Combined Heat And Power Economic Dispatch Problem Research Articles

Solving large-scale combined heat and power economic dispatch problems by using deep reinforcement learning based crisscross optimization algorithm

The extensive interconnection in bulk power systems brings great challenges in the economic dispatch problems, especially the large-scale combined heat and power economic dispatch (CHPED), which is quite intractable due to complex thermal and electrical couplings in cogeneration units. Most meta-heuristic algorithms cannot work well while considering non-convexity, discontinuity, and non-differentiability. Particularly, when it comes to the high dimensional and large-scale CHPED problems, these algorithms are either easy to trap in the local optimum or quite time-consuming. To address these issues, a novel deep reinforcement learning (DRL) based crisscross optimization (CSO) algorithm is proposed for the first time, which can (1) improve the searching ability of CSO, (2) enhance the overall searching efficiency, and (3) perform extraordinarily well for the large-scale CHPED problems. Firstly, to further improve the global search ability, DRL is employed to reduce dimensionality and narrow the search space of the initial population of the CSO algorithm. Then, DRL is updated by the deep deterministic policy gradient (DDPG) strategy, which can facilitate an instantaneous decision in accelerating CSO. Thereafter, by adopting each decision provided by DRL, a great difference may occur in the same scenario to speed up the crossover procedure and guide the upcoming search round. On this basis, the enhanced CSO algorithm could quickly carry out crossovers with search space contraction and dimensionality reduction. Finally, experiments on four test systems have substantiated the effectiveness of the proposed algorithm, especially the superiority over other state-of-the-art techniques in solving large-scale CHPED problems.

Solving the Combined Heat and Power Economic Dispatch Problem in Different Scale Systems Using the Imperialist Competitive Harris Hawks Optimization Algorithm.

The aim of electrical load dispatch (ELD) is to achieve the optimal planning of different power plants to supply the required power at the minimum operation cost. Using the combined heat and power (CHP) units in modern power systems, increases energy efficiency and, produce less environmental pollution than conventional units, by producing electricity and heat, simultaneously. Consequently, the ELD problem in the presence of CHP units becomes a very non-linear and non-convex complex problem called the combined heat and power economic dispatch (CHPED), which supplies both electric and thermal loads at the minimum operational cost. In this work, at first, a brief review of optimization algorithms, in different categories of classical, or conventional, stochastic search-based, and hybrid optimization techniques for solving the CHPED problem is presented. Then the CHPED problem in large-scale power systems is investigated by applying the imperialist competitive Harris hawks optimization (ICHHO), as the combination of imperialist competitive algorithm (ICA), and Harris hawks optimizer (HHO), for the first time, to overcome the shortcomings of using the ICA and HHO in the exploitation, and exploration phases, respectively, to solve this complex optimization problem. The effectiveness of the combined algorithm on four standard case studies, including 24 units as a medium-scale, 48, 84, units as the large-scale, and 96-unit as a very large-scale heat and power system, is detailed. The obtained results are compared to those of different algorithms to demonstrate the performance of the ICHHO algorithm in terms of better solution quality and lower fuel cost. The simulation studies verify that the proposed algorithm decreases the minimum operation costs by at least 0.1870%, 0.342%, 0.05224%, and 0.07875% compared to the best results in the literature.

Optimal solution of the combined heat and power economic dispatch problem by adaptive fitness-distance balance based artificial rabbits optimization algorithm

