integer encoding. A multi-objective fitness function is used to evolve the digital circuits in order to obtain a variety of feasible circuits with minimal number of gates in the design. A comparative study indicates the superior performance of the hybrid quantum evolution-particle swarm inspired algorithm over the particle swarm and other evolutionary algorithms (such as genetic algorithms) independently

Evolving Combinational Logic Circuits Using a Hybrid Quantum Evolution and Particle Swarm Inspired Algorithm

In this paper, an algorithm inspired from quantum evolution and particle swarm to evolve combinational logic circuits is presented. This algorithm uses the framework of the local version of particle swarm optimization with quantum evolutionary algorithms, and integer encoding. A multi-objective fitness function is used to evolve the combinational logic circuits in order obtain feasible circuits with minimal number of gates in the design. A comparative study indicates the superior performance of the hybrid quantum evolution-particle swarm inspired algorithm over the particle swarm and other evolutionary algorithms (such as genetic algorithms) independently

TOWARDS A UNIFIED VIEW OF METAHEURISTICS

This talk provides a complete background on metaheuristics and presents in a unified view the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. The key search components of metaheuristics are considered as a toolbox for: - Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems. - Designing efficient metaheuristics for multi-objective optimization problems. - Designing hybrid, parallel and distributed metaheuristics. - Implementing metaheuristics on sequential and parallel machines

TOWARDS A UNIFIED VIEW OF METAHEURISTICS

This talk provides a complete background on metaheuristics and presents in a unified view the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. The key search components of metaheuristics are considered as a toolbox for: - Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems. - Designing efficient metaheuristics for multi-objective optimization problems. - Designing hybrid, parallel and distributed metaheuristics. - Implementing metaheuristics on sequential and parallel machines

Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework

Simplicity and flexibility of meta-heuristic optimization algorithms have attracted lots of attention in the field of optimization. Different optimization methods, however, hold algorithm-specific strengths and limitations, and selecting the best-performing algorithm for a specific problem is a tedious task. We introduce a new hybrid optimization framework, entitled Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL), which combines the strengths of different evolutionary algorithms (EAs) in a parallel computing scheme. SC-SAHEL explores performance of different EAs, such as the capability to escape local attractions, speed, convergence, etc., during population evolution as each individual EA suits differently to various response surfaces. The SC-SAHEL algorithm is benchmarked over 29 conceptual test functions, and a real-world hydropower reservoir model case study. Results show that the hybrid SC-SAHEL algorithm is rigorous and effective in finding global optimum for a majority of test cases, and that it is computationally efficient in comparison to algorithms with individual EA