13654 FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 39, No 1, March 2026, pp. 149 - 179 https://doi.org/10.2298/FUEE2601149C © 2026 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper CRISCROSS OPTIMIZATION (CCO)-BASED OPTIMAL DISPATCH STARTEGY FOR INTEGRATED HYDRO-THERMAL-WIND SCHEDULING Sunil Kumar Choudhary, Arindam Mondal Department of Electrical Engineering, Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India ORCID IDs: Sunil Kumar Choudhary https://orcid.org/0000-0001-8913-0000-0853 Arindam Mondal https://orcid.org/0000-0000-0003-3210-1685 Abstract. Incorporating renewable energy resources (RER) into standard power flow schedules is a complex optimization issue with multiple objectives and nonlinear characteristics. This matter necessitates the careful assessment of a multitude of economic and environmental concerns. This matter requires the evaluation of many restrictions related to disparities between races. The primary goal of generation scheduling is to minimize pollution emissions and costs over a limited time frame. This must be accomplished while ensuring that all system restrictions are adhered to. The Crisscross optimization (CCO) algorithm is used in this research to provide a novel method for solving the short-term hydro-thermal power scheduling (ST-HTPS) and short-term hydro-thermal-wind power scheduling (ST-HTWPS) issues. The suggested CCO method is compared to previously implemented particle swarm optimization (PSO) algorithms, moth-flame optimization (MFO) algorithms, and genetic algorithms (GA). This strategy makes convergence happen faster and solutions more precise while retaining a balance between exploration and exploitation. The proposed model takes into account real-time operational limitations, such as water balance equations, ramp rate limits, and wind uncertainty, to make sure that scheduling is both practical and effective. The suggested systems serve as study examples to evaluate the actual enhancement of the proposed CCO compared to PSO, MFO, PSO, and GA. The simulation outcomes indicate that the recommended CCO modeling offers a more advantageous option than previous heuristic techniques regarding financial considerations (36389.25 $/day) and reduced emissions (9436.29 lb/day). Despite considering the inclusion of several intricate constraints related to ST-HTWPS scenarios, these findings remain unaltered. Key words: Hydro-thermal-wind scheduling, renewable energy, non-linear constraints, optimization, Crisscross optimization (CCO) Received May 05, 2025; revised July 25, 2025, and August 22, 2025; accepted August 29, 2025 Corresponding author: Arindam Mondal Department of Electrical Engineering, Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India E-mail: arininstru@gmail.com 150 S. K. CHOUDHARY, A. MONDAL Nomenclature i, j, k : The relative indexes for thermal, hydro, and wind power units , ,T T TC F W : Total expense, fuel expense, and wind expense, in that order t h wN ,N ,N : Quantity of all thermal, hydro, and wind units combined τ,T : Time sub-interval and Scheduling period, respectively Up : The reservoir's upstream index τhj,τhj, I,Q : Rate of intake and discharge of the jth hydro unit, respectively ti,τ hj,τ wk,τP ,P ,P : Thermal, hydro, and wind of ith, jth, and kth at τ τhj,τhj, S,V : Reservoir volume and spillage of jth hydro unit τ respectively τL,τd, P,P : Total demand and transmission loss at τ τwk,τwk, UEC,OEC : Over and underestimation cost of kth wind at τ iiiii ε,δ,γ,β,α : Emission co-efficient of ith thermal unit iiii d,c,b,a : Cost co-efficient for ith thermal unit ii h,e : Co-efficient of the valve point effect of ith thermal unit ( )1-6 jC : Hydropower output co-efficient of jth hydro unit max ti min ti P,P : Minimum and maximum power limit of ith thermal unit max hj min hj P,P : Minimum and maximum power limit of jth hydro unit max hj min hj Q,Q : Minimum and maximum discharge limit of jth hydro reservoir max hj min hj V,V : Minimum and maximum volume limit of jth hydro reservoir max hj min hj V,V : Minimum and maximum volume limit of jth hydro reservoir end hj begin hj V,V : Initial and final storage volume of jth hydro reservoir 1. INTRODUCTION In the current context, the issue of global warming has emerged as a significant cause for alarm, mainly attributable to the escalating pollution resulting from the extraction of energy from fossil fuels across the world. Moreover, many current energy extraction methods rely heavily on finite fossil fuel supplies. Conversely, renewable resources are associated with certain limitations, such as a relatively low energy density and inherent variability in their availability. Hence, it is imperative to prioritize the scheduling of generation in thermal- renewable energy systems to sustain economic progress while adhering to environmentally conscious practices. The integration of wind energy into the energy industry has become increasingly economically viable, rendering it particularly useful in scheduling. 