A New Multi-Heuristic Method to Optimize the Ammonia–Water Power/Cooling Cycle Combined with an HCCI Engine

Abstract

Nowadays, sustainability is one of the key elements which should be considered in energy systems. Such systems are essential in any manufacturing system to supply the energy requirements of those systems. To optimize the energy consumption of any manufacturing system, various applications have been developed in the literature, with a number of pros and cons. In addition, in the majority of such applications, multi-objective optimization (MOO) plays an outstanding role. In related studies, the MOO strategy has been mainly used to maximize the performance and minimize the total cost of a trigeneration system with an HCCI (homogeneous charge compression ignition) engine as a prime mover based on the NSGA-II (non-dominated sorting genetic algorithm-II) algorithm. The current study introduces a novel multi-heuristic system (MHS) that serves as a metaheuristics cooperation platform for selecting the best design parameters. The MHS operates on a proposed strategy and prefers short runs of various metaheuristics to a single long run of a metaheuristic. The proposed MHS consists of four multi-objective metaheuristics collaborating to work on a common population of solutions. The optimization aims to maximize the exergy efficiency and minimize the total system cost. By utilizing four local archives and one global archive, the system optimizes these two objective functions. The idea behind the proposed MHS is that metaheuristics will be able to compensate for each other’s shortcomings in terms of extracting the most promising regions of the search space. Comparing the findings of the developed MHS shows that implementing the suggested strategy decreases the total unit costs of the system products to 25.85 USD/GJ, where the total unit cost of the base system was 28.89 USD/GJ, and the exergy efficiency of the system is increased up to 39.37%, while this efficiency was 22.81% in the base system. The finding illustrates significant improvements in system results and proves the high performance of the proposed method.

1. Introduction

Nowadays, industrial manufacturers waste a lot of energy, and the exhaust gases they produce are returned to the atmosphere. Hence, the sustainability of the environment is one of the big deals for researchers. On the other hand, the costs of manufacture and the efficiency of the plants is increased and reduced, respectively. Accordingly, recovering the wasted heat by utilizing the cogeneration (power and heat) or trigeneration (power, heat and cooling) systems becomes desirable. Many studies have been carried out with the aim of designing systems for energy conversion to obtain higher performance [1,2,3]. Optimizing the energy systems in terms of sole thermodynamics or economics, such as single objective optimization for maximizing the exergy or improving economic factors, may cause conflict in which it can increase the overall system costs or reduce the exergy efficiency. In order to overcome this issue, multi-objective optimization methods are strongly recommended for altering both the thermodynamic and economic aspects concurrently. Multi-objective optimization (MOO) methods are applied to discover a group of feasible solutions (Pareto front) to balance the trade-off between objectives at the same time. Some state-of-the-art studies for optimizing the energy systems are presented as follows.

Khaljani et al. [4] suggested a HCCI (homogenous charge compression ignition) engine heat recovery based combined cycle using two organic Rankine cycles. Authors applied the NSGAII method as an optimization method to obtain the best system design parameters in terms of thermodynamic and economic aspects. The obtained results showed that exergy efficiency is increased to 46.02% from 44.96%. In addition, it showed a 1.3% decrease in the total cost. Meanwhile, the results showed that design parameters are in conflict with each other in terms of effects on objective functions.

Hajabdollahi et al. [5] employed NSGAII for optimizing an organic Rankine cycle to recover diesel engine waste heat. Authors considered R123, R134a, R245fa, and R22 as refrigerants in the working fluids. The obtained results demonstrated that by considering economic and thermodynamic factors, R123 can be selected as the best-performing fluid. Likewise, R245fa obtains the second rank, and R134a and R22 are in the third and fourth rank, respectively.

Wang et al. [6] applied NSGAII for multi-objective optimization of an organic Rankine cycle. The objective functions considered by the authors were cost exergy efficiency and capital. The results of the study found the values between 1.8 and 2.3 as optimal values for turbine pressure and 90 C as the optimal value for turbine temperature.

