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Economic load dispatch (ELD) is a crucial problem in the power system which is tackled by distributing the required generation power through a set of units to minimize the fuel cost required. This distribution is subject to two main constraints: (1) equality and inequality related to power balance and power output, respectively. In the optimization context, ELD is formulated as a non-convex, nonlinear, constrained optimization problem which cannot be easily solved using calculus-based techniques. Several optimization algorithms have been adapted. Due to the complexity nature of ELD search space, the theoretical concepts of these optimization algorithms have been modified or hybridized. In this paper, the grey wolf optimizer (GWO) which is a swarm intelligence is hybridized with β -hill climbing optimizer (β HC) which is a local search algorithm, to improve convergence properties. GWO is very powerful in a wide search, while β HC is very powerful in deep search. By combining the wide and deep search ability in a single optimization framework, the balance between the exploration and exploitation is correctly managed. The proposed hybrid algorithm is named β -GWO which is evaluated using five different test cases of ELD problems: 3 generating units with 850 MW; 13 generating units with 1800 MW; 13 generating units with 2520 MW; 40 generating units with 10,500 MW; and 80 generating units with 21,000 MW. β -GWO is comparatively measured using 49 comparative methods. The results obtained by β -GWO outperform others in most test cases. In conclusion, the proposed β -GWO is proved to be a powerful method for ELD problem or for any other similar problems in the power system domain. [ABSTRACT FROM AUTHOR]

Flower pollination algorithm (FPA) is a recent swarm-based evolutionary algorithm that was inspired by the biological evolution of pollination of the flowers. It deals with a panmictic population of pollens (or solutions) at each generation, using global and local pollination operators, to improve the whole population at once. Like other evolutionary algorithms, FPA has a chronic shortcoming that lies in its inability to maturely converge. This is conventionally known as a premature convergence where the diversity of the population is loosed and thus the search is stagnated. Island model is one of the successful structured population techniques that were utilized in the theoretical characteristics of several evolutionary-based algorithms. In this model, the population is divided into a set of islands. The knowledge is distributed among those islands using a migration process that is controlled by migration rate, topology, frequency, and policy. In this paper, the island model is utilized in the evolution process of FPA to control diversity. The proposed approach is called IsFPA. The ability of IsFPA in maintaining the diversity during the search process, and in producing impressive results, can be interpreted by utilizing the island model in the FPA optimization framework. To assess the efficiency of IsFPA, 23 benchmark functions with various sizes and complexities were used. The best parameter configurations of IsFPA were investigated and analyzed. Comparing the results of IsFPA with those of state-of-the-art methods which are FPA, genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), multi-verse optimizer (MVO), island bat algorithm (iBA), and island harmony search (iHS), the comparison results show that the IsFPA is able to control the diversity and improves the outcomes where IsFPA is ranked first followed by FPA, iBA, iHS, GSA, MVO, GA, PSO, respectively, based on the Friedman test with Holm and Hochberg as post hoc statistical test. [ABSTRACT FROM AUTHOR]

In this paper, the update process of harmony search (HS) algorithm is modified to improve its concept of diversity. The update process in HS is based on a greedy mechanism in which the new harmony solution, created in each generation, replaces the worst individual in the population, if better. This greedy process could be improved with other updates mechanisms in order to control the diversity perfectly. Three versions of HS have been proposed: (1) Natural Proportional HS ; (2) Natural Tournament HS; (3) Natural Rank HS. These three HS versions employed the natural selection principle of the “survival of the fittest”. Instead of replacing the worst individual in population, any individual can be replaced based on certain criteria. Four versions of economic loading dispatch (ELD) problems with valve point have been used to measure the effect of the newly proposed HS versions. The results show that the new HS versions are very promising for ELD domain. This claim is proved based on the comparative evaluation process where the new HS versions are able to excel the state-of-the-art methods in almost ELD problems used. [ABSTRACT FROM AUTHOR]