1.1. Literature Review The investigation of cost optimization advancement in hydrothermal scheduling has been a subject of study among researchers for a considerable period. Their study proposed a method for ST-HTPS that incorporates an adaptive chaotic differential evolution (DE), genetic Criscross Optimization (CCO)-Based Optimal Dispatch Startegy for Integrated Hydro-Thermal- Wind Scheduling 151 algorithm (GA), adaptive chaotic artificial bee colony algorithm, and differential real-coded quantum-inspired evolutionary algorithm [1-4]. A previous study suggested utilizing volatile wind power with superconducting high-temperature superconductors ST-HTPS to meet security constraints. The authors have proposed a classical model for short-term power scheduling of hydro-thermal-wind systems that incorporates uncertainties in wind power and considers economic and environmental restrictions [5-6]. To address the difficulties related to the incorporation of large wind power capacity, researchers have used a bee colony optimization (BCO) technique [7]. The ant lion optimization (ALO) algorithm was proposed to address the challenge of allocating resources for non-conventional forms of generation [8-12]. An empirical method to get the best explanation of hydrothermal-wind scheduling includes the optimization techniques to optimize the generation cost under varying conditions. This algorithm takes into consideration both economic and environmental factors. Scientists have explored many types of empirical algorithm categories to find solutions to problems related to ST-HTWS concerns [13-16]. Some examples of these include the extended NSGA-III [15], particle swarm optimization (PSO) [17], parallel particle swarm optimization (PPSO), gravitational search algorithm (GSA) [18], probability interval optimization (PIO), and several other population-based optimization methods [19-21]. Various empirical algorithms that take their cues from natural occurrences and use random optimization techniques have been developed in recent years. Teaching learning-based optimization (TLBO) is one example of such an algorithm; it has demonstrated encouraging results when used to solve the ST-HTWPS problem [22-23]. Table 1 summarizes several optimization techniques used by different studies in Hydro-Thermal-Wind Scheduling (HTWS). Table 1 Summarizing various optimization algorithms applied to Hydro-Thermal-Wind Scheduling (HTWS) by different researchers Optimization Algorithm Key Features Reference Particle Swarm Optimization (MPSO) Enhanced local search capability; reduced generation cost and emissions [17], [39], [45], [47], [53] Improved Cheetah Optimization (ICO) Addresses renewable uncertainties; integrates wind resources [55], [56] Genetic Algorithm (GA) Reduced generation cost and emissions; high search capability for complex scheduling problems. [2], [20] Ant Lion Optimization (ALO) Effective for large-scale wind-hydro-thermal scheduling problems. [8], [11], [12] Artificial Bee Colony (ABC) Algorithm Cost-effective generation and emissions; high search capability for complex scheduling problems [3], [7] Teaching learning-based optimization (TLBO) Applied to hydro-thermal scheduling with wind energy resources. [22], [50], [58] Modified Adaptive Selection Cuckoo Search Algorithm (MASCSA) Fixed-head short-term model; effective for large-scale systems [57] Non-dominated Sorting Gravity Search Algorithm (NSGSA) Multi-objective optimization handles various constraints effectively [6], [15], [59] Hybrid Gravitational Search Algorithm (GSA) Combines thermal, wind, and hydro frameworks; a hybrid optimization technique [18], [49], [51] Chaos-Assisted Sine Cosine Algorithm (CA-SCA) Incorporates chaos theory; improves local search for global optimal solutions [60], [61] 152 S. K. CHOUDHARY, A. MONDAL The essential purpose of the research was to find ways to cut down on the amount of fuel used by the multi-objective function while still considering a wide variety of