Feng et al. [7] used NSGA as a MOO method for optimizing the RORC and BORC in which they stand for “Regenerative Organic Rankine Cycle” and “Basic Organic Rankine Cycle”. Obtained outcomes demonstrated that improving the exergy efficiency causes an increase in LEC, which stands for “Levelized Energy Cost”. Meanwhile, the results exhibited that the optimal exergy efficiency and LEC in the extracted Pareto front are 8.1% and 21.1% higher than the corresponding BORC values, respectively.

In another study, a mutual cycle based on the Brayton power and ejector expansion refrigeration cycles was proposed by Jamali et al. [8]. They applied a MOGA (multi-objective genetic algorithm) for minimizing the heat exchangers’ size and maximizing the exergy efficiency.

More examples of using multi-objective optimization methods for optimizing the energy systems can be found in the literature e.g., the particle swarm optimization (PSO) method [9,10], the grouping evolution strategies method [11,12], and mixed-integer programming methods [13,14].

In a previous study by one of the authors [15], NSGAII was used to carry out a parametric study and MOO strategy for a tri-generation system. The aim of the system was to use an AWM (ammonia–water mixture) cycle to produce cooling and power by employing the waste heat generated by the HCCI engine. The findings showed that a 16.34% gain in energy efficiency and a 10% decrease in cost criterion were attained. The objective functions in the system were considered as exergy efficiency and total costs of the production systems. In order to further improve the performance of the system as a whole, this study proposes a unique framework for metaheuristic collaboration that implements four multi-objective metaheuristics. The proposed framework is called a multi-heuristic system (MHS), in which it increases energy efficiency while reducing system costs. Several metaheuristics that are known for their success are chosen to be used in the proposed multi-heuristic system (MHS). Non-dominated sorting genetic algorithm II (NSGA II) [16,17], multi-objective differential evolution (MODE) [18], multi-objective particle swarm optimization (MOPSO) [19], and the strength Pareto evolutionary algorithm (SPEA 2) [20] are the chosen metaheuristics.

The novelty of the suggested MHS is managing the strategies to run the system and combining the results in order to improve the solutions. The idea behind the proposed MHS is that different metaheuristics will be able to cover the inabilities of each other in terms of discovering the promising parts of the search space. Likewise, the proposed method works based on a predefined novel strategy to make all the metaheuristics collaborate and cooperate. MHS works iteratively in sessions consisting of two consecutive steps. By utilizing four local archives and one global archive, the system optimizes the two objective functions of the system.

Comparative analysis of the obtained results illustrated that the suggested multi-heuristic system reaches better efficiency than the previous work.

The sections of this paper are as follows. Section 2 provides a brief explanation of the multi-objective metaheuristic algorithmic principles used in the proposed system. In Section 3, the problem is defined in detail. The suggested MHS for MOO is clearly described in Section 4. Algorithm parameters, results, and comparative analysis are described in Section 5. Section 6 presents conclusions and some potential future projects.

2. Short Definitions of Metaheuristics Applied in the Developed MHS

2.1. Non-Dominated Sorting Genetic Algorithm (NSGA II)

NSGAII is a popular evolutionary MOO method proposed by Deb et al. [16]. It uses elitism and crowd operations in order to protect and keep good solutions. In addition, it increases the solution distribution in the Pareto front. NSGAII first generates the initial population randomly, then calculates the ranks of individuals. The value of a rank for an individual is the number of solutions which dominate it. Hence, the rank value demonstrates the particular Pareto front. Later on, NSGAII sorts all solutions in ascending order regarding the rank values. Thereafter, a rank-fitness is assigned to them corresponding to their levels. By using the calculated rank-fitness, all genetic operators (selection, recombination, and mutation) are applied for producing the kids’ population. In the next step at the end of each generation, the algorithm combines parents and kids’ populations. Therefore, a new population is created based on lower rank-fitness. Some of the solutions are removed according to the crowding distance values when the number of solutions in the new population becomes more than the fixed predefined population size. The aforementioned steps are iterated until the termination conditions are met. NSGAII is robust in finding and discovering the PFs close to the optimal PF in problems with many parameter interactions.

