1. Introduction
After achieving successful results of privatization in several sectors, i.e., telecommunication, toll plaza, airlines, and many more, the reformation of the power industry was also started. The reformation of the power industry is termed the restructuring or deregulation of the electricity market (EM). The reason for deregulation in the EM is to restrict the monopolies of government or government authorities and provide a competitive platform for suppliers and buyers [
1]. A competitive platform in the EM forces the generators to evaluate the cost in such a manner that they are in a risk-free zone. To reduce the risk of loosening the game with uncertainties of monopolistic market structure leads the EM to innovate a new structure of market termed oligopolistic market structure [
2].
Due to certain limitations, i.e., large investment size, transmission constraints, transmission losses, etc., there are a limited number of buyers and sellers in an oligopolistic market. The aim of both buyer and seller in an oligopolistic market is to maximize their profit. All applicants submit their bids (for quantity (MW) and price ($/MW)) in a sealed envelope to the system operator (SO). The SO will finalize the market clearing price (MCP) after receiving the bids from all applicants (supplier and consumer). MCP is the effective price of the market that is found by the crossing point of the supply and load curve. In pay as bid market, market price is set through uniform price clearing mechanism; greater is the bid revenue greater the profit. Thus, every generating company (Genco) bids higher to attain higher profit but they jeopardy of losing the competition with this higher bid. Thus, for a Genco to catch an optimal bid in an oligopolistic market is a complex problem and is known as the strategic bidding problem of a Genco. Many researchers were published their work on strategic bidding problems due to their stochastic rather than deterministic nature. In these research articles, stochastic optimization approaches were used to solve this stochastic problem.
The three ways as given in the literature to solve strategic bidding problems in the EM are the game theory-based, dynamic based approaches and stochastic based approaches. Game theory approaches assumes that rival GENCO’s cost functions and complete bid information are public. This is practically not true. Additionally, multiple Nash equilibriums required for large number of players. Dynamic optimization techniques such as Lagrange Relaxation, Dynamic Programming, etc. These techniques fail for realistic non-differentiable, multi constraint and multi-objective problems and require nonlinear simplification, if adopted. Stochastic based approach gives accurate results, fast convergence, global optimum solution and reliable solution tools in an EM [
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22].
In [
3], the authors consider a methodology called the fuzzy adaptive particle swarm optimization for a thermal generator in a uniform price spot market, taking into account a precise model of nonlinear operating cost function and unit commitment minimum up/down limitations. The normal PDF is used to model the bidding behavior of other competing Genco’s. In [
4], researchers offer particle swarm optimization (PSO) algorithms for determining market price and volumes in a competitive power market in this work. To locate solutions, the first approach combines a traditional PSO algorithm. The second approach combines the PSO strategy with a decomposition technique. This new decomposition-based PSO outperforms the traditional PSO significantly. In this research [
5], a new agent-based simulation model based on the Ant Colony Optimization (ACO) algorithm is developed to compare three different wholesale electricity markets clearing strategies, namely uniform, pay-as-bid, and extended Vickery rules. In this study [
6], a unique computational intelligence technique for solving the Nash optimization issue is presented. This novel process is based on the PSO algorithm, which employs the SA method to prevent particles from becoming caught in local minima or maxima and improve particle velocity functions. Other computer intelligence techniques such as PSO, Genetic Algorithm (GA), and a mathematical method (GAMS/DICOPT) are compared to the results of this operation. The IEEE 39-bus test system is used to demonstrate and validate the suggested technique’s outcomes.
In order to optimize its own profit as a market participant, the article [
7] provides a new approach for bidding strategy in a day-ahead market from the perspective of a generating business (GENCO). The fuzzy adaptive gravitational search algorithm (FAGSA) is used in a unique stochastic optimization approach to tackle the optimal bidding strategy problem in a pool based power market [
8]. In this research [
9], a unique algorithm based on the Shuffled Frog Leaping Algorithm is used to address the optimal bidding strategy problem (SFLA). It is a memetic meta-heuristic that does a heuristic search to find a global optimal solution. It combines the advantages of the Memetic Algorithm (MA) based on genetics with the Particle Swarm Optimization (PSO) based on social behavior. As a result, it has a more precise search, which prevents premature convergence and operator selection. As a result, the suggested method overcomes the limitations of the Genetic Algorithm (GA) and the PSO method in terms of operator selection and premature convergence. In this study [
10], a new strategy for developing optimal double-sided bidding strategies in security-constrained power sector is described, with pollution emission as a secondary goal. Both Generation Companies (Gencos) and Distribution Companies (DisCos) in the suggested algorithm seek to maximize their profit by implementing optimal strategies, despite the fact that they have imperfect knowledge about the rivals and the market mechanism of payment is locational marginal pricing. The optimal bidding strategy is developed using a hybrid technique based on information gap decision theory (IGDT) and modified particle swarm optimization (MPSO) in this work [
11].