Combined heat and power economic dispatch (CHPED) problem is one of the most widely handled, optimization problem by researchers in modern power systems. CHPED problem is a complicated, non-continuous, and non-convex optimization problem due to the constraints. Moreover, considering the valve-point loading effect (VPLE), transmission losses (TLs), and prohibited operating zones (POZs) of power-only units as constraints, the complexity of CHPED problem increases. Therefore, a powerful optimization algorithm needs to be introduced to find global solution that meets all constraints. In this paper, a novel adaptive fitness-distance balance based artificial rabbits optimization (AFDB-ARO) is developed to solve CHPED problems. AFDB-based guiding mechanism was implemented to enhance the exploration capability of ARO and to strengthen exploitation-exploration balance. A comprehensive experimental study was realized to prove the performance of the proposed algorithm on the CHPED and benchmark problems. In experimental study between AFDB-ARO variants and ARO on 40 benchmark problems, according to Wilcoxon analysis results, all AFDB-ARO variants outperformed the base ARO, and the best AFDB-ARO variant won victory in 20 of 40 problem and achieved similar results in other 20 problem. In other experimental study, AFDB-ARO algorithm was implemented on the CHPED systems with 4-, 5-, 7-, 24-, 48-, 96-, and 192-units, and fifteen case studies were considered using these systems, VPLE, TLs, and POZs. One of the important points of this study was that POZs were considered for the first time in 96- and 192-units system. The results show that AFDB-ARO achieved the best optimal solution in ten of fifteen cases, was same in one case, and obtained almost same results in four cases compared to the literature. Moreover, the stability of the AFDB-ARO and base ARO algorithms in solving the CHPED problem were tested by performing stability analysis. While the mean success rate, mean iteration number, and mean search time were obtained 87.62%, 353.63, and 2.91 sec of AFDB-ARO, respectively, ARO managed to find the optimal solution in two cases. Thus, the superior performance of AFDB-ARO algorithm is confirmed by experimental studies and analysis against ARO algorithm. The source codes of the AFDB-ARO algorithm (proposed method) can be accessed at this link: https://www.mathworks.com/matlabcentral/fileexchange/136846-afdb-aro-an-improved-aro-algorithm-for-optimization-problem.

A new solution approach for non-convex combined heat and power economic dispatch problem considering power loss

The combined heat and power economic dispatch (CHPED) problem is a non-convex multivariate global optimization problem. The objective of the problem is to reduce total production costs while imposing a variety of constraints and meeting the demand for power and heat. Three recently presented metaheuristic approaches, Slime Mould Algorithm (SMA), COOT algorithm and Marine Predators Algorithm (MPA), are applied for solving CHPED problem. Studies dealing with the CHPED problem in the literature often do not consider valve points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, all at once. Furthermore, power losses are neglected especially in large-scale problems. In this study, the CHPED problem is solved by considering all operational constraints including active power transmission losses. Three separate case studies with dimensions of 11 units, 48 units, and 96 units were used in the tests under various limitations. The experimental results revealed that MPA outperformed not only SMA, and COOT but also the algorithms proposed previously in the literature.

A novel multi-agent based crisscross algorithm with hybrid neighboring topology for combined heat and power economic dispatch

Combined heat and power economic dispatch (CHPED) is a challenging optimization problem with characteristics like non-convexity, discontinuity, and non-differentiability. Although the crisscross optimization (CSO) algorithm can alleviate the premature convergence faced by most swarm optimization algorithms, it has a slow convergence speed to approximate the global optimum, especially at the late period of evolutionary process. To address the issue, a novel hybrid neighboring topology based multi-agent crisscross algorithm (HNT-MACSO) is proposed to enhance the balance ability of exploration and exploitation. First, based on the graph theory, the population particles of CSO are structured with two topologies, i.e., the random topology and the small world topology respectively. Second, a hybrid neighboring topology is established by applying the information relay register, aiming to improve the robustness of CSO. Third, the separate CSOs assigned to different topologies are deployed on a multi-agent system (MAS), which enables a flexible and robust distributed evolving environment for all agents to search in an independent and asynchronous optimization manner. Furthermore, five cogeneration systems are tested, and experimental results show that the proposed HNT-MACSO outperforms other state-of-the-art algorithms in terms of solution accuracy and runtime, which confirms the effectiveness and superiority of HNT-MACSO for large-scale CHPED problems.

