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Economic dispatch (ED) problem is a popular optimization problem in electrical engineering. Many studies that handled ED problem employed metaheuristics as the optimization technique. Unfortunately, these metaheuristics are old or the existing ones. Meanwhile, ED problem is not the favourite constrained case in studies that introduced a novel metaheuristic. This research introduces a novel metaheuristic called quadratic time optimization (QTO). QTO comprises three sequential searches where both diversification and intensification are blended in every search. But the portion of both orientations changes by following the quadratic time. The appraisal of QTO is performed by employing it to solve both unconstrained and constrained problems. The 23 traditional functions represent the unconstrained problem while economic load dispatch (ELD) problem with valve point effect and spinning reserve problem represents the constrained problem. In both appraisals, there are five novel metaheuristics represent the benchmarks, including: walrus optimization algorithm (WaOA), coati optimization algorithm (COA), total interaction algorithm (TIA), addax optimization algorithm (AOA), and language education optimization (LEO). The result shows the competitiveness of the proposed QTO in handling both unconstrained and constrained problems. QTO becomes the first best in 8 functions out of 23 functions including five high dimension unimodal functions, two high dimension multimodal functions, and one fixed dimension multimodal functions. The result also shows that QTO is competitive in three use cases in ELD problems as the ratio between the range and average total cost among metaheuristics for the first, second, and third cases is 0.72, 0.04, and 0.02 percent consecutively. [ABSTRACT FROM AUTHOR]

As stated in the no-free-lunch (NFL) theory, there is not any optimizer suitable for all problems. This circumstance becomes the motivation of introducing a new swarm-based metaheuristic called best couple algorithm (BCA). BCA is constructed as a swarm-based metaheuristic where the swarm is split into two sub-swarms. There are two types of splitting. The first split is dividing the swarm into the first half and second half of swarms. The second split is dividing the swarm into the odd indexed swarm members and even indexed swarm members. There is a sub swarm leader representing the highest quality swarm member in every sub swarm. There are two sequential searches for every split: the motion toward the middle between two sub swarm leaders and the motion relative to the middle between two randomly picked sub swarm members. In the benchmark assessment, BCA is compared with total interaction algorithm (TIA), coati optimization algorithm (COA), language education algorithm (LEO), osprey optimization algorithm (OOA), and walrus optimization algorithm (WaOA). The result shows that BCA is superior to these five contenders as it is better than TIA, COA, LEO, OOA, and WaOA in 18, 18, 16, 18, and 18 functions respectively out of 23 functions. [ABSTRACT FROM AUTHOR]

In the recent years, there are a lot of swarm-based stochastic optimization techniques i.e., metaheuristics were introduced. Most of these techniques were tested to solve the sets of theoretical functions. Some of them were enriched with practical tests where the common use cases are the mechanical engineering designs. On the other hand, the similar studies that utilized the optimization in power system are difficult to find. Moreover, the environmental issues become major considerations in engineering field. Based on this evidence, this paper constructs a new swarmbased optimization technique called stay-jump optimizer (SJO). The equal size swarm split is applied in the beginning of the process. Then, two directed searches toward the highest quality sub-swam members and two randomly selected higher quality sub swarm members are employed. The performance investigation is performed by employing SJO to find the optimal solution of 23 classic functions and the economic emission dispatch (EED) problem. The use-case for EED is the Java-Bali power grid system in Indonesia that consists of six steam power plants and two hydro-electric power plants. Five new optimization techniques including addax optimization algorithm (AOA), dollmaker optimization algorithm (DOA), giant armadillo optimization algorithm (GAO), zebra optimization algorithm (ZOA), and total interaction algorithm (TIA). The result shows that SJO is superior to its opponents as it is better than AOA, DOA, GAO, ZOA, and TIA in 17, 17, 16, 19, and 14 functions out of 23 functions respectively. SJO also becomes the best in the EED problem. [ABSTRACT FROM AUTHOR]