In order to handle the profit maximizing process in a continuously changing market, a novel form of Grey Wolf Optimizer (GWO) called the Intelligent Grey Wolf Optimizer (IGWO) is developed by the authors [
12]. The Krill Herd algorithm (KHA) is used to develop an optimal bidding strategy in this article [
13]. Supplier and buyer bidding coefficients are carefully chosen. The proposed KHA’s code was written in MATLAB. It was put through its paces on an IEEE 30 bus power system. The Invasive Weed Optimization technique was used to solve the Optimal Bidding Strategy problem in this paper [
14]. The utilities compete in order to maximize their profits. The proposed technique was written in MATLAB and tested using the IEEE 30 bus standard. Authors [
15] present an alternate methodology for determining revenue-maximizing strategic bids when the opponents’ bidding strategy is uncertain. To achieve an optimal bidding strategy in the electricity market, a hybrid architecture combining metaheuristic and supervised learning is proposed in this study [
16]. The Salp Swarm Algorithm (SSA) is combined with a neural network in the suggested architecture (NN). The suggested architecture is compared to the results of SSA and Opposition-based SSA on the IEEE-14 bus system, IEEE-30 bus system, and 75-bus Indian Practical System (OSSA). To ensure increased effectiveness, a selected learning approach for strategic bidding is presented in the paper [
17]. The suggested system uses an ensemble technique, in which many machine learning algorithms are used to predict the price and give a bidding recommendation. The most appropriate ones will be chosen to dominate the bidding approach as the clearing iteration advances.
In this work [
18], author presents a model of neural network using Harris Hawk optimizer (HHO) to solve the problem of optimal bidding in the EM. The issue that arises when a group of small prosumers participate in the energy market is discussed in this study [
19]. The aggregator takes advantage of the appliances’ flexibility to lower market net costs. There are two optimization techniques suggested. In order to reduce the cost of acquiring energy, how can a time-shiftable load, which may itself be made up of a number of smaller time-shiftable subloads, submit its demand bids to the day-ahead and real-time markets? This is the topic that this study [
20] aims to address. In this study [
21], authors tackle the issue of competitive bidding for a big price-maker regulatory resource in performance-based regulation markets. In order to assist an aggregator of prosumers in defining bids for the day-ahead energy and secondary reserve markets, this study [
22] offers a two-stage stochastic optimization model.
In this research work, a new variant of Whale Optimization Algorithm (WOA) [
18], named AWOA, is proposed for solving the optimal bidding problem in a day-ahead EM. WOA is a recently developed meta-heuristic algorithm [
23] and as seen from the past research papers that, WOA performs very well on real life applications [
24,
25,
26,
27,
28]. The WOA is a revolutionary nature-inspired meta-heuristic optimization algorithm that replicates the social behavior of humpback whales. The bubble-net hunting methodology motivated the algorithm. Twenty-nine mathematical optimization problems and six structural design challenges are used to evaluate WOA in [
23]. To estimate short-term wind power, a hybrid forecasting model based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) and Whale Optimization Algorithm (WOA)-Kernel Extreme Learning Machine (KELM) is designed to deal with the intermittent and fluctuating characteristics of wind power time series signals [
24]. CEEMD first reduced the non-stationary wind power time series into a number of generally stationary components. In this study [
25], authors suggest a hybrid model that is an evolution of the hGADE algorithm for addressing the Unit Commitment Scheduling Problem, a mixed-integer optimization problem. For the computation of the overall operation cost of power system operation, the Whale Optimization Algorithm was used. In [
26], simulations are run on a test smart grid with loads varying in two service zones, one for residential consumers and the other for commercial users. By comparing the findings with spider monkey optimization and biogeography-based optimization, WOA demonstrates its usefulness. Simulation results show that the proposed demand side management solutions save money while lowering the smart grid’s peak load demand. The electric power system is examined in two phases in this paper [
27]: decentralized and centralized ways to reduce operational costs. The Tuned Whale Optimization Algorithm (TWOA), a new artificial intelligence technique, is used to solve these phases. The IEEE 48-bus power system is used to accomplish these concepts. The IEEE 48-bus system is made up of two zones connected by transmission lines. Variations in TWOA’s regulating factors are also discussed.