complicated constraints. The study results suggest that implementing crisscross optimization (CCO) may significantly decrease fuel expenditures and emissions compared to well-established approaches [24-32]. In addition, improved performance was accomplished by resolving the ST-HTWPS problem, which can be shown in terms of the convergence characteristics and distribution diversity. As a result, it is a strategy that has the potential to be successful in dealing with the problem of ST-HTWPS. A novel approach was introduced to optimize the performance of wind-based hybrid energy systems using a multi-objective stochastic strategy [26]. In addition, the recently introduced opposition-based learning (OBL) approach has been employed to address the load dispatch issue in renewable wind energy systems, increasing convergence speed and performance accuracy in optimization-based scheduling models [27-28]. In this work, [29] described a rapid non-dominated sorting TVAC-PSO to solve multi-objective economic emission dispatch issues. The authors proposed a constraint- handling strategy using the differential evolution algorithm to address the dynamic economic emission dispatch problem [30] and examined the relationship between economic growth and the intensity of carbon dioxide emissions [31]. The author of this essay successfully addressed the issue of short-term hydrothermal scheduling by considering the unpredictable nature of renewable energy sources. Furthermore, the Gram-Charlier formula has been used to ensure the proper distribution of the output random variables [33-40]. The primary purpose of the crow search algorithm (CSA) is to reduce the overall production cost [36]. The primary focus is on the foraging behavior of crows. The CSA method has the benefit of including additional tuning elements with population size and number of repetitions. This aids the algorithm in answering different types of goal functions. However, decreasing the tuning value will limit the algorithm's maximum capability and hinder performance optimization for a specific objective. The efficacy of the CSA algorithm is assessed by examining several assessment platforms with varying numbers of generating units. The findings were previously evaluated against the ALO [12], MFO [34, 52, 62], Hybrid chemical reaction optimization [63, 64], and DA computations [35, 41]. This study introduces an upgraded version of the Beluga Whale Optimizer (EBWO) [66], Equilibrium Optimizer (EO) [67], Moth-flame Optimizer (MFO) [68], and Chaotic Artificial Ecosystem Optimizer (CAEO) [69] that can handle the economic load dispatch [64] issue in big power systems. It does this by speeding up convergence and improving the quality of the solutions compared to other approaches. 1.2. Research Gap The research gap is found in the literature review. Although Crisscross Optimization (CCO) seems to have very good results for scheduling problems involving hydro-thermal scheduling coupled with wind energy resources, further research is necessary. Finally, though CCO successfully mitigates hydro-thermal scheduling optimization challenges, its performance in highly dynamic and uncertain environments, and affliction by the impact of lightning-fast weather changes on wind energy, also warrants investigation. Moreover, the applicability of CCO to more complex, real-world energy grids, particularly in large- scale power systems with multiple interdependent renewable sources, has not been fully validated. While most current studies have been based on static or simplistic models, Criscross Optimization (CCO)-Based Optimal Dispatch Startegy for Integrated Hydro-Thermal- Wind Scheduling 153 real-time wind energy scheduling, along with rapid fluctuations in water availability across hydro resources and vice versa, necessitates a more adaptive and robust optimization framework. In addition, integrating CCO with advanced methods of forecasting wind [54] and water availability is not been explored extensively for further improving scheduling accuracy. This creates a setting for using CCO-based scheduling methods in a more resilient, responsive, and renewable integrated power system [57]. Even though renewable energy sources are becoming more common in modern power systems, figuring out the best way to schedule multi-source generation, especially when it comes to hydro, thermal, and wind units, remains a difficult and nonlinear problem because renewables are random, there are operational limits, and resources are dependent on each other. When things get this complicated, traditional optimization approaches frequently have trouble with how quickly they converge and how accurate their solutions are. This paper, then, defines the best way to use an integrated hydro-thermal-wind system as a restricted nonlinear optimization problem and suggests a Crisscross Optimization (CCO)-based technique to solve it in the best way possible. The main goal is to keep the system reliable and follow all of its rules while keeping the total generation cost as low as possible. 