An elitist cuckoo search algorithm for combined heat and power economic dispatch

Combined heat and power economic dispatch (CHPED) is one of the foremost subjects in the operation of power systems. In this article, a new variant of cuckoo search (CS) algorithm, elitist CS (yECS), is advanced to tackle CHPED. During the optimisation process of the original CS as well as lots of its variants, the guidance of search directions relies merely upon the best individual, causing the loss of other beneficial information and further influencing their performance potentials. Therefore, in yECS, an elitist mechanism is developed to fully utilise the beneficial information of other elite individuals. Specifically, three new iterative strategies are developed, one for the global search phase and the other two for the local search phase. Further, a coordinated mechanism is put forward to effectively integrate the local iterative strategies, thus helping yECS in maintaining an appropriate balance between exploitation and exploration. The superior performance of yECS is firstly substantiated via CEC 2017 test suite and two engineering design problems and then it is utilised to address CHPED problems. All optimal dispatch results acquired by yECS are feasible and in most cases display remarkable improvements over the results determined by other CS variants and some recently-published literature results.

Neighborhood-based differential evolution algorithm with direction induced strategy for the large-scale combined heat and power economic dispatch problem

The combined heat and power economic dispatch (CHPED) problem is a complicated non-convex optimization problem with several constraints that has been a challenging and important task in the power system. Great efforts have been made to solve the small-scale CHPED problem, and there is considerable scope for research in the large-scale CHPED problem with lots of local optima. This paper presents a neighborhood-based differential evolution algorithm with direction induced strategy (NDIDE) to solve the large-scale CHPED problem. In NDIDE, a novel mutation strategy, named neighborhood nonelite direction induced strategy based on DE/rand/1 (DE/ldrand/1), is proposed to explore some untrodden areas of a search space using the direction information of pointing to inferior solutions within a small neighborhood. Such a strategy helps to strengthen the exploitation of some selected neighborhoods. Consequently, a good balance between exploration and exploitation abilities could be achieved. NDIDE is implemented on the CHPED systems with 7, 84, 96 and 192 units. The dispatch schedules obtained from NDIDE are feasible in three large CHPED systems and show the advantages of NDIDE in terms of cost savings and the robustness over the results obtained by three state-of-the-art differential evolution algorithms as well as recent works in this field.

Optimization of Combined Heat and Power Systems by Meta-Heuristic Algorithms: An Overview

Combined heat and power (CHP) plants are known as efficient technologies to reduce environmental emissions, balance energy costs, and increase total energy efficiency. To obtain a more efficient system, various optimization methods have been employed, based on numerical, experimental, parametric, and algorithmic optimization routes. Due to the significance of algorithmic optimization, as a systematic method for optimizing energy systems, this novel review paper is focused on the meta-heuristic optimization algorithms, implemented in CHP energy systems. By considering the applied objective functions, the main sections are divided into single-objective and multi-objective algorithms. In each case, the units’ combination is briefly detailed, the objective functions are introduced, and analyses are conducted. The main aim of this paper is to gather a database for the optimization of CHPs, demonstrate the effect of the applied optimization methods on the objective functions, and finally, introduce the most efficient methods. The most significant feature of this paper is that it covers all types of CHP optimization issues including scheduling, sizing, and designing problems, finding the extent of each optimization issue in the relevant papers in the last decade. Based on the findings, in the single-objective problems the combined heat and power economic dispatch (CHPED) issue as a subcategory of the scheduling problems is introduced as the most paid topic; the designing issue is known as the lowest paid topic. In the multi-objective problems, working on various types of CHP optimization problems has been conducted with an almost similar share. The combined heat and power economic emission dispatch (CHPEED) problem with the most share, and the sizing issue with the lowest share. The CHP designing and sizing optimization issues could be introduced as topics to work on more in the future. Additionally, the numerical results of CHPED and CHPEED problems solved by various algorithms are presented and compared. In this regard, specified test systems are considered.