Metaheuristic has been utilized extensively to optimize power system. Meanwhile, the no-free-lunch (NFL) theory becomes the major consideration in the massive development of metaheuristic as there is not any ideal metaheuristic can solve all problems superiorly. Based on this problem, this work is aimed at introducing a novel metaphorfree swarm-based metaheuristic called iteration-controlled mixture optimizer (ICMO). ICMO contains three directed searches where the reference in each search is constructed by two entities. The first reference is the mixture between the finest entity and the mean of the finer entities. The second reference is the mixture between the finest entity and a randomly chosen entity. The third reference is the mixture between the finest entity and any generated entity within space. The portion between the first and second entities in each reference is controlled by the iteration. Then, ICMO is compared with five new swarm-based metaheuristics: attack leave optimization (ALO), total interaction algorithm (TIA), fully informed search algorithm (FISA), walrus optimization algorithm (WaOA), and ono-to-one based optimization (OOBO). The assessment result shows that ICMO is better than ALO, TIA, FISA, WaOA, and OOBO in 15, 13, 20, 12, and 20 functions out of 23 functions respectively. Then, ICMO is also challenged to solve the economic load dispatch (ELD) problem in the Java-Bali electricity system in Indonesia. The result shows that ICMO is competitive compared to these five metaheuristics in solving this practical problem. The result shows that the range between the best and worst metaheuristics in this problem is narrow as it represents the integer-based problem. [ABSTRACT FROM AUTHOR]

This article introduces a novel stochastic optimization method termed the Best-Other Algorithm (BOA). The nomenclature reflects its reliance on the best member, which is amalgamated with other entities. BOA, a metaphor-free swarm-based metaheuristic, comprises three directed searches. The first involves subtracting the best member from a randomly selected member. The second entails determining the midpoint between the best member, and another randomly chosen member. The third centers around the midpoint between the best member and a random solution along the space. The efficacy of BOA is evaluated by challenging it to solve a collection of 23 functions. In this evaluation, BOA is pitted against five other metaheuristics: Northern Goshawk Optimization (NGO), Zebra Optimization Algorithm (ZOA), Coati Optimization Algorithm (COA), Migration Algorithm (MA), and Osprey Optimization Algorithm (OOA). The findings indicate the superiority of BOA over its counterparts. BOA outperforms NGO, ZOA, COA, MA, and OOA in 21, 15, 16, 15, and 17 functions, respectively. These results underscore the pivotal role of the best member as a reference and the comparatively lesser significance of the neighborhood search as the search space diminishes during the iteration. [ABSTRACT FROM AUTHOR]

This paper promotes a new metaheuristic called the half mirror algorithm (HMA). As its name suggests, HMA offers a new kind of mirroring search. HMA is developed by hybridizing swarm intelligence and the evolution system. Swarm intelligence is adopted by constructing several autonomous agents called swarms. On the other hand, the evolution system is adopted using arithmetic crossover based on a particular reference called a mirror. Four mirrors are used in HMA: the best swarm member, a randomly selected swarm member, the central point of the space, and the corresponding swarm member. During the confrontative assessment, HMA is confronted with average and subtraction-based optimization (ASBO), total interaction algorithm (TIA), walrus optimization algorithm (WaOA), coati optimization algorithm (COA), and clouded leopard optimization (CLO). The result shows that HMA is superior to ASBO, TIA, WaOA, COA, and CLO in 20, 19, 19, 20, and 20 out of 23 functions, respectively. Moreover, HMA has found the global optimal of eight functions. It means the superiority of HMA occurs in almost entire functions. In the future, the mirroring search can be combined with the guided and neighborhood search to construct a more powerful metaheuristic. [ABSTRACT FROM AUTHOR]

There are two problems in the development of swarm-based metaheuristic. First, there are not any metaheuristic is able to solve all problems superiorly. Second, the cross-dimension mapping between the entity and its reference during performing the directed search is rare to find. Based on these problems, this work introduces a new metaphorfree swarm-based metaheuristic called the triple-shake algorithm (TSA). As its name suggests, TSA consists of three directed searches. The reference in the first search is the balance mixture between the finest entity and the member of permutation set. The reference in the second search is the balance mixture between the finest entity and a randomly chosen entity. The reference in the third search is the finest entity only. But the cross-dimension mapping is performed in this third search with 50 percent probability. In the benchmark assessment, TSA is compared with zebra optimization algorithm (ZOA), walrus optimization algorithm (WaOA), migration algorithm (MA), total interaction algorithm (TIA), and one-toone based optimization (OOBO). The result indicates the dominance of TSA among its comparators. TSA is better than ZOA, WaOA, MA, TIA, and OOBO in 21, 19, 17, 19, and 22 functions consecutively out of 23 functions. [ABSTRACT FROM AUTHOR]