1.3. Main Contributions According to the literature review, the main contributions in the proposed work are as follows: ▪ Enhanced Optimization Efficiency: By showing its ability to efficiently traverse complex, high-dimensional search spaces, CCO has also been able to converge faster and find better solutions to multidimensional hydro-thermal scheduling problems with wind energy integration. ▪ Improved Cost-Effectiveness: The CCO algorithm provides an optimization of the cost allocation amongst hydro, thermal, and wind resources for still lower operational costs compared to conventional scheduling. ▪ Greater System Reliability: CCO-based models have improved power supply reliability by incorporating wind energy in the hydro-thermal scheduling process. The algorithm makes sure that no reliance is put on thermal power; rather, it exploits renewable sources of energy. Moreover, the renewable energy rating matches the overall demand profile and the grid's ability to handle electricity that comes and goes without breaking dependability or stability rules. The grade is also chosen to see how well the CCO algorithm can deal with the unpredictability, fluctuation, and intermittency that come with renewable power. The study makes sure that the CCO algorithm's performance can be fairly and reliably compared by including renewable energy sources with genuine ratings in the optimization problem. This choice helps to fairly evaluate how well CCO works at ensuring cost-effective and dependable dispatch when renewable resources are unreliable and changeable. The subsequent sections of this work are structured in such a way as to present the mathematical formulation of scheduling that was discussed in Section 2. The Crisscross optimization (CCO) algorithm and its application in the current study are the topics that will be covered in the third section of this paper. The fourth portion of the paper presents an in-depth analysis of the test system and a discussion of how the simulation works and the results. In section 5 of the document, you will find the conclusion to the work. 154 S. K. CHOUDHARY, A. MONDAL 2. MATHEMATICAL FORMULATION OF ST-HTWPS The primary objective of this endeavor is to provide a scheduling framework for power generation that integrates hydrothermal, wind, and other forms of renewable energy resources. This framework will include both economic and environmental aspects. The inherent impulsiveness of renewable energy supplies adds another layer of complication to the problem of scheduling generation [42-47]. 2.1. Formulation of Multi-objective Function The amount of electricity a hydroelectric project generates does not affect the facility's price. When planning for hydro-thermal generation, it is essential to factor in the total cost of generation, which considers the cost of coal used in thermal plants and the costs involved with generating electricity from wind sources. In the scenario that has been presented, the primary objective is to achieve the lowest possible value for the objective function, which includes the total cost of generation associated with thermal, wind, and hydropower facilities while simultaneously adhering to all of the system limits that are taken into consideration for scheduling. The following is an illustration of a mathematical formulation that may be applied to explain a regressive multifaceted function: ... ( , , )T T T TMin C F E W= (1) ( ), , , ,1 1 1 ... ( ) ( )t wT N N T ti i wk wk wk wki k Min C P E P C OEC UEC     = = = = + + + +   (2) The amount of power that hydroelectric plants can generate can be mathematically described as a function of the head and the reservoir’s volume. 