Figure 1 represents the flowchart of the NSGAII algorithm, which is an improved NSGAII algorithm for mixed model assembly line balancing proposed by Wu et al. [21]. In general, since NSGA II uses fast non-dominated sorting and crowded distance sorting mechanisms, it has a better distribution and convergence. In contrast, due to applying an inefficient simulated binary crossover algorithm, its convergence speed is low.

2.2. MODE Algorithm

The differential evolution algorithm (DE) is extended to work as a multi-objective optimization method. Xue et al. [18] introduced MODE with much similarity with the DE. MODE works as a Pareto-based method to choose a best solution as follows. When the candidate solution is dominated, the best one is selected among non-dominated solutions (NDS); otherwise, the candidate solution is chosen as the best one. In this algorithm, Pareto ranking and crowding distance methods are applied to collect individuals with good spread on the extracted PF. This algorithm discovers better solutions compared to the SPEA (strength Pareto evolutionary algorithm) method when it is utilized for solving unconstrained problems with high dimensionality.

MODE is a simple and easy method which is widely used, and one that is not affected by extreme values, such as arithmetic mean. In contrast, MODE has not been clearly defined. In addition, the sampling fluctuations can affect MODE. Figure 2 illustrates the flowchart for the MODE algorithm, which has been proposed by Khademi and Zandi [22].

2.3. MOPSO Algorithm

Multi-objective particle swarm optimization (MOPSO) proposed by Coello et al. is the extended version of the standard PSO for solving MOO problems [19]. Similar to the majority of methods, MOPSO keeps the non-dominated solutions (NDS) extracted so far in an external global archive. In addition, it uses the PF concept for finding the direction. Since the coordinates of a particle in MOPSO are specified corresponding to the values of objectives, the generation of hypercubes becomes the main trouble in MOPSO. This algorithm applies hypercubes to choose the global best, which is used for computing the velocity.

The flowchart of the MOPSO algorithm has been proposed by Hou et al. [23]. The advantages of MOPSO are its fast searching speed, high efficiency, and good compatibility. Furthermore, it can be extensively used in engineering applications.

2.4. SPEA2 Method

The SPEA2 method proposed by Zitzler et al. [20] is an evolutionary multi-objective optimization algorithm that applies an ordinary population with an external archive to keep the NDS. SPEA2 assigns a strength value, STR(i), for each element i in archive, SOL(i). This value is the number of individuals in population which is dominated by or the same as element i. Furthermore, the fitness value of SOL(i) is calculated as FITA(i). Meanwhile, the fitness of each element i in population, FITP(j), is computed. The fitness value is the sum of STR(i) values in the archive which dominate P(j). To produce fitness values not equal to zero, 1 is added to the summation values. FITA(i) and FITP(j) values are named as raw fitness, and they are able to bring some ranking difficulties when there is no dominancy between most of the solutions. For overcoming this issue, the algorithm separates solutions with equal raw fitness values by using density values. Hence, the algorithm calculates the summation of raw fitness and density values to find the actual fitness values.

This way, the heuristic discovers non-dominated individuals by merging the population and archive elements. Therefore, the external archive is updated in a better way. Eventually, the tournament selection is applied to select parents from updated archive elements. SPEA2 generates the offspring using genetic operators (crossover and mutation). Experimental results over popular test benchmarks showed that SPEA2 performance is similar to NSGAII.

Figure 3 represents the flowchart of the SPEA2 method that has been developed by Mehrdad et al. [24]. Above the red line, shows the parent, and below illustrates the way of generating children. SPEA2 can strongly support convergence and diversity, since it guarantees a better distribution.

3. Problem Definition

The diagram for the trigenerational system under consideration is shown in Figure 4, where the steps of the process have been mentioned using numbers in this figure. The technology under consideration compresses the engine intake air before sending it to two intercoolers. In order to provide a requested job for the compressor, the system expands the exhaust gases (which are exited from engine) in turbine 1. The task of the bottoming cycle is to retrieve the exhaust gases energy at a 525.1 K temperature. AWCC is the mix of absorption refrigeration cycles and Rankine, in which it generates power and refrigeration concurrently at the same time. The trigeneration system pumps the ammonia solution with low pressure to high pressure. Later on, the system heats the solution via a heat exchanger and enters it into the generator. The exchanger divides the solution into weak solution and ammonia-rich vapor, in which the week solution has a lower ammonia concentration. Afterwards, the vapor before condensing to liquid in condenser 2 is transmitted to condenser 1. The system transfers the weak ammonia–water solution coming out of the previous phase to the boiler.