Improved SNS algorithm with high exploitative strategy for dynamic combined heat and power dispatch in co-generation systems

The principal aim of the combined heat and power economic dispatch (CHPED) is to optimize power generation, heat generation, and both heat and power obtained from co-generators with consideration of fuel cost minimization and a variety of constraints. In this article, the CHPED issue is studied using a newly proposed Strong Exploitation Strategy (SES) with Social Network Search (SNS) optimizer to form an improved SNS (ISNS) to increase the performance of the SNS by boosting the searching around the best view of all users. In addition to this, an adaptable parameter to aid in the exploitation of iterations, in the end, is proposed. The proposed strategy and the adaptable parameter aim to reduce the generation cost and improve its convergence rate. Additionally, the presence of transmission losses and valve point effect is added to the constraints. The efficacy of ISNS is proven through four examples corresponding to multiple test systems, ranging in size from seven units to ninety-six units with transmission losses and valve point loading effects constraints. The proposed ISNS’s minimal, mean, and maximum generation costs are all near to each other which demonstrates its robustness. Moreover, the applications are tested and carried out with the power and heat loading conditions at daily variation. The results manifest that ISNS is an efficient method and a good candidate for handling small-scale, medium-scale, and large-scale CHPED problems.

A hybrid chameleon swarm algorithm with superiority of feasible solutions for optimal combined heat and power economic dispatch problem

Combined heat and power economic dispatch (CHPED) is a challenging important optimization task in the economic operation of power systems that aims to minimize the production cost by scheduling the generation and heat outputs to committed units. The interdependency of heat and power production of the CHPED task exhibits non-convexity and non-linear natures in its modeling and optimization. Therefore, this paper introduces a novel hybrid approach comprising chameleon swarm algorithm (CSA) and mayfly optimization (MO), named CSMO, for solving the CHPED problem. The proposed CSMO algorithm has a better capability to evade from the trapping in local optima with faster rate of convergence pattern than the traditional CSA. Also the proposed CSMO algorithm employs the MO’ phase to assist the CSA to search based on deeper exploration/exploitation capabilities as MO utilizes two populations of male and female mayflies with crossover-based matting process. The effectiveness of the proposed CSMO algorithm is validated on CEC 2017 benchmark functions and two systems of the CHPED problem. The obtained results are compared with some successful optimizers. The simulation outcomes are portrayed based on the number of occasions where CSMO performs superior/equal/inferior to the other optimizers by considering the smaller mean values obtained by each algorithm for all test suites. Accordingly, it is exposed that the occasions achieved by the proposed CSMO are 29/1/0, 30/0/0, 30/0/0, 28/2/0, and 30/0/0 against some implemented algorithms, i.e., ISA, GOA, GBO, EO, and the original CSA. Similarly, the number of occasions achieved by the proposed CSMO are 30/0/0, 30/0/0, 30/0/0, 30/0/0, 30/0/0, 29/1/0, and 22/2/6 when the simulations are portrayed against some competitors from literature including the PSO, FA, FFPSO, HPSOFF, HFPSO, HGSO, and Q-SCA, respectively. Furthermore, the results of total cost found by CSMO are 9257.07 $/h for system 1 and 10094.25 $/h for system 2 of the CHPED problem, with percentage of improvement 0.02% and 14.42% on the original CSA, respectively. In addition, further assessments based on the Wilcoxon test, and convergence characteristic are reported. Based on the recorded results, it is portrayed that the CSMO can efficiently deal with the CEC 2017 benchmark functions and CHPED problem.

A Piecewise Linearization Approach to Non-Convex and Non-Smooth Combined Heat and Power Economic Dispatch

The important role of electricity generation in the power system is evident and is growing more and more with innovative technologies and requirements. Hence, addressing the combined heat and power economic dispatch (CHPED) as one of the relatively new issues in the power system operation and control is more importance. Since the CHPED problem is a non-smooth, highly non-linear, and non-convex one, it is required to solve it so that an optimal global solution can be achieved. In this paper, by applying the piece-wise linearization approach the CHPED problem is solved so that the problem reformulated to a quadratic optimization problem with linear and quadratic constraints. To demonstrate the applicability of the proposed model, four case studies are implemented in the GAMS software environment and the results compared to the literature.