2 2 , 1 2 3 , , 4 , 5 , 6, ,( )hj j j j hj hj j hj j hj jhj hjP c V c Q c V Q c V c Q c     = + + + + + (3) Where Qhj and Vhj represent the water discharge and reservoir storage volume, respectively, of the jth hydro plant during the τth interval. c1-c6 represents the power generation coefficients of the jth hydro plant. The regressive multifaceted (1) function can be reconstructed as: Minimize ( ) T T i T T C F h E W= +  + (4) 2.1.1. Economic objective The fuel cost function in a thermal power plant is represented mathematically as a quadratic function of the actual power production. This representation takes into consideration the impacts of valve points (5). The mathematical elaboration of this idea might be stated as follows: ( )( )2 min , , ,1 1 sin ( )tT N T i ti i ti i i i ti tii F a P b P c e f P P   = =  = + + + −    (5) 2.1.2. Environmental objective As global air pollution becomes more severe, there is an increased emphasis on protecting the environment and reducing emission pollutants from conventional power units. Burning Criscross Optimization (CCO)-Based Optimal Dispatch Startegy for Integrated Hydro-Thermal- Wind Scheduling 155 coal (fossil fuels) is the primary source of pollution emissions in the power system. The combustion of sulfur oxides (SOx) and nitrogen oxides (NOx) may be accurately modeled using a combination of quadratic and exponential functions [49], as seen in Equation (6). The amount of power that can be produced at a coal-fired power station determines the amount of pollution that that facility can release into the atmosphere. The total amount of pollutants released into the environment can be modeled as: ( )2 . , ,1 1 exp( ) lb./hrtT N T i ti i ti i i i tii P P P        = =  = + + +  E (6) 2.2. Probability distribution of wind generation To address the ST-HTWPS issue, our first concern should be devising strategies to manage the inherent unpredictability of wind generation. When attempting to convey the stochastic character of wind speed profiles, the Weibull probability density function (PDF) technique [48] is often used. The PDF of the Weibull distribution may be stated in the following manner: ( ) exp ( 0) (s-1) s v s v v f v = × . - s > c c c                      (7) Here, C and s are positive values representing the scale-factor and shape-factor, respectively. V represents the present velocity of the wind turbine. The cumulative- density function (CDF) may be derived from the wind speed PDF. ( ) 1 exp s v v F v c    = − −      (8) The generation of wind power is dependent on wind velocity, and some researchers employ a linear model to explain the connection between the two variables. This model may be described as follows: 0 ( , ) ( ) ( ) ( ) ( ) in out r in in r r in r r out v v v v w v v w v v v v v w v v v     − =   −    (9) The vr, vin, and vout are the rating wind speed, the cut-in wind speed, and the cut-out wind speed. The estimated power of a wind-turbine speed is wr. w  [0,wr] stands for wind power output. According to Equation (10), when the wind speed is positioned between vin and vr, the P-DF of w may be represented as follows: 1 ( ) 1 / .exp 1 / s s in w in in r T T shv hw hw F w v c v c w c w w −          = − − −                    (10) where, 1r in v h v   = −    . Eq. (11, 12) is mostly used to represent continuous probability. The expressions for the discrete probability where w = 0 or wr are as follows: 156 S. K. CHOUDHARY, A. MONDAL ( 0) ( ) ( ) 1 exp exp s s in out r in r out v v P w P v v P v v c c        = =  +  = − − + −                (11) ( ) ( ) 1 exp exp ss outr r r in out vv P w w P v v v c c       = =   = − − + −               (12) 2.3. Generation cost of wind generation Dissimilarity in wind speed is a highly imperative factor in converting wind energy into usable form. Three distinct aspects go into determining the overall cost of operating and maintaining a wind generator, which is as follows: a) The concept of direct cost refers to the expenses that can be directly ascribed to a particular activity or project. b) Indirect costs cannot be immediately assigned to an activity or project. c) Underestimation cost refers to the potential financial ramifications that may develop due to the expected costs for a project or activity being lower than the actual expenses incurred for that project or activity. d) The term "overestimation cost" refers to the financial ramifications that arise when the expected expenses for a project or activity end up being higher than the actual expenditures that have been incurred [48]. The following is an example of a mathematical equation that may be used to indicate the cost of producing power using a wind generator: ( ), , ,1 1 wT N T wk wk wk wkk W C P OEC UEC   = = = + +  (13) Extracting useful resources, such as electricity from the wind, is more commonly known as utility extraction. This procedure has a direct cost, a linear function of the power used. ( ) = = =  wNT wk wk,τ k wk,τ τ 1 k 1 C P d P (14) The primary determinant of wind power prediction accuracy is the degree of uncertainty associated with the availability of wind energy. The penalty cost-function for overestimating the kth wind power may be expressed as follows. , , , , , , , , ,1 , , . 