Thus, before being superheated in the super heater, the system heats it and turns it into saturated vapor. Then, the system sends superheated vapor to turbine 2, aiming to generate power. Later on, to refrigerate the space, the liquid ammonia is transferred to the evaporator via the expansion valve. The ammonia vapor with low pressure, which comes out from the evaporator, is transferred via the absorber. Eventually, the cycle is accomplished after producing the basic ammonia–water which has been saturated liquid.

For evaluating the system from a thermodynamic point of view, each part of the system as a control volume takes on the conservation of mass principal. Previous studies [15,25] can be used to find additional information about the system, as well as exergetic, exergoeconomic, and energetic relations for the system components. The study aims to reach higher exergy efficiency (η(II,AWCC)) while the products’ total cost (c(p,total)) is reduced. In this study, AWMT inlet pressure (P(in,AWM Turbine)), generator temperature (TGen), mass fraction of ammonia (Xb), turbine isentropic efficiency (ηT), and pinch point temperature difference (ΔTPinch) are selected as decision variables. Figure 5 represents a flowchart for the modeling of equations to provide an overview upon the considered trigeneration system.

Exergy efficiency and sum of the unit costs of the system products are considered as objective functions of the optimization problem.

In the current work, the exergy efficiency has been defined based on [15,25]. Exergy efficiency, which evaluates the cycle performance, is calculated through the following Equation (1):

$${\eta }_{II,AWCC}=\frac{{\dot{E}}_{evap}+{\dot{W}}_{net,AWCC}}{{\dot{E}}_{in}}$$

(1)

where ${\dot{E}}_{evap}$ is the exergy of the refrigeration output, ${\dot{W}}_{net,AWCC}$ is the net power output of the AWCC system, and ${\dot{E}}_{in}$ is the rate of exergy of exhaust gasses at point 6. These parameters are calculated by the following equations:

$${\dot{E}}_{in}={\dot{m}}_{exhaust}[\left(h_6-h_0\right)-T_0\left(s_6-s_0\right)]$$

(2)

$${\dot{E}}_{evap}={\dot{m}}_{evap}[\left(h_{i,evap}-h_{o,evap}\right)-T_0\left(s_{i,evap}-s_{o,evap}\right)]$$

(3)

$${\dot{W}}_{net,AWCC}={\dot{W}}_{Turbine 2}-{\dot{W}}_{Pump}$$

(4)

The sum of the unit costs of the system products as the second objective assesses the system from the economic standpoint. A detailed description of this equation can be found in [15,25], and it is calculated as the following Equation (5):

$$c_{p,tot}=\frac{{\sum }_{k=1}^{n_k}{\dot{Z}}_k+{\sum }_{i=1}^{n_f}{c}_{f_i}{\dot{E}}_{f_i}}{{\sum }_{i=1}^{n_p}{\dot{E}}_{p_i}}$$

(5)

The term ${\dot{Z}}_k$ represents the entire cost rate related to capital investment and operation and maintenance costs of component k. The term $c_f$ is the average cost per exergy unit of fuel (all exergy additions to a component are considered as the fuel and all exergy removals from it are counted as the product).

4. The Developed Multi-Heuristic Method to Optimize the Proposed System

The proposed unique multi-heuristic system (MHS) and new collaboration technique are presented in this section for the multi-objective optimization of the ammonia–water power and cooling cycle [25]. The proposed system incorporates four multi-objective metaheuristics, as briefly explained above. These metaheuristics cooperate to find shared solutions in order to improve the objective functions, which are energy efficiency and total system cost. Figure 6 represents an architectural description of the suggested framework, and Figure 7 shows a flowchart of the described method.