A hybrid Grasshopper Optimization Algorithm and Harris Hawks Optimizer for Combined Heat and Power Economic Dispatch problem

The Combined Heat and Power Economic Dispatch (CHPED) is a real-world optimization problem with several complex constraints that has been a topic of studies around energy systems and optimization processes. This paper attempts to conceptualize a potent algorithm by combining the Modified Grasshopper Optimization Algorithm (MGOA) and the Improved Harris Hawks Optimizer (IHHO) for attaining a better balance between the beginning stages of global search and the latter stages of global convergence. The proposed attempt is abbreviated as MGOA-IHHO. Firstly, the chaotic and Opposition-Based Learning (OBL) methods are invoked to generate the initial population. Second, the mathematical model of the conventional Grasshopper Optimization Algorithm (GOA) is modified using Sine–Cosine Acceleration Coefficients (SCAC) to simulate the global exploration at the initial iterations and graduating to the global convergence at the final stages of optimization. Hence, it is named MGOA. Finally, the adaptive search mechanism integrates the two improved search phases of HHO with a search phase of MGOA to improve the performance of the proposed optimization method. This mechanism investigates the best solution for the aging level of the individual during the optimal evaluation process for choosing an appropriate search phase in MGOA-IHHO. The intended effect of the proposed MGOA-IHHO method is verified with other nature-inspired methods on standard single-objective test functions including 23 benchmark problems, 30 test suits of IEEE Congress on Evolutionary Computation 2017 (CEC2017), and four CHPED problems. The statistical results ascertain that the proposed hybridized MGOA-IHHO is capable of providing promising results when compared with its variants and optimization algorithms introduced in the literature.

An Amalgamated Heap and Jellyfish Optimizer for economic dispatch in Combined heat and power systems including N-1 Unit outages

One of the critical optimization issues in the economic management of power and heat systems is the Combined heat and power economic dispatch (CHPED). The valve-point effects of thermal units as well as the interdependency of CHP outputs make the nonlinearity and non-convexity in optimization and dispatch models. A novel Amalgamated Heap-based and JellyFish Optimizer (AHJFO) is proposed, in this paper, to improve the efficiency of two newly developed techniques, Heap-based Optimizer (HO) and Jellyfish Optimizer (JFO). The proposed AHJFO incorporates an adjustment strategy function (ASF) to increase the explorative characteristic at the beginning of iterations by upgrading the produced solutions using HO. Further, as iterations go, it improves the exploitative characteristic by expanding the created solutions using JFO. The proposed AHJFO provides higher effectiveness compared to HO and JFO to obtain the solution of CHPED problem for medium 24 and large 96-unit systems. The simulation results show that the proposed AHJFO based on ASF aids in the avoidance of premature convergence and improves solution accuracy. Besides, the proposed AHJFO is successfully applied to the CHPED issue involving (N-1) unit outages. A re-dispatch strategy based on AHJFO is presented and the impact of outages of all units is analyzed after (N-1) unit outages. Also, further applications of the proposed AHJFO for ED problem are carried out with/without additional constraint models of power flow considering the IEEE 30-bus system. The simulation results show the superiority of the proposed AHJFO compared to HO, JFO and other algorithms for solving the CHPED and ED issues. Moreover, feasibility study is demonstrated of the solutions obtained for the CHPED and ED issues with additional constraint models.