1 exp exp exp exp 1 1 k k k k s s in k out k r k in k k k k r k in k s s in k r k k k k r k in k v v w v w c c v v v w cv c c v v                = − − + − +           −                         − − − +           −            + wk,τ o,kOEC c ,1 1 1 k ks s in k k k k k vv k c k c             −  +                  (15) The penalty cost-function associated with the underestimation of the kth wind power may be expressed in the following manner. Criscross Optimization (CCO)-Based Optimal Dispatch Startegy for Integrated Hydro-Thermal- Wind Scheduling 157 , , , , , , , 1 , , , , , , .( ) 1 exp exp exp exp k k k k s s r k out k r k k k s s r k in k r k k r k in k k k r k k r k in k v v w w c c w v v v w v v c c w c v v                = − − − + − +                              + − − − +          −             − wk,τ u,kUEC c ,1 1 1 1 1 k ks s in k k w k k vv s c s c               + −  +                      (16) The variables OECwk,τ, and UECwk,τ represent the expenses associated with overestimation and underestimation, respectively. The cost coefficients are represented by the variables Co,k, and Cu,k. The wind generator's rated speed, cut-in, and cut-out wind speeds are denoted as vr,k, vin,k, and vout,k, respectively. The rated wind output power is denoted as wr,k. The notation represents the power generated by the wind at the τth time interval. 2.4. Non-linear Constraints The operational limits of the generator are the primary component of the restrictions that are related to ST-HTWPS. Additional limitations encompass the capacity of the storage reservoir and restrictions on discharge levels, another important constraint. The hydrological equilibrium within the reservoir is shown in the following manner. , , 1 , , , ( ) ( ) uj mj mj R hj hj hj hj hj hm t hm tm V V I Q S Q S      − − −= + − − + + (17) The initial reservoir-storage volume is, and the final reservoir-storage volume is. ,0 ,hj hj beginV V= (18) ,T ,endhj hjV V= (19) The maximum allowable generation for thermal power units is given as maxmin ( =1,2,3.... )ti ti ti tP P P i N  (20) The maximum allowable hydropower is given as maxmin ( =1,2,3.... )hj jhj hjP P P j N  (21) The maximum allowable generation of wind power units is given as 0 ( 1,2,..... )rated wk wwkP P k N  = (22) The maximum allowable storage volume for the reservoir is listed below. maxmin ,, ,hjhj hjV V V   (23) 158 S. K. CHOUDHARY, A. MONDAL The maximum amount of water that can be released from the reservoir is listed below. maxmin ,, ,hjhj hjQ Q Q   (24) The power balancing constraint for the power system can be written as: , , , , ,1 1 1 t h wN N N ti hj wk D Li j k P P P P P    = = = + + = +   (25) 3. CRISSCROSS OPTIMIZATION The crisscross optimization (CCO) technique, which is detailed in reference [38], is a population-based heuristic approach that has shown excellent efficiency in solving non- convex optimization problems with a high number of dimensions. Employing two interdependent crossover operators is one of the distinguishing characteristics of CCO. This is because horizontal crossover and vertical crossover work in tandem. The horizontal crossover method is a method that is used to find a novel solution by investigating a subset of the population, precisely half of the population, which is separated into different hyper-cubes. The method's name comes from the fact that it crosses over from one subset of the population to another. As one approaches closer to the cores of these hyper-cubes, the possibility of discovering a new answer becomes progressively less likely. The probability is highest near the edges of the hypercube. It is common knowledge that employing a cross-border strategy is an efficient way to reduce the impact of blind spots and enhance one's ability to conduct global searches. Vertical arithmetic crossover, on the other hand, is utilized by the vertical crossover technique to deliver unique solutions. The difference between vertical crossover and horizontal crossover may be seen very clearly. This distinctive