Penalty-based boundary intersection (PBI) method is a frequently used scalarizing method in decomposition based multi-objective evolutionary algorithms (MOEAs). It works well when a proper penalty ...value is provided, however, the determination of a suitable penalty value depends on the problem itself, more precisely, the Pareto optimal front (PF) shape. As the penalty value increases, the PBI method becomes less effective in terms of convergence, but is more capable of handling various PF shapes. In this study, a simple yet effective method called Pareto adaptive PBI (PaP) is proposed by which a suitable penalty value can be adaptively identified, which therefore can maintain fast convergence speed, meanwhile, leading to a good approximation of the PF. The PaP strategy integrated into the state-of-the-art decomposition algorithm, MOEA/D, denoted as MOEA/D-PaP, is examined on a set of multi-objective benchmarks with different PF shapes. Experimental results show that the PaP strategy is more effective than the weighted sum, the weighted Tchebycheff and the PBI method with (representative) fixed penalty values in general. In addition, the MOEA/D-PaP is examined on a real-world problem – multi-objective optimization of a hybrid renewable energy system whose PF is unknown. The outcome of the experiment further confirms its feasibility and superiority.
Due to the scarcity of conventional energy resources and the greenhouse effect, renewable energies have gained more attention. This paper proposes methods for multi-objective optimal design of hybrid ...renewable energy system (HRES) in both isolated-island and grid-connected modes. In each mode, the optimal design aims to find suitable configurations of photovoltaic (PV) panels, wind turbines, batteries and diesel generators in HRES such that the system cost and the fuel emission are minimized, and the system reliability/renewable ability (corresponding to different modes) is maximized. To effectively solve this multi-objective problem (MOP), the multi-objective evolutionary algorithm based on decomposition (MOEA/D) using localized penalty-based boundary intersection (LPBI) method is proposed. The algorithm denoted as MOEA/D-LPBI is demonstrated to outperform its competitors on the HRES model as well as a set of benchmarks. Moreover, it effectively obtains a good approximation of Pareto optimal HRES configurations. By further considering a decision maker’s preference, the most satisfied configuration of the HRES can be identified.
The integration of renewable energies into combined cooling, heating, and power (CCHP) systems has become increasingly popular in recent years. However, the optimization of renewable energies ...integrated CCHP (RECCHP) systems (i.e., optimal component configurations) is far from being well addressed, especially in isolated mode. This study aims to fill this research gap. A multi-objective optimization model characterizing the system reliability, system cost, and environmental sustainability is constructed. In this model, the objectives include minimization of annual total cost (ATC), carbon dioxide emission (CDE), and loss of energy supply probability (LESP). The decision variables representing the configuration of the RECCHP system include the number of photovoltaic (PV) panels and wind turbines (WTs), the tilt angle of PV panels, the height of WTs, the maximum fuel consumption, and the capacity of battery and heat storage tanks (HSTs). The multi-objective model is solved by a multi-objective evolutionary algorithm, namely, the preference-inspired coevolutionary algorithm (PICEA-g), resulting in a set of Pareto optimal (trade-off) solutions. Then, a decision-making process is demonstrated, selecting a preferred solution amongst those trade-off solutions by further considering the decision-maker preferences. Furthermore, on the optimization of the RECCHP system, operational strategies (i.e., following electric load, FEL, and following thermal load, FTL) are considered, respectively. Experimental results show that the FEL and FTL strategies lead to different optimal configurations. In general, the FTL is recommended in summer and winter, while the FEL is more suitable for spring and autumn. Compared with traditional energy systems, RECCHP has better economic and environmental advantages.
For remote structures in military applications located in high mountains and outlying islands, the configuration of isolated microgrids constructed in these locations is highly important. To denote ...oxygen generation/seawater desalination devices and military battery packs in practical applications, shiftable load models and mobile energy storage models are used. A multiobjective optimization model, including the annual system cost, demand shortage rate, and the ratio of diesel energy supply, is constructed for configuration design. This model is solved using the improved preference-incentive coevolution algorithm (PICEA-ng) presented in this paper. Based on practical data and numerical simulation, the utilization strategy in terms of lost time and output power for mobile energy storage, stationary energy storage, diesel generators, and shiftable loads are generated and validated. Finally, the operational performance of the shiftable load and mobile energy storage over the entire microgrid system is analyzed and discussed.
Finding the optimal size of a hybrid renewable energy system is certainly important. The problem is often modelled as an multi-objective optimization problem (MOP) in which objectives such as ...annualized system cost, loss of power supply probability etc. are minimized. However, the MOP model rarely takes the load characteristics into account. We argue that ignoring load characteristics may be inappropriate when designing HRES for a place with intermittent high load demand. For example, in a training base the load demand is high when there are training tasks while the demand decreases to a low level when there is no training task. This results in an interesting issue, that is, when the loss of power supply probability is determined at a specific value, say 15%, then it is very likely that most of loss of power supply would occur right in the training period which is unexpected. Therefore, this study proposes a constraint multi-objective model to deal with this issue—in addition to the general multi-objective optimization model, the loss of power supply probability over a critical period is set as a constraint. Correspondingly, the non-dominated sorting genetic algorithm II with a relaxed
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constraint handling strategy is proposed to address the constraint MOP. Experimental results on a real world application demonstrate that the proposed model and algorithm are both effective and efficient.