The suggested multi-heuristic system (MHS) consists of four metaheuristics with embedded local archives, one fixed-sized population, and one global archive. The sessions with two phases in this method are subsequently iterated. In the first phase, all solutions are mixed up and randomly divided into four subpopulations of a similar size. Subpopulations are later provided, one for each metaheuristic. Then, the second step applies metaheuristics to operate on their assigned subpopulation of solutions. In each epoch, new subpopulations are assigned to metaheuristics and the epoch continues until the termination criteria are met. Each metaheuristic in MHS has a separate local archive that needs to be purged at the start of each epoch. The system includes a global archive to retain NDS extracted by all metaheuristics in all epochs, whilst the local archives are updated throughout the metaheuristic execution and utilized to maintain all NDS solutions extracted in one epoch. This means that the global archive resembles the Pareto front and it is reconstructed at the end of each epoch by merging the local archives with the global archive. The system merges the obtained global archive with the new local archives and eliminates any dominated solutions. At the conclusion of each era, all subpopulations are combined to create a global population that will be employed in the following epoch. In this manner, the metaheuristics collaboration is carried out via sharing their obtained results and experiences in which the modified subpopulations are aggregated in a shared global population, and all discovered local archives are collected in a global archive.

NSGAII, SPEA2, MODE, and MOPSO are the four metaheuristics included in the newly released MHS. Instead of one long run of a single metaheuristic, the suggested multi-heuristic system favors brief runs of several different metaheuristics. Metaheuristics will be able to compensate for other metaheuristics’ limitations by extracting more promising portions of the search area in this way. Furthermore, it is possible to simply add or remove a new metaheuristic to or from the proposed MHS. Meanwhile, no conversion is necessary when the solutions are transferred among metaheuristics, because all metaheuristics apply identical representation. The evaluation of the suggested MHS is carried out in the next section. Evaluation results shown in the tables exhibited that all aims of the suggested MHS are reached.

5. Evaluation Results

This section illustrates the experimental results of the suggested MHS in comparison to the previous study [15]. The parameter values of all applied algorithms within the MHS are presented in

Table 1. Values of parameters for the metaheuristics applied in the MHS.

Metaheuristic	Parameter Values
MOPSO	C1 = 2.0	C2 = 2.0	ωmax = 0.9	ωmin = 0.4
MODE	Scaling factor = 0.5	PC =0.7
SPEA2	PC = 0.9	Pm = 1.0/Variable num	Distribution index = 20
NSGAII	PC =0.9	Pm = 1.0/Variable num	Distribution index = 20

, where the value of |Pop| for all methods is 75, which is 300 in total for each metaheuristic. These values have been taken from the standard type of the metaheuristics. The proposed MHS is implemented using the Matlab^® programming language.

In the implementation, the number of generations for each metaheuristic is adjusted as 250 generations, similar to Bahlouli et al. [15]. Therefore, the proposed new method does not add any extra time complexity to the method compared to that study. However, it speeds up the convergence process and extracts better results.

Table 2. The parameter ranges in the optimization.

Parameter	Range
$P_{in,AWM turbine}\left(bar\right)$	15–30
$T_{GE}\left(k\right)$	420–440
$X_b$	0.34–0.4
$\Delta T_{pp}\left(K\right)$	10–20
${ɳ}_T$	0.7–0.9

shows parameter ranges for the decision variables.

As mentioned in previous sections, the problem has two objective functions: the exergy efficiency ${ɳ}_{II,AWCC}$ should be maximized, and the total unit costs of the system products $C_{p,tot}$ should be minimized.

The plot of the computed Pareto front retrieved by MHS for the two-objective test problem with 500 non-dominated solutions is shown in Figure 8.

To compare the results of the proposed method, Figure 9 exhibits two Pareto fronts extracted by MHS which were published in [15]. Due to the fact that increasing the exergy efficiency from 36% to 39% increases the product cost trivially, a solution (point B in

Table 3. Parameter values obtained by MHS and [15].

Design Parameter	Base	Point B Optimized (NSGAII)	Point A Optimized (MHS)
${\mathrm{P}}_{\mathrm{in},\mathrm{AWM} \mathrm{Turbine}} \left(\mathrm{bar}\right)$	20.00	29.89	30.00
${\mathrm{T}}_{\mathrm{Gen}} \left(\mathrm{K}\right)$	430.0	420.2	420.0
${\mathrm{X}}_{\mathrm{b}}$	0.400	0.342	0.340
${\mathsf{\Delta }\mathrm{T}}_{\mathrm{Pinch}}\left(\mathrm{K}\right)$	15.00	10.01	10.00
${\mathsf{\eta }}_{\mathrm{T}}$	0.85	0.90	0.90
${\mathsf{\eta }}_{\mathrm{P}}$	0.70	0.70	0.70
Performance of the AWCC
Exergy efficiency(%)	22.8144	39.1596	39.3708
Total unit costs (USD/GJ)	28.89	25.97	25.85

) with an exergy efficiency of 39.16% and a total product cost of 25.97 USD/GJ was designated as the last optimized solution. Similarly, the ultimate optimized solution in this study is a solution (point A in Table 3) with an exergy efficiency of 39.37% and a total unit cost of the products of 25.85 USD/GJ.

The following three solutions are shown in Table 3 along with their decision variables and thermodynamic characteristics: base point, point B of the multi-objective optimization strategy using the NSGA-II, and point A of the multi-objective optimization system using the multi-heuristic system (MHS) suggested in the current work. The results comparison for point A and point B shows that the proposed MHS has better capability in maximizing the exergy efficiency and minimizing the system’s total unit costs in comparison with NSGA-II used in the previous study. When MHS is used in the optimization process, the increase in energy efficiency is around 0.56% larger than when NSGA-II is used. In addition, MHS reduces the total unit cost of the system products 0.45% more than the previous method [15].

The distance between two competing algorithms is determined using the IGD (inverted generational distance) metric [26,27]. The IGD is used to measures convergence and diversity at the same time.

Let PF1 be a set of all the NDS found by MHS and PF2 is the set of all the NDS discovered in the literature [16].

$$IGD=\frac{{\sum }_{v\in PF1, x\in PF2}d\left(v,x\right)}{\left|PF1\right|}$$

(6)

The shortest distance between points v and x is denoted by the symbol d(v,x). The computed IGD value for Figure 9 is 74.134, demonstrating the significant separation between the two Pareto fronts and their separation from one another.

The distributions of five decision variables are plotted in Figure 10 to provide a visual vision over the design variables. According to Figure 10, there is much consistency between the obtained results and those reported in the literature [15]. It is clear that AWMT inlet pressure (Figure 10a) and AWMT isentropic efficiency (Figure 10e) have approached their maximum values, while the opposite is true for the ammonia mass fraction and generator temperature plotted in Figure 10b,c. It can be interpreted that in order to reach better optimization results, even a slight increase and decrease in the values could be very helpful e.g., the exergy efficiency increases and the total unit cost of the products decreases while the AWMT inlet pressure is increasing. Meanwhile, Figure 10d shows that the fourth design variable is scattered, disappeared, and that it can play remarkable role in affecting exergy efficiency and total unit cost trade-off.

6. Conclusions

In this study, a unique approach to designing a multi-heuristic system (MHS) is proposed for an ammonia–water power/cooling cycle connected with an HCCI engine. Four metaheuristics, namely NSGAII, MODE, MOPSO, and SPEA2, are implemented in the system using the suggested approach. The system divides the global population into subpopulations randomly and then it assigns subpopulations to metaheuristics for improving them. In comparison with the earlier work [15], the results show that implementing the suggested strategy decreases the total unit costs of the system products to 25.85 USD/GJ, where the total unit cost of the base system was 28.89 USD/GJ, and the exergy efficiency of the system is increased up to 39.37%, while this efficiency was 22.81% in the base system. The finding illustrates significant improvements in system results and proves the high performance of the proposed method.

In future works, the proposed MHS can be extended by adding more multi-objective optimization methods and different cooperation strategies to find practical and cost-effective solutions to challenges in mechanical engineering and energy systems. In addition, the developed solution method in this study may be used to solve other multi-objective problems in industry, such as energy systems, manufacturing systems, etc.