The whale optimization technique for loss minimization employing FACTS devices in the transmission system is reported in this article [
28]. This investigation will use a thyristor controlled series compensator (TCSC). In this research, WOA is used to determine the appropriate FACTS device size for power system loss minimization. To verify the effectiveness of the suggested technique, an IEEE 30-bus RTS was employed as the test system. Opposition-based leaning [
29,
30,
31,
32] and CM operator [
33,
34,
35,
36] are fused with WOA and experimented with over 23 benchmark functions (unimodal, mutimodal, and fixed-dimension multimodal).
The benefits of OEL and Cauchy mutation that are listed below have encouraged authors to use these in WOA in light of this research review. These qualities are listed below:
The curse of dimensionality problem can be solved with the help of the OEL paradigm. Due to the issue of formulating strategic bidding, the huge search space and stochastic nature of the variables make the curse of dimensionality inevitable (rival bids). The job of locating a global optimum in dynamic simulations might thus be challenging. A unique solution to this issue is provided by OEL, which also offers a way out of the neighborhood minima trap. By generating opposing points in the search space, OEL improve any algorithm’s exploration capabilities;
The characteristics of probable candidates that can address the strategic bidding dilemma should assist them in avoiding premature convergence. Due to the inclusion of stochastic variables throughout the simulation process, the issue of premature convergence in the strategic biding problem is significant. The introduction of OEL improves convergence speed while also guarding against premature convergence of the solver;
By boosting the exploratory power of whales with Cauchy distribution, Cauchy operator aids in preventing the stagnation in local optimums. Thus, the greedy selection maintains a healthy balance between the current and prior placements of whales while the Cauchy operator aids in enhancing the capacity of whales in terms of exploration and exploitation.
The WOA modified version of WOA is then applied for the bidding problem in dynamic EM. To solve this problem there are two critical parameters such as convergence of the algorithm and clarification superiority. Convergence problems are intently related to the fitness value and computation time which may be stimulating revenue and workout market circumstances. To train the rival’s performance four probability distributions are used namely: Normal, Lognormal, Gamma, and Weibull PDF [
37] that is built from past market data analysis. Framing a bidding method with incomplete information about rival behavior is a huge assignment for the design engineer. Monte Carlo (MC) simulations [
38] are considered powerful gear as they can be hired as sampling, optimization, and assessment gear. For the optimization of strategic bidding trouble, those MC simulations are employed wherein the goal feature is deterministic and randomness is brought artificially to greater emerald search [
39]. The above-discussed application and unique feature of MC simulations inspire authors to employ MC simulations in strategic bidding problems. Slow convergence and being stuck in local optima are issues with WOA. The amended WOA method is a novel, nature-inspired heuristic technique that is proposed in this research as a means of overcoming these shortcomings when solving the strategic bidding dilemma. This strategy serves as an alternative to other current, recent algorithms. After having a bird’s eye view of the literature about the strategic bidding problem following research objectives are outlined for this manuscript:
- (a)
To test the Amended Whale Optimization Algorithm (AWOA) on benchmark functions and resolve issue of bidding in the EM by confirming enhanced exploration and an optimum exploitation of search space through Oppositional Enabled Learning (OEL) and Cauchy Mutation (CM) Operator;
- (b)
To search the performance of this novel variant i.e., AWOA with parent WOA (Whale Optimization Algorithm) and some recently developed algorithms are applied on benchmark functions;
- (c)
To achieve different statistical assessments with Wilcoxon rank sum, box plot analysis and convergence investigation for the testing the effectiveness of the developed model;
- (d)
To construct rival bidding prices using (normal, lognormal, gamma and Weibull) PDF, interpret them using the MC approach, and design a bidding strategy for the day-ahead market by entrancingly taking into account all inter-temporal limits;
- (e)
To represent a fair evaluation between the outcomes acquired through optimization procedure based on profit, MCP (Market Clearing Price) calculation and solution quality.