The no-free-lunch (NFL) theory has become the main reason of developing new metaheuristics in decades. Besides, the strict dimension mapping has been implemented in many population-based metaheuristics, especially the swarm-based metaheuristics. Regarding this problem, this paper proposes a new swarm-based metaheuristics called focus and shake algorithm (FSA). FSA has novel approach in the dimension mapping between the agent and its reference during the directed motion. It combines the strict dimension mapping called as focus approach and the randomized dimension mapping called as shake approach to enhance its exploration ability. FSA deploys two directed motions based on two references. The first reference is constructed based on the balance mixture between two finer agents while the second reference is constructed based on the balance mixture of the finest agent and a randomly picked agent. In the competing assessment, FSA competes with five brand new swarm-based metaheuristics: migration algorithm (MA), total interaction algorithm (TIA), lyrebird optimization algorithm (LOA), osprey optimization algorithm (OOA), and kookaburra optimization algorithm (KOA). The result exhibits that FSA is finer than MA, TIA, LOA, OOA, and KOA in 19, 21, 21, 19, and 20 functions out of 23 functions respectively. The result also shows that the superiority of FSA takes place in both unimodal and multimodal problems. In the future, the cross-dimension mapping can be more explored to develop finer swarm-based metaheuristics. [ABSTRACT FROM AUTHOR]

This paper introduces a novel metaheuristic named the stochastic shaking algorithm (SSA), which is rooted in swarm intelligence principles. The innovation lies in its unique utilization of iteration for selecting references during guided searches through a stochastic approach. The optimization process involves two sequential steps: the primary reference in the first step is the finest swarm member, while in the second step, it is the mean of all finer swarm members plus the finest one. This primary reference is then combined with a randomly chosen solution within the space, serving as the secondary reference. SSA undergoes evaluation in two contexts. The first involves assessing its performance using a set of 23 classic functions as a theoretical use case. The second involves tackling the economic load dispatch problem (ELD), a practical use case featuring a system with 13 generators of various energy resources. The study compares SSA against five other metaheuristics--One to One Based Optimization (OOBO), Kookaburra Optimization Algorithm (KOA), Language Education Optimization (LEO), Total Interaction Algorithm (TIA), and Walrus Optimization Algorithm (WaOA). Results indicate SSA's superiority over OOBO, KOA, LEO, TIA, and WaOA in 21, 13, 11, 16, and 14 functions out of 23 functions, respectively. Additionally, the evaluation of the economic load dispatch problem reveals intense competition among the six metaheuristics. [ABSTRACT FROM AUTHOR]

In recent years, there is massive development of new metaheuristics as stochastic methods. Meanwhile, there is not any metaheuristics is powerful to handle all problems as stated in the no-free-lunch (NFL) theory. Based on this circumstance, this paper introduces a new swarm-based metaheuristics with the main strategy moving toward the resultant of better swarm members and avoiding the resultant of worse swarm members called group better-worse algorithm (GBWA). It consists of five searches: moving toward the best swarm member, moving toward the resultant of better swarm members, moving away from the resultant of worse swarm members, searching locally, and jumping to the opposite area. GBWA is then evaluated in three ways. The first evaluation is a comparative evaluation where GBWA is compared to five recent metaheuristics: coati optimization algorithm (COA), average and subtraction-based optimization (ASBO), clouded leopard optimization (CLO), total interaction algorithm (TIA), and osprey optimization algorithm (OOA). The second evaluation is the individual search evaluation. The third evaluation is hyperparameter test. The collection of 23 classic functions is chosen as the use case in all evaluations. The result of the first evaluation shows that GBWA is better than COA, ASBO, CLO, TIA, and OOA in 20, 21, 20, 21, and 21 functions consecutively. Meanwhile, the result of the second evaluation shows the equal contribution between the motion toward the best swarm member and the motion toward the resultant of better swarm members. [ABSTRACT FROM AUTHOR]

