Algorithms are important tools for solving problems computationally. All computation involves algorithms, and the efficiency of an algorithm largely determines its usefulness. This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation. A brief history of recent nature-inspired algorithms for optimization is outlined in this chapter.

Introduction to Algorithms

The Whale Optimization Algorithm

Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and harmony search are now becoming powerful methods for solving many tough optimization problems. In this paper, we propose a new metaheuristic method, the Bat Algorithm, based on the echolocation behaviour of bats. We also intend to combine the advantages of existing algorithms into the new bat algorithm. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing algorithms, including genetic algorithms and particle swarm optimization. Simulations show that the proposed algorithm seems much superior to other algorithms, and further studies are also discussed.

A New Metaheuristic Bat-Inspired Algorithm

Salp Swarm Algorithm

Many optimization problems in various fields have been solved using diverse optimization al gorithms. Traditional optimization techniques such as linear programming (LP), non-linear programming (NL...

A New Heuristic Optimization Algorithm: Harmony Search

A newly developed heuristic algorithm, Harmony Search, is applied to the parameter estimation problem of the nonlinear Muskingum model. Harmony Search found better values of parameters in the nonlinear Muskingum model than five other methods including another heuristic method, genetic algorithm, in terms of SSQ (the sum of the square of the deviations between the observed and routed outflows), SAD (the sum of the absolute value of the deviations between the observed and routed outflows), DPO (deviations of peak of routed and actual flows), and DPOT (deviations of peak time of routed and actual outflow). Harmony Search also has the advantage that it does not require the process of assuming the initial values of design parameters. The sensitivity analysis of Harmony Memory Considering Rate showed that relatively large values of Harmony Memory Considering Rate makes the Harmony Search converge to a better solution.

Parameter estimation of the nonlinear Muskingum model using Harmony Search

The Pipe network design problem is considered by choosing least-cost diameter pipes to satisfy flow demands and minimum head restrictions. Harmony and innovation are brought together as in music to devise a search pattern that can identify a large number of local optima in pipe network design. Improvization is brought in by varying the pitch rate parameter, and harmony is maintained by accumulating improving solutions. Because in pipe networks optimization by its very nature removes any redundancy, a minimum power loss criterion is introduced to enhance feasibility. The efficacy of the algorithm is demonstrated by solving a test nonlinear program and a pipe network problem from the literature to global optimum. Several near-optimal solutions are reported.

Harmony Search Optimization: Application to Pipe Network Design

Multi-objective water cycle algorithm (MOWCA) is proposed for solving constrained and engineering multi-objective problems.Generational distance, metric of spread, and Δ metric are used as performance criteria.Optimal Pareto fronts are finely covered by the MOWCA with a good distribution of the non-dominated solutions.MOWCA is able to approach a full optimal Pareto front and provide a superior quality of solutions.MOWCA is better able to find a wider range of solutions compared with the other optimizers in this paper. In this paper, a metaheuristic optimizer, the multi-objective water cycle algorithm (MOWCA), is presented for solving constrained multi-objective problems. The MOWCA is based on emulation of the water cycle process in nature. In this study, a set of non-dominated solutions obtained by the proposed algorithm is kept in an archive to be used to display the exploratory capability of the MOWCA as compared to other efficient methods in the literature. Moreover, to make a comprehensive assessment about the robustness and efficiency of the proposed algorithm, the obtained optimization results are also compared with other widely used optimizers for constrained and engineering design problems. The comparisons are carried out using tabular, descriptive, and graphical presentations.

Water cycle algorithm for solving constrained multi-objective optimization problems

WCA concepts are inspired by nature and based on water cycle process.New concepts of evaporation rate for rivers and streams are applied in the ER-WCA.Variable evaporation rate is utilized in the ER-WCA to evaporate the water adaptively.ER-WCA forces new generated streams to search near sea using the concept of variance.ER-WCA outperforms or equals other methods in terms of function evaluations and solution quality. This paper presents a modified version of the water cycle algorithm (WCA). The fundamental concepts and ideas which underlie the WCA are inspired based on the observation of water cycle process and how rivers and streams flow to the sea. New concept of evaporation rate for different rivers and streams is defined so called evaporation rate based WCA (ER-WCA), which offers improvement in search. Furthermore, the evaporation condition is also applied for streams that directly flow to sea based on the new approach. The ER-WCA shows a better balance between exploration and exploitation phases compared to the standard WCA. It is shown that the ER-WCA offers high potential in finding all global optima of multimodal and benchmark functions. The WCA and ER-WCA are tested using several multimodal benchmark functions and the obtained optimization results show that in most cases the ER-WCA converges to the global solution faster and offers more accurate results than the WCA and other considered optimizers. Based on the performance of ER-WCA on a number of well-known benchmark functions, the efficiency of the proposed method with respect to the number of function evaluations (computational effort) and accuracy of function value are represented.

Joong Hoon Kim

Papers

A New Heuristic Optimization Algorithm: Harmony Search

Parameter estimation of the nonlinear Muskingum model using Harmony Search

Harmony Search Optimization: Application to Pipe Network Design

Water cycle algorithm for solving constrained multi-objective optimization problems

Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems