Hybrid Multi-objective Evolutionary Algorithm Research Articles

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

Feature selection for sentiment analysis using hybrid multiobjective evolutionary algorithm

As the volume of data continues to grow, the significance of text classification is on the rise. This vast amount of data majorly exists in the form of texts. Effective data preparation is essential to extract sentiment data from this vast amount of text, as irrelevant and redundant information can impede valuable insights. Feature selection is an important step in the data preparation phase as it eliminates irrelevant and insignificant features from the huge features set. There exist a large body of work related to feature selection for image processing but limited research is done for text data. While some studies recognize the significance of feature selection in text classification, but there is still need for more efficient sentiment analysis models that optimize feature selection and reduce computational. This manuscript aims to bridge these gaps by introducing a hybrid multi-objective evolutionary algorithm as a feature selection mechanism, combining the power of multiple objectives and evolutionary processes. The approach combines two feature selection techniques within a binary classification model: a filter method, Information Gain (IG), and an evolutionary wrapper method, Binary Multi-Objective Grey Wolf Optimizer (BMOGWO). Experimental evaluations are conducted across six diverse datasets. It achieves a reduction of over 90 percent in feature size while improving accuracy by nearly nine percent. These results showcase the model’s efficiency in terms of computational time and its efficacy in terms of higher classification accuracy which improves sentiment analysis performance. This improvement can be beneficial for various applications, including recommendation systems, reviews analysis, and public opinion observation. However, it’s crucial to acknowledge certain limitations of this study. These encompass the need for broader classifier evaluation, and scalability considerations with larger datasets. These identified limitations serve as directions for future research and the enhancement of the proposed approach.

A hybrid multi-objective evolutionary algorithm with high solving efficiency for UAV defense programming

Emerging Unmanned Aerial Vehicle (UAV) application patterns, including the Loyal Wingman and Unmanned Swarms, have significantly challenged the administration and defense against illegal or trespassing UAVs. The weapon-target assignment (WTA) problem, a famous combinatorial optimization problem in military operations research, is decisive for the success of UAV defense programming. Related investigations face two main challenges: 1) Constructing a multi-objective optimization model reflecting the complexities of new UAV application patterns, and 2) solving the time-consuming WTA problem with high-dimension decision variables as it is NP-complete. This paper introduces a modified differential evolution based on a new mapping method called Pareto-Optimal-Matching that solves multi-objective binary optimization problems and constructs a 3 objective Sensor-Weapon-Target Assignment model. The proposed algorithm overcomes the inherent limitation of traditional differential evolution, which only performs well in continuous problems. Promising results were obtained based on different simulation metrics under various problems (proposed model, MOKP, and ZDT5), validating the superior performance of the proposed algorithm.

A Two-Stage Hybrid Multi-Objective Optimization Evolutionary Algorithm for Computing Offloading in Sustainable Edge Computing

A Two-Stage Hybrid Multi-Objective Optimization Evolutionary Algorithm for Computing Offloading in Sustainable Edge Computing

Integrated location and routing for cold chain logistics networks with heterogeneous customer demand

The critical interdependence between facility location and vehicle routing is a fundamental component of cold chain logistics management (CCLM). Furthermore, integrating information within CCLM has the potential to enhance operational efficiency, reduce costs, improve risk management, and elevate product quality, ultimately ensuring that temperature-sensitive goods are delivered in best condition. This paper introduces a novel non-linear multi-objective model designed to concurrently optimize warehouse facility location and vehicle routing, addressing the challenges inherent in cold chain logistics processes. The model seeks to minimize the aggregate costs related to transportation, facility location, and delivery tardiness. The study accounts for several pragmatic assumptions to address real-world scenarios: multiple delivery requests per customer, handling mixed commodities, and distributing mixed commodities using a single vehicle. This paper firstly studies simultaneous pickup and delivery with multiple requests and heterogeneous customer demands, each of which should be preserved in a different range of temperatures and needs different vehicle types. The epsilon-constraint method is employed to validate the proposed model, and a set of advanced, hybrid multi-objective evolutionary algorithms (MOEA) are presented to tackle the problem in a real-world context. A comprehensive set of performance metrics is utilized supported by rigorous statistical testing.

A humanitarian vehicle routing problem synchronized with drones in time-varying weather conditions

This paper applies the cooperative delivery mode of trucks synchronized with drones to humanitarian logistics (HVRP-SD), considers the impact of time-varying weather conditions on the synchronous delivery from two dimensions (HVRP-SD-TVW): drone safety and drone delivery efficiency, and investigate a multi-objective optimization problem. This issue concerns not only the delivery timeliness of relief supplies, but also the fairness of supplies allocation. First, we establish a basic multi-objective mixed integer programming model for HVRP-SD, and then establish an extended mathematical model for HVRP-SD-TVW. To solve the multi-objective optimization problem, we develop a hybrid multi-objective evolutionary algorithm (HMOEA). According to the characteristics of HVRP-SD-TVW, HMOEA designs a variable-length two-dimensional array encoding method, fitness evaluation rules, multimodal mutation, and specialized local search operators. A set of numerical experiments prove that HMOEAS is highly competitive, and both the multimodal mutation and local search have significant effects on improving the quality of solutions. Further, taking the emergency supplies distribution in flood-stricken areas of Gongyi City, China in 2021 as a sample case, we prove that weather conditions play an important role in the truck-drone synchronized delivery decision by comparing the results of the basic model and extended model. In addition, we respectively analyze the variation in solutions under different weather scenarios, departure times, and drone risk resilience to guide decision-making.

μMOSM: A hybrid multi-objective micro evolutionary algorithm

In multi-objective optimization problems (MOPs), several mutually conflicting objectives are optimized simultaneously. In such scenarios, there is not a unique solution to the problem; instead, there is a set of solutions known as the Pareto front, representing the trade-off between objectives. Multi-objective evolutionary algorithms (MOEAs) can approximate these solutions in a single run. However, due to their resource-intensive nature, MOEAs are not suitable for solving real-time and engineering MOPs such as the optimization of manufacturing processes and energy consumption in wireless networks, where a fast convergence rate with less computational cost is required. Fortunately, micro versions of MOEAs can meet this requirement by utilizing a tiny population size. However, this can result in a rapid loss of diversity and the algorithm may easily fall into a local optimum. While some approaches such as the restart technique have been proposed to address this issue, hybrid techniques such as integrative, collaborative, and decomposition-based methods have not been effectively considered in the design of micro algorithms, despite hybridization being a widely accepted method for enhancing the diversity of evolutionary algorithms. In this study, we propose a hybrid micro MOEA called μMOSM that can effectively tackle the diversity loss problem and accelerate the convergence rate in approximating Pareto front solutions. Experimental results on benchmark test suites and a real-world MOP demonstrate the advantages of our proposed algorithm and confirm that μMOSM outperforms state-of-the-art MOEAs and micro MOEAs such as MOSM, ADE-MOIA, MMOPSO, NSGA-III, MOEA/D-FRRMAB, μFAME, and ASMiGA.

Service Composition and Optimal Selection of Low-Carbon Cloud Manufacturing Based on NSGA-II-SA Algorithm

As a new model of networked manufacturing services, cloud manufacturing (CMfg) aims to allocate enterprise manufacturing resources, realize rational utilization of manufacturing resources, and adapt to increasingly complex user needs. However, previous studies on service composition and optimal selection (SCOS) in CMfg environments do not incorporate carbon emissions into the quality of service (QoS) evaluation indicators. Therefore, a SCOS model for CMfg under a low-carbon environment is firstly proposed in this paper. Secondly, based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) algorithm, a hybrid multi-objective evolutionary algorithm, named the NSGA-II-SA algorithm, is proposed to solve the model and obtain the Pareto optimal solution set. Then, an algorithm result optimization strategy combining subjective and objective is proposed to filter the Pareto optimal solution set, so as to make the final decision. Finally, taking natural gas cylinder head production as an example, the proposed algorithm is compared with other algorithms, and the results show that the proposed algorithm can obtain more non-dominated solutions, and the quality of the solutions in the four dimensions is better than the other. Therefore, it is proved that the proposed algorithm has better comprehensive performance in SCOS under a low-carbon environment.

A new hybrid evolutionary algorithm for multi-objective optimal power flow in an integrated WE, PV, and PEV power system

• A novel hybrid multi-objective evolutionary algorithm (MOEA) was developed based on the decomposition and invasive weed optimization (IWO) techniques for solving the MOOPF problem. • The conventional MOOPF problem was modified by taking stochastic WE, PV, and PEV powers into consideration. • Modeling the stochastic nature of WE, PV, and PEV sources was done using probability distribution functions (PDFs) and calculating its uncertainty cost was done with Monte Carlo simulations. • Using an effective constraint handling method (CHM) known as the superiority of feasible solution (SF) was done to address difficult constraints. • The one-way analysis of variance (ANOVA) test was deployed to give a certain level of confidence to our study. This study proposes a novel hybrid multi-objective evolutionary algorithm (MOEA) based on decomposition and invasive weed optimization (IWO) algorithm for the optimal power flow (OPF) problem in transmission networks. The conventional OPF is modified as a stochastic OPF with the integration of WE, PV, and PEV systems uncertainty. This paper proposes a new constraint-handling method (CHM) that adds the penalty adaptively and avoids parameter reliance on penalty computation. The selection features in the IWO method are deployed to improve the diversity of the proposed method. The OPF problem is represented as a multi-objective optimization (MOO) problem using four objectives: generation cost, emission, power loss, and voltage variation. The generation costs of WE, PV, and PEV sources are evaluated using Monte Carlo simulations to mitigate the whole cost and the influence of intermittency of these systems is investigated in terms of affordability and feasibility. Weibull, lognormal, and normal probability distribution functions (PDFs) are employed to define the uncertainty of WE, PV, and PEV sources respectively. The suggested method's viability is evaluated on IEEE 57 and IEEE 118- bus systems under all conceivable scenarios. In addition, one-way ANOVA test, a statistical approach, is used to evaluate the superiority of the suggested algorithm.

A hybrid multi-objective Evolutionary Programming-Firefly Algorithm for different type of Distributed Generation in distribution system

With the rise in electricity demand, various additional sources of generation, known as Distributed Generation (DG), have been introduced to boost the performance of power systems. A hybrid multi-objective Evolutionary Programming-Firefly Algorithm (MOEPFA) technique is presented in this study for solving multi-objective power system problems which are minimizing total active and reactive power losses and improving voltage profile while considering the cost of energy losses. This MOEPFA is developed by embedding Firefly Algorithm (FA) features into the conventional EP method. The analysis in this study considered DG with 4 different scenarios. Scenario 1 is the base case or without DG, scenario 2 is for DG with injected active power, scenario 3 is for DG injected with reactive power only and scenario 4 is for DG injected with both active and reactive power. The IEEE 69-bus test system is applied to validate the suggested technique.

A hybrid multi-objective evolutionary algorithm for solving an adaptive flexible job-shop rescheduling problem with real-time order acceptance and condition-based preventive maintenance

Production scheduling and maintenance planning are two of the most important tasks in the modern manufacturing workshop. Meanwhile, due to the dynamic order arrival and real-time machine monitoring information updating, the integrated optimization of them becoming more complex and meaningful. Therefore, this study intends to address an adaptive flexible job-shop rescheduling problem with real-time order acceptance (ROA) and condition-based preventive maintenance (CBPM). More precisely, the main innovative works are described as follows: (1) a CBPM policy with both imperfect preventive maintenance (PM) and four inspection strategies is designed to find the optimal maintenance planning for each production machine; (2) a multi-objective optimization model is developed for the concerned problem; and (3) a hybrid multi-objective evolutionary algorithm (HMOEA) with hybrid initialization method, hybrid local search operators and adaptive rescheduling strategies is proposed. In the numerical simulation, the performance and competitiveness of the proposed CBPM policy are first demonstrated by comparing with other maintenance policies. Second, the effectiveness and superiority of parameter setting, order sorting rules, improved operators and overall performance of the proposed algorithm are verified by internal analysis of the algorithm. Third, an adaptive rescheduling strategy pool is constructed by running three rescheduling strategies on all rescheduling scenarios. Finally, a comprehensive sensitivity analysis is performed to illustrate the impact of several critical parameters on the adaptive rescheduling problem, and the results and comparisons show that the proposed HMOEA algorithm and order acceptance strategy have good robustness in most parameters.

Hybrid multiobjective evolutionary algorithm considering combination timing for multi-type vehicle routing problem with time windows

Vehicle routing problem (VRP) has been a classical combinatorial optimization challenge, which has been extensively investigated in recent decades. As a VRP typical variant, multi-type vehicle routing problem with time windows (MT-VRPTW) has been concerned with multiple types of heterogeneous fleets of vehicles, within the delivery time window and limited capacity constraints. For such complicated multiobjective optimization problems, hybrid multiobjective evolutionary algorithm (HMOEA) has become an effective method, however, the research on hybrid algorithms and combination timing is still challenging. This study proposes a hybrid multiobjective evolutionary algorithm based on combination timing (HMOEA-CT) to solve MT-VRPTW with the criteria of minimizing the number of vehicles and wasting time simultaneously. The HMOEA-CT combines a fast convergence in multiple directions (FCMDs)-based global search and a problem-specific difference (PSD)-based local search in different evolutionary stages. The FCMD is assumed to be the global exploration search strategy, which converges faster at the center and edge regions of the Pareto front. The PSD is used to improve the local exploitation search ability by directing poor-performing individuals closer to better-performing individuals. Furthermore, the PSD cooperates with FCMD at the right time according to the different evolutionary stages to improve efficiency. Experimental results on Solomon benchmark problems demonstrate the competitive performance comparison of the HMOEA-CT with traditional multiobjective evolutionary