Solution of Combined Heat and Power Economic Dispatch Problem Using Direct Optimization Algorithm

This paper presents the solution to the combined heat and power economic dispatch problem using a direct solution algorithm for constrained optimization problems. With the potential of Combined Heat and Power (CHP) production to increase the efficiency of power and heat generation simultaneously having been researched and established, the increasing penetration of CHP systems, and determination of economic dispatch of power and heat assumes higher relevance. The Combined Heat and Power Economic Dispatch (CHPED) problem is a demanding optimization problem as both constraints and objective functions can be non-linear and non-convex. This paper presents an explicit formula developed for computing the system-wide incremental costs corresponding with optimal dispatch. The circumvention of the use of iterative search schemes for this crucial step is the innovation inherent in the proposed dispatch procedure. The feasible operating region of the CHP unit three is taken into account in the proposed CHPED problem model, whereas the optimal dispatch of power/heat outputs of CHP unit is determined using the direct Lagrange multiplier solution algorithm. The proposed algorithm is applied to a test system with four units and results are provided.

Society-based Grey Wolf Optimizer for large scale Combined Heat and Power Economic Dispatch problem considering power losses

Combined Heat and Power Economic Dispatch (CHPED) reflects a momentous optimization and operation problem in the power systems for optimally allocating the produced heat and power to the committed Power-only (PO), Heat-only (HO), and CHP units. In this work, a new society-based optimization algorithm using social hierarchy of grey wolves, namely Society-based Grey Wolf Optimizer (SGWO) is proposed for the CHPED problem. This scheme divides the group of wolves to some societies so that each society has its own leader. These leaders follow the dominant wolf and also guide their societies in which the classification of wolves is based on the social hierarchy. Moreover a novel attacking and hunting the prey is suggested to change the effects of dominant, ordinate, and subordinate wolves in their new roles in societies. In order to verify the capabilities of the SGWO, simulations are conducted through two large-scale CHPED problems with the related challenges like Valve-Point Loading Effect (VPLE) and Prohibited Zones (PZ) of PO units, mutual dependency of produced heat and power of CHP units, and especially transmission power losses. Moreover, it is evaluated on twenty-three standard functions to verify its stability on different low- and high-dimensional functions. Comparisons based on the obtained solutions by different methods demonstrate the robustness and superior performance of the presented technique to fast provide better optimum point (more economical benefits) and solution quality meeting all equality and inequality constraints. In addition, the results of CHPED indicate that ≈0.5% reduction in the production cost results in up to $2.6−$34×106 increase in Annual Cost Saving (ACS). Also, the transmission losses and PZs of POs can increase the production cost by about 1.4% which leads to over $1.3×107 reduction in ACS in comparison with ignoring them. Moreover, this condition increases the computational time by about 35% while the proposed method can still be up to 13−26 times faster than the other analysed algorithms.

Optimal Solution of Combined Heat and Power Dispatch Problem Using Whale Optimization Algorithm

In this article whale optimization algorithm (WOA) has been applied to solve the combined heat and power economic dispatch (CHPED) problem. The CHPED is energy system which provides both heat and power. Due to presence of valve point loading and the prohibited working region, the CHPED problems become more complex one. The main objective of CHPED problem is to minimize the total cost of fuel as well as heat with fulfill the load demand. This optimization technique shows several advantages like having few input variables, best quality of solution with rapid computational time. The recommended approach is carried out on three test systems. The simulation results of the present work certify the activeness of the proposed technique.

Combined heat and power economic dispatch using an adaptive cuckoo search with differential evolution mutation

In power system operation, the combined heat and power economic dispatch (CHPED) is an attractive and momentous optimization problem where the major objective is to find an optimal generation schedule of heat and power to meet the heat and power demands with the minimum cost, while satisfying various practical operation constraints. This paper puts forward an adaptive cuckoo search with differential evolution mutation (ACS-DEM) for solving the CHPED problem. Compared with the basic cuckoo search (CS), there are three main improvements in the proposed ACS-DEM. The first improvement is that adaptive parameters are employed and therefore no parameter adjustment is required. The second is the incorporation of a Gaussian sampling strategy into the global search phase of the algorithm to increase the exploration capability. The third is the introduction of an improved differential evolution mutation strategy into the local search phase to replace the simple biased random walk in the basic CS, thus discouraging the blindness and enhancing the exploitation capability. The outstanding performance of ACS-DEM is first confirmed through the test suite from the 2017 Conference on Evolutionary Computation and then demonstrated on several CHPED problems. The obtained dispatch schedules from ACS-DEM are feasible and in most cases exhibit a distinct improvement over the results offered by six other CS-based algorithms, one state-of-the-art differential evolution algorithm, as well as recent works in this field.