Many recent swarm-based metaheuristics are trapped in the exploitation of the highest quality as the main or the only reference and the neighbourhood search with the reduction of local search space during the iteration. Regarding to this issue, this paper introduces a novel metaheuristic called swarm space hopping algorithm (SSHA). SSHA consists of three searches. First, a directed search toward the highest quality is performed. Second, the directed search toward the resultant of better agents or away from the other agent is performed. Third, the arithmetic crossover between the agent and a randomized solution in the first half or second half of space is performed. In this work, three evaluations are performed to assess the performance of SSHA. The first evaluation is the benchmark evaluation to compare the performance of SSHA with other recent metaheuristics: northern goshawk optimization (NGO), zebra optimization algorithm (ZOA), clouded leopard optimization (CLO), osprey optimization algorithm (OOA), and total interaction algorithm (TIA). The result exhibits that SSHA is better than NGO, ZOA, CLO, OOA, and TIA in 21, 20, 17, 17, and 21 functions. In the second evaluation, the individual search evaluation to compare the contribution between the first and second searches is performed, with the result that the second search outperforms the first search. The third evaluation is performed to assess the contribution of the third search in the optimization process, and the result shows that the contribution of the third search is significant only in three functions. [ABSTRACT FROM AUTHOR]

This paper presents a new metaphor-free metaheuristic search called the swarm bipolar algorithm (SBA). SBA is developed mainly based on the non-free-lunch (NFL) doctrine, which mentions the non-existence of any general optimizer appropriate to answer all varieties of problems. The construction of SBA is based on splitting the swarm into two equal-sized swarms to diversify the searching process while performing intensification within the subswarms. There are two types of finest swarm members: the finest swarm member for the whole swarm and the finest swarm member in every sub-swarm. There are four directed searches performed in every iteration: (1) search toward the finest swarm member, (2) search toward the finest sub-swarm member, (3) search toward the middle between two finest sub-swarm members, and (4) search relative to the randomly picked swarm member from another sub-swarm. The performance of SBA is assessed through two assessments with a set of 23 functions representing the optimization problem. In the benchmark assessment, SBA is contended with five metaheuristics: northern goshawk optimization (NGO), language education optimization (LEO), coati optimization algorithm (COA), fully informed search algorithm (FISA), and total interaction algorithm (TIA). The result presents the superiority of SBA among its contenders by being better than NGO, LEO, COA, FISA, and TIA in 21, 16, 16, 21, and 18 functions. The single search assessment is performed to evaluate each strategy involved in SBA. The result shows that the search toward the middle between the two finest sub-swarm members is the best among the four searches in SBA. [ABSTRACT FROM AUTHOR]

A new swarm-based metaheuristic, namely the enriched coati osprey algorithm (ECOA), is proposed in this paper. As its name suggests, ECOA hybridizes two new metaheuristics, the coati optimization algorithm (COA) and the osprey optimization algorithm (OOA). ECOA is constructed by five searches performed sequentially by the swarm members. The first three are directed searches, while the last two are neighborhood searches. All three directed searches are adopted from COA and OOA. Meanwhile, the four-bordered neighborhood search is developed based on a new approach. During the assessment, ECOA was challenged to overcome the set of 23 functions and contended with five new metaheuristics: total interaction algorithm (TIA), golden search optimization (GSO), average and subtraction-based optimization (ASBO), COA, and OOA. The result shows that ECOA outperforms TIA, GSO, ASBO, COA, and OOA in 16, 23, 18, 21, and 21 functions. Meanwhile, the individual search test result shows that the directed searches perform better than the neighborhood searches. Moreover, the directed search toward the best member becomes the most dominant search. [ABSTRACT FROM AUTHOR]

There has been a massive development of metaheuristic algorithms in the latest decade where swarm intelligence becomes the fundamental approach. Meanwhile, there is still no ideal metaheuristic that can solve all problems superiorly, as declared in the no-free-lunch (NFL) theory. This work introduces a novel swarm-based metaheuristic named as migration-crossover algorithm (MCA). In MCA, the swarm intelligence is enriched with the crossover technique and the neighbourhood search with unbalanced local search space. The global finest solution becomes the reference in the first step while the middle between two stochastically chosen solutions becomes the reference in the second step. The neighbourhood search is performed in the third step. The collection of 23 functions become the use case during the evaluation of MCA. In the first evaluation, MCA is compared with five new metaheuristics: total interaction algorithm (TIA), osprey optimization algorithm (OOA), migration algorithm (MA), coati optimization algorithm (COA), and walrus optimization algorithm (WaOA). The result reveals that MCA is finer than TIA, OOA, MA, COA, and WaOA in 20, 19, 17, 20, and 17 functions subsequently. The result of the second evaluation reveals that the global finest solution becomes the dominant contributor in the high dimension functions while the middle between two stochastically chosen solutions becomes the dominant contributor in the fixed dimension functions. [ABSTRACT FROM AUTHOR]