In this paper, alternative selection mechanisms in the bat-inspired algorithm for global optimization problems are studied. The bat-inspired algorithm is a recent swarm-based intelligent system which mimics the echolocation system of micro-bats. In the bat-inspired algorithm, the bats randomly fly around the best bat locations found during the search so as to improve their hunting of prey. In practice, one bat location from a set of best bat locations is selected. Thereafter, that best bat location is used by local search with a random walk strategy to inform other bats about the prey location. This selection mechanism can be improved using other natural selection mechanisms adopted from other advanced algorithms like Genetic Algorithm. Therefore, six selection mechanisms are studied to choose the best bat location: global-best, tournament, proportional, linear rank, exponential rank, and random. Consequently, six versions of bat-inspired algorithm are proposed and studied which are global-best bat-inspired algorithm (GBA), tournament bat-inspired algorithm (TBA), proportional bat-inspired algorithm (PBA), linear rank bat-inspired algorithm (LBA), exponential rank bat-inspired algorithm (EBA), and random bat-inspired algorithm (RBA). Using two sets of global optimization functions, the bat-inspired versions are evaluated and the sensitivity analyses of each version to its parameters studied. Our results suggest that there are positive effects of the selection mechanisms on the performance of the classical bat-inspired algorithm which is GBA. For comparative evaluation, eighteen methods are selected using 25 IEEE-CEC2005 functions. The results show that the bat-inspired versions with various selection schemes observing the “survival-of-the-fittest” principle are largely competitive to established methods. [ABSTRACT FROM AUTHOR]

Harmony search (HS) algorithm is a recent meta-heuristic algorithm that mimics the musical improvisation concepts. This algorithm has been widely used for solving optimization problems. Moreover, many modifications in this algorithm have been carried out in order to improve the performance of the search. Island model is a structured population mechanism used in evolutionary algorithms to preserve the diversity of the population and thus improve the performance. In this paper, the island model concepts are embedded into the main framework of HS algorithm to improve its convergence properties where the new method is refer to as island HS ( i HS). In the proposed method, the individuals in population are distributed into separate sub-population named (islands). Then the breeding loop is separately involved in each island. After specific generations, a number of individuals run an exchange through a process called migration. This process is performed to keep the diversity of population and to allow islands to interact with each other. The experimental result using a set of benchmark function shows that the island model context is crucial to the performance of i HS. Finally the sensitivity analysis and the comparative study for i HS prove the efficiency of the island model. [ABSTRACT FROM AUTHOR]

In this paper, a modified version of the Multi-objective Grey Wolf Optimizer (MGWO), known as linked-based GWO (LMGWO), is proposed for the Appliances Energy Scheduling Problem (AESP). The proposed LMGWO is utilized by combining the MGWO searching mechanism with a novel strategy, called neighbourhood selection strategy, to improve local exploitation capabilities. AESP is a problem that can be tackled by searching for the best appliances schedule according to a set of constraints and a dynamic pricing scheme(s) utilized for optimizing energy consumed at a particular period. Three objectives are considered to handle AESP: improving user comfort while reducing electricity bills and maintaining power systems' performance. Therefore, AESP is modelled as a multi-objective optimization problem to handle all objectives simultaneously. In the evaluation results, the LMGWO is tested using a new dataset containing 30 power consumption scenarios with up to 36 appliances. For comparative purposes, the same linked-based neighbourhood selection strategy is utilized with other three optimization algorithms, including particle swarm optimization, salp swarm optimization, and wind-driven algorithm. The performance of the modified versions is compared with each other and that of the original versions to show their improvements. Furthermore, the proposed LMGWO is compared with eight state-of-the-art methods using their recommended datasets to show the viability of the proposed LMGWO. Interestingly, the proposed LMGWO is able to outperform the compared methods in almost all produced results. [ABSTRACT FROM AUTHOR]

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors. The memory consideration and population update are modified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS. [ABSTRACT FROM AUTHOR]

This paper presents a novel meta-heuristic algorithm so-called White Shark Optimizer (WSO) to solve optimization problems over a continuous search space. The core ideas and underpinnings of WSO are inspired by the behaviors of great white sharks, including their exceptional senses of hearing and smell while navigating and foraging. These aspects of behavior are mathematically modeled to accommodate a sufficiently adequate balance between exploration and exploitation of WSO and to assist search agents to explore and exploit each potential area of the search space in order to achieve optimization. The search agents of WSO randomly update their position in connection with best-so-far solutions, to eventually arrive at the optimal outcome. The performance of WSO was comprehensively benchmarked on a set of 29 test functions from the CEC-2017 test suite for several dimensions. WSO was further applied to solve the benchmark problems of the CEC-2011 evolutionary algorithm competition to prove its reliability and applicability to real-world problems. A thorough analysis of computational and convergence results was presented to shed light on the efficacy and stability levels of WSO. The performance score of WSO in terms of several statistical methods was compared with 9 well-established meta-heuristics based on the solutions generated. Friedman's and Holm's tests of the results showed that WSO revealed reasonable solutions, in terms of global optimality, avoidance of local minima and solution quality, compared to other existing meta-heuristics. [ABSTRACT FROM AUTHOR]