Motivated by some practical applications of post-disaster supply delivery, we study a multi-trip time-dependent vehicle routing problem with split delivery (MTTDVRP-SD) with an unmanned aerial ...vehicle (UAV). This is a variant of the VRP that allows the UAV to travel multiple times; the task nodes’ demands are splittable, and the information is time-dependent. We propose a mathematical formulation of the MTTDVRP-SD and analyze the pattern of the solution, including the delivery routing and delivery quantity. We developed an algorithm based on the simulation anneal (SA) framework. First, the initial solution is generated by an improved intelligent auction algorithm; then, the stochastic neighborhood of the delivery route is generated based on the SA algorithm. Based on this, the model is simplified to a mixed-integer linear programming model (MILP), and the CPLEX optimizer is used to solve for the delivery quantity. The proposed algorithm is compared with random–simulation anneal–CPLEX (R-SA-CPLEX), auction–genetic algorithm–CPLEX (A-GA-CPLEX), and auction–simulation anneal–CPLEX (A-SA) on 30 instances at three scales, and its effectiveness and efficiency are statistically verified. The proposed algorithm significantly differs from R-SA-CPLEX at a 99% confidence level and outperforms R-SA-CPLEX by about 30%. In the large-scale case, the computation time of the proposed algorithm is about 30 min shorter than that of A-SA. Compared to the A-GA-CPLEX algorithm, the performance and efficiency of the proposed algorithm are improved. Furthermore, compared to a model that does not allow split delivery, the objective function values of the solution of the MTTDVRP-SD model are reduced by 52.67%, 48.22%, and 34.11% for the three scaled instances, respectively.
The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a ...constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termed Population1 and Population2 . In c-DPEA, a novel self-adaptive penalty function, termed saPF , is designed to preserve competitive infeasible solutions in Population1 . On the other hand, infeasible solutions in Population2 are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, named bCAD , is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.
In addition to the search for feasible solutions, the utilization of informative infeasible solutions is important for solving constrained multiobjective optimization problems (CMOPs). However, most ...of the existing constrained multiobjective evolutionary algorithms (CMOEAs) cannot effectively explore and exploit those solutions and, therefore, exhibit poor performance when facing problems with large infeasible regions. To address the issue, this article proposes a novel method, called DD-CMOEA, which features dual stages (i.e., exploration and exploitation) and dual populations. Specifically, the two populations, called mainPop and auxPop, first individually evolve with and without considering the constraints, responsible for exploring feasible and infeasible solutions, respectively. Then, in the exploitation stage, mainPop provides information about the location of feasible regions, which facilitates auxPop to find and exploit surrounding infeasible solutions. The promising infeasible solutions obtained by auxPop in turn help mainPop converge better toward the Pareto-optimal front. Extensive experiments on three well-known test suites and a real-world case study fully demonstrate that DD-CMOEA is more competitive than five state-of-the-art CMOEAs.
Hybrid renewable energy system (HRES) has continuously been demonstrated effective in making use of renewable energies, e.g., solar, wind. This study proposes a novel multi-objective model and ...algorithm for optimizing the size of a typical stand-alone HRES that is composed of photovoltaic (PV) panels, wind turbines, battery banks and diesels. Notably, the proposed model considers minimization of annualized system cost (economy), loss of power supply probability (reliability) and greenhouse gas emission (environment), and enables a decision maker to optimize both the number and the type of PV panel, wind turbine, battery and diesel generator as well as the PV panel installation angle, the wind turbine installation height. To effectively solve the model, in particular, dealing with mixed types of decision variables including integer, real and categorical values, the non-dominated sorting algorithm II (NSGA-II) embedded with a re-ranking based genetic operators is proposed. Lastly, a case study is presented to demonstrate the effectiveness and efficiency of the proposed model and algorithm.
•An effective multi-objective model for the design of stand-alone HRES.•A re-ranking technique based evolutionary algorithm.•A real-world HRES design study.
•Adaptive strategies are proposed to detect the knee point, and obtain the corresponding Pareto knee front, respectively.•The adaptive knee strategy can be integrated into NSGA-II and MOEA/D as well ...as other MOEAs.•A comparison of different knee detection metrics is conducted. The distance-based metric is the most competitive.•The proposed method performs well on MOPs with up to 15 objectives.
Approximating the entire Pareto front (PF) in many-objective optimization is challenging but often unnecessary because a decision maker is usually only interested in a small portion of the PF. Assuming no preference, we argue that a more appropriate way to address many-objective optimization problems (MaOPs) is to find Pareto-optimal knee solutions—solutions where small improvements in one objective will lead to severe degradation in at least one other objective. Herein, we propose such a method, which uses a distance-based indicator to first identify knee points (knee-detection phase) and then uses a refined fitness assignment strategy to select solutions near the knee points (knee-selection phase). The proposed method is integrated into two traditional algorithms, resulting in k-NSGA-II and k-MOEA/D. We discuss the effects of the parameter that controls the width of the knee region(s) and then analyze the effects of different methods for identifying knee points in the knee-detection phase. Finally, we examine the performances of k-NSGA-II and k-MOEA/D on a set of knee benchmark problems. The experimental results show that k-NSGA-II is competitive on knee test problems with 2 and 4 objectives, while k-MOEA/D performs better than k-NSGA-II with 6 and 8 objectives.
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