The rest of the article is prepared as shown in
Figure 1.
2. Problem Statement
To decipher the issue of strategic bidding in this article, we assumed m+1 Generating Companies (Genco’s). Genco-k is the generator whose profit has to be maximized by finding the optimal bids with m competitors in the energy market. In the EM, all the m+1 Genco’s and consumers submit their bids in a sealed envelope (contains quantity (MW) and price ($\MW)) to the system operator (SO). After the last date of submission of bids from supplier and consumer, the SO arranges the supplier’s bids in increasing order, and consumer’s bids in decreasing order where X-axis represents quantity (MW) and Y-axis shows the price($\MW). The point where both curves intersect each other is the called the equilibrium point and after drawing a horizontal line from that point to Y-axis, market clearing price (MCP) is received.
A Genco can bid for multiple (maximum l) blocks. It is preferable to bid on multiple blocks rather than just one at a time to ensure financial security. The rival’s bidding block size is supposed to be acknowledged from the past data and their bidding prices are deliberate by Probability Distribution Factor (PDF) through probability statistical analysis of historical bidding data. In this paper, we generate the input data using four different types of PDFs [
32]. Thus, we create four cases to solve the problem.
Case I. The Normal distribution;
Case II. The Lognormal distribution;
Case III. The Gamma distribution;
Case IV. The Weibull distribution.
Before a unit is committed/not-committed, there is already a least-defined time subsequent of which it can be not-committed/committed again. Inter-temporal operating limits of Genco-K, such as minimum/up and minimum/downtimes have been regarded in the effort. Considering non-differentiable, non-convex cost function, nonlinear (exponential) start/up cost function, and constant shut/down cost, the operating cost function for the lth block of Genco-K is expressed as:
where
Due to the consecutive opening of a large number of valves to obtain ever-increasing output of the unit, input-output characteristics for large thermal generators are not always smooth [
40]. A rippling effect on the unit curve is common as each steam admission valve in a turbine begins to open. [
41] Approximated the rippling effect of valve point loading as a periodic rectified sinusoidal function. [
42] Established the effect of valve point loading on economic dispatched output of units, confirming the need of applying a precise production cost function in strategic bidding. Equation (2) signifies this sinusoidal nonlinear characteristic, in which c
0, c
1, and c
2 are cost coefficients and c
3 and c
4 are the coefficients of the valve point loading impact. An exponential characteristic is considered in Equation (3), to signify the association between the start-up value and the shut-down time. Although, any present start/up cost characteristic can be used. The value received in begin-up and begin/down is united inside the running cost characteristic so that the actual advantage is taken into consideration and the Genco’s are committed/not-committed accordingly. The OBS for Genco-k can be achieved with profit maximization in the terms of output power dispatched (
) and MCP (
). The product of
and
is defined as revenue acquired. The increasing profit of lth blocks of the Genco-k overtime period “T” is uttered as:
Subject to constraints
- 2.
Minimum uptime
- 3.
Minimum downtime
- 4.
Limitations on the bid price
The optimization limits described in (4)–(8) may be explained to acquire the finest block bid price of the lth block of Genco-K at hour t, signified as pl(t). In (4), pl(t) and
do now not clearly emerge but those are indirectly involved within the procedure of decisive MCP. Equations (5)–(7) are the operating constraints, while (8) looks like it represents the bid price limit, i.e.,
. With the usage of the PDF’s defined above competitor’s bidding prices may be received from past bidding records. Formation of the Optimal Bidding Strategy (OBS) for Genco-k, with objective function (4) and constraints (5)–(8), be remodeled a stochastic optimization concern, to be resolved by MC founded WOA. The data taken in
Table 1 is used to generate the competitor’s bidding data for all the cases explained above. We generate 1000 competitor’s bidding samples in 3 blocks as shown in
Figure 2.
In following section, research methodology is presented.
5. Application of AWOA on Strategic Bidding Problem
The inclusion of OEL has significantly improved the exploration and exploitation capabilities of WOA, as is clear from the findings presented in the preceding section. This section now explores how the developed variant can be used to the strategic bidding challenge. We used the proposed version on a case study involving power systems to demonstrate the effectiveness of the proposed variant. This test case simulates a strategic bidding situation where Generating company-k (Genco-k) competes in an auction with four competitor for the IEEE-14 bus test system.