A niching differential evolution algorithm for the large-scale combined heat and power economic dispatch problem

The combined heat and power economic dispatch (CHPED) problem, which aims at minimizing system cost to supply system demand under various constraints, is one of the most challenging problems in the power system. Numerous researches are concentrated on solving the CHPED problem with small size, ignoring implementation of the large-scale CHPED problem with lots of local optimal solutions. This paper proposes a niching differential evolution algorithm (NDE), which incorporates niching methods into differential evolution algorithm (DE), to solve the large-scale CHPED problem. In NDE, a modified DE/best/1 strategy inspired by the neighborhood concept of niching methods, called DE/best/1/nh, is developed to generate diverse solutions. A two-phase selection that utilizes the deterministic crowding of niching methods and greedy selection is designed to remain promising solutions. The two strategies help to balance the global and local search capabilities of the algorithm. The performance of NDE is evaluated by a comparative analysis with other existing approaches on the five CHPED systems with 7, 24, 84, 96 and 192 units. The numerical results demonstrate the feasibility and effectiveness of NDE in solving the large-scale CHPED problem.

A combination of FA and SRPSO algorithm for Combined Heat and Power Economic Dispatch

This paper represents a hybrid Firefly and Self-Regulating Particle Swarm Optimization (FSRPSO) algorithm to solve optimal Combined Heat and Power Economic Dispatch (CHPED) problem. Valve point effect on fuel cost function of pure generation units, electrical power losses in transmission systems and feasible operating zones are taken into account in the CHPED problem. The CHPED refers to minimize total costs of fuel for electricity and heat generation supply to load demand. The proposed FSRPSO attempts to determine the start of the local search process properly by checking the previous global best. Thus, the FSRPSO is able to exploit strong points of both Firefly Algorithm (FA) and SRPSO mechanisms in order to balance between exploration and exploitation phases. Besides, for the sake of validation the proposed hybrid method, the FSRPSO is examined on 21 well-known benchmarks, and also a real engineering case i.e., two power systems for evaluating its performance compared with the SRPSO, FA, PSO, and other state-of-the-art algorithms. The obtained optimization results show that the proposed FSRPSO provides fast, mature and reliable optimum solutions and outperform other compared algorithms in diverse categories of benchmarks along with the studied CHPED problem.

An improved real-coded genetic algorithm with random walk based mutation for solving combined heat and power economic dispatch

Combined heat and power economic dispatch (CHPED) is an energy management problem that minimizes the operation cost of power and heat generation while a vast variety of operational constraints of the system should be met. The CHPED is a complicated, non-convex and non-linear problem. In this study, a new real-coded genetic algorithm with random walk-based mutation (RCGA-CRWM) is under study, which is effective in solving large-scale CHPED problem with minimum operation cost. In the presented optimization method, a simple approach is introduced to combine the positive features of different probabilistic distributions for the step size of random walk. Using the presented approach, while the genetic algorithm is speeded up, the premature convergence is also avoided. After verifying the performance of the presented method on the benchmark functions, two large-scale and two medium-scale case studies are used for determining the algorithm strength in solving the CHPED problem. Despite the fact that the complexity of the CHPED rises dramatically by increasing its dimensionality, the algorithm has solved the problems accurately. The application of RCGA-CRWM method improves the results of the CHPED problem in terms of both operation cost and convergence speed in comparison with other optimization methods.