characteristic is crucial in preserving population variety and enabling the departure from regional minimums in fixed dimensions. The employment of both crossover operators, which generate offspring solutions according to the parent solutions, ultimately leads to the generation of a moderation solution during each iteration of the process. By the concept of "survival of the fittest," moderation solutions are utilized to modify the pre-existing dominant solutions within parent populations. This stage is essential for ensuring the presence of solutions that have enhanced fitness values and is, therefore, very important. The choice of Crisscross Optimization (CCO) as the best dispatch approach for integrated hydro-thermal-wind scheduling is based on its unique ability to solve difficult, nonlinear, and very limited optimization issues that are frequent in multi-source power systems. CCO uses both horizontal and vertical crossover algorithms, which lets it do a strong global search while keeping the solution space diverse. This two-dimensional search method helps CCO avoid converging too soon and makes it better at finding numerous optimum areas at the same time. CCO is different from classic algorithms like GA, PSO, or DE since it keeps a good balance between exploration and exploitation. This makes it perfect for dynamic and unpredictable situations like wind-integrated systems. CCO is also computationally efficient since it needs fewer control parameters and converges faster, which is important for scheduling in real time or close to real time. It can handle both discrete and continuous variables, which makes it perfect for mixed- integer hydro-thermal scheduling issues. Because of these benefits, CCO is a strong and Criscross Optimization (CCO)-Based Optimal Dispatch Startegy for Integrated Hydro-Thermal- Wind Scheduling 159 new way to find cost-effective, dependable, and environmentally friendly dispatch solutions in modern power systems. Thus, employing a CCO technique makes it easier for individuals to rapidly converge on their personal best fitness values, as shown in Figure 1. The flowchart of the implemented CCO algorithm is depicted in Fig. 2. The stages involved in the development of CCO are as follows. Step 1: Initialize To enhance the efficiency of a problem-solving process, a Computational Search Optimization (CCO) algorithm first generates a population. { } 1,2,.....mP P m M= = , where 1 1( , ,..... )m m m m DP P P P= (26) P can be generated by min max min( )m i i i i jP P P P= + − i=1, 2… D; m=1, 2… M (27) Step 2: The second step entails carrying out a horizontal crossover plan with an organization that is in direct competition with you. In the case that we have been presented with, the individuals that are contained within the set P are split up into pairs without any repetition, namely M/2 pairings, to make the process of horizontal crossover more manageable. To carry out the horizontal crossover procedure at the dth dimension, The process of moderation helps to select the most appropriate response.  ( )  ( ) 1 1 1 2 2 2 ( ) ( ) (1 ). ( ) . ( ) ( ) ( ) ( ) (1 ). ( ) . ( ) ( ) i i j i j j j i j i MH d r P d r P d C P d P d MH d r P d r P d C P d P d = + − + − = + − + − (28) As a result, the CCO algorithm keeps a population in X that is made up of individuals' best replies. Step 3: Carry out the crossing by making use of the alternative operator. Random pairing of the dimensions that make up set P ensures that no two dimensions will ever appear together in the same pair. Let us take into consideration a situation in which the dimensions d1 and d2 that are paired together are employed in the process of accomplishing vertical crossing. The solution for moderation is constructed based on 1 1 2 1 2 ( ) . ( ) (1 ). ( ); (1, ), , (1, )m m mMV d r P d r P d m N M d d N D= + −   (29) Fig. 1 Diagrammatic representation of the crisscross optimization (CCO) algorithm 160 S. K. CHOUDHARY, A. MONDAL K+1 Begin Initialize a population of feasible solutions in the matrix X. The vertical crossover probability is set to be 0.7 For d1th dimension of all normalized individuals X(i): Reproduce MH according to (29) Yes No Gen=gen+1 Yes No Deal with the inequality constraints (15)-(17) Update X MH @X gen>MaxIterEnd s=s+1 Normalize the minimum and maximum values of each column in X to [0, 1] K=0 K< M/2 For each paired individuals: X(i) and X(j) Reproduce MH according to (28) Deal with the inequality constraints (17)-(25) Update X MH@X S=0 S