To test the efficacy of the proposed AWOA, a numerical example is presented based on the problem formulation in
Section 2. In rapidly evolving environments, this problem is formulated and bidding strategies for a day-ahead market are built for multi-hourly trading.
Figure 9 displays a daily load curve for 24 h.
The parameters of all three blocks of Genco-k are given in
Table 8 [
3].
The bidding performance of competitors is represented in this test case as illustrated in
Figure 2. The opponent bid limit size, mean and standard deviations for all blocks for a normal distribution are provided in [
40]. In this case, we used a normal probability distribution. The problem of attaining OBS is solved by AWOA, WOA, GWO, SCA, MFO, GSA and ALO. After successful testing, the results are shown in
Figure 10, in this we observed that the outcomes of AWOA are competing and yield more profit for the Genco-k for a multi exchanging hour in a day-ahead market. Optimal block bid price and MCP of Genco-k using a normal distribution with AWOA algorithm shown in
Figure 11. In this figure bidding prices of Genco-k in 3 blocks are given with MCP.
The profit curve and MCP obtained by AWOA is shown in
Figure 11. From the figure, it is concluded that AWOA outpaces over the competitors as the profit computed by this algorithm is suggestively greater. A steep surge in the profit is perceived in the 10th hour and 12th hour as the profit of the Genco-k becomes
$15,478 and
$18,667 respectively. Fall in MCP results in fall in profit this phenomenon can be observed in the results of block 2, where the profit reduces drastically at 13th hour. This fall in MCP is observed from (36.87
$/MWh) to (25
$/MWh). At 14th hour again the profit goes more due to the high MCP
$32.13. Cumulative profit calculated through AWOA is
$180,616.
Table 9 shows the LD calculated using the WOA method for each generator taking part in an auction with a standard MCP. The N-D status in the table denotes units that were not deployed because of a high bid offer.
Table 9 also displays the conducted results for the Genco-k from algorithm AWOA using standard PDF.
- i.
The third block of Genco-k is not dispatched during the hours with a negative benefit (from 1 to 8 h) due to its high production cost and low system demand;
- ii.
Due to the third block’s prolonged shutdown, cold startup costs are included in its production costs when it is committed at nine hours (8 h);
- iii.
At the end of 12th h, 3rd block is again non-dispatched due to low system demand, and minimum down time constraint is active (4 h);
- iv.
Third block is again dispatched at 15th h, and hot start-up cost is accounted in the making cost, because it has been shut-down for a short time (2 h);
- v.
Third block is again non-dispatched from 20 to 24 h due to low system demand;
- vi.
Optimal bid price of 3rd Block is shown zero during 1–8 h, 13–14 h, 18 h and 20–24 h, when it is non-dispatched.
In this case study, we used a lognormal probability distribution. After successful testing, the results are shown in
Figure 12. The optimal block bid price and MCP of Genco-k using a lognormal distribution with AWOA algorithm are shown in
Figure 13.
The profit curve derived by AWOA is shown in
Figure 12. This number makes it obvious that AWOA outperforms the rest of the opposition since the profit determined by this algorithm is much higher. The profit of the Genco-k rises dramatically in the 10th and 15th hours, reaching
$13,489 and
$13,515, respectively. For block 2, the profit decreases sharply in the 13th hour. The total profit as determined by AWOA is
$185,362.5.
Table 10 presents the LD obtained from AWOA for all the Genco’s competing in a market under a uniform MCP. In
Table 10 N-D signifies the non-dispatched units due to offering of high bids by the Genco. The amount of unit dispatched attained from AWOA using lognormal PDF for the Genco-k are also shown in
Table 10.
- i.
The third block of Genco-k is non-dispatched in the hours of negative profit (from 1 to 7 h) because of its great production cost and small system load;
- ii.
Because the third block has been shut-down for a while, the cost of a cold start-up is included in its production costs when it is dispatched at 8 h (7 h);
- iii.
The third Block is once more not dispatched at the end of 12th hours due to low system demand, and the minimum downtime constraint kicks in at 13th hours;
- iv.
Due to a short period of shutdown, the third block’s hot start-up cost is included in this hour’s output costs when it is dispatched at 14th h (1h);
- v.
The third block is again non-dispatched from 20th h to 24th h due to decrement in the system load;
- vi.
Optimal bid price of the third Block is shown as zero during 1–10 h, 13–14 h, 16–24 h, when it is non-dispatched.
In this case study, we used a gamma probability distribution for constructing the rival behavior. After successful testing, the results are shown in
Figure 14. Optimal block bid price and MCP of Genco-k using gamma distribution with AWOA algorithm are shown in
Figure 15.
The profit curve obtained by AWOA is shown in
Figure 15. This number makes it obvious that AWOA outperforms the rest of the opposition since the profit determined by this algorithm is much higher. The profit of the Genco-k rises sharply to
$15,478 in the tenth h and
$18,667 in the 12th h, respectively. For block 2, the profit decreases significantly at the 13th hour as a result of the MCP dropping from 28.51 to 24.03 dollars per megawatt hour. Due to the high MCP
$29.39, the profit increases once more at the 14th hour. The total profit as determined by AWOA is
$180,616.
Table 11 displays the LD determined by the WOA algorithm for each generator taking part in an auction with a standardized MCP. The N-D status in
Table 11 denotes units that were not dispatched because of a high bid offer.
Table 11 also displays the transmitted results for the Genco-k from algorithm AWOA utilizing gamma PDF.
- i.
The third block of Genco-k is non-dispatched in the hours of negative benefit (from 1 to 9 h) because of its great production cost and small system demand;
- ii.
When the third block is dispatched at 10th hours, the cost of a cold start-up is taken into consideration because it has been idle for a while (9 h);
- iii.
Due to low system demand at the end of the 12th hour, the third block is once more not dispatched, and the minimum downtime constraint is in effect (3 h);
- iv.
The third block is re-dispatched at the 13th hour, and as it was briefly shutdown; the hot start-up cost is included in the production cost of this hour;
- v.
Due to less system load, the third block was once again not dispatched from 20 to 24 h;
- vi.
The optimal bid price of the third block is shown as zero during 1–9 h, 13–14 h and 18–24 h, when it is non-dispatched.
In this case study, we used the Weibull probability distribution. After successful testing, the results are shown in
Figure 16. The optimal block bid price and the MCP of Genco-k using Weibull distribution with AWOA algorithm are shown in
Figure 17.
The profit curve obtained by AWOA is shown in
Figure 17. This number makes it obvious that AWOA outperforms the rest of the opposition since the profit determined by this algorithm is much higher. The profit of the Genco-k rises sharply to
$15,478 in the 10th h and
$18,667 in the twelfth hour, respectively. For block 2, the profit drops significantly at the 13th h as a result of the MCP falling from 34 to 21.42 dollars per megawatt hour. Due to the high MCP
$31.43 at the fourteenth hour, the profit increases once more. The total profit as determined by AWOA is
$180,616.
Table 12 displays the LD determined by the WOA algorithm for each generator taking part in an auction with a standardized MCP. The N-D status in
Table 12 denotes units that were not dispatched because of a high bid offer.
Table 12 also displays the transmitted results for the Genco-k from algorithm AWOA utilizing Weibull PDF.
- i.
Block 3 of Genco-k is not supplied during the hours of adverse benefit due to its high manufacturing cost and less system needs (from 1 to 8 h);
- ii.
Because the block 3 has been shut-down for a while, the cost of a cold start-up is included in its production costs when it is dispatched at nine hours (8 h);
- iii.
At the conclusion of 12th h, the third block is once more not delivered due to decrement in system demand, and the minimal downtime constraint is in effect (4 h);
- iv.
The third block is re-dispatched at 15th h, and because it was shut-down for a brief period of time, the hot start-up cost is included in the cost of production for this hr;
- v.
The third block is again non-dispatched from the 20th to 24th h due to less system load;
- vi.
Optimal bid price of the third block is exposed zero during 1–8 h, 13–14 h and 20–24 h when it is non-dispatched.
The supremacy of the AWOA method is established through the evaluation of simulation results with former methods. Results of
Figure 18 evidence that the finest block bid price resolute by the AWOA delivers high profits than that gained by the former methods such as WOA, GWO, SCA, ALO, MFO and GSA using four different PDFs i.e., Lognormal, Normal, Gamma, and Weibull. Thus, it approves that the AWOA is well skilled in describing the results near-global OBS. After analyzing the dispatched status of the units as suggested by AWOA, it is observed that the AWOA is able to have more dispatched units as compared to other optimization algorithms. Hence, the results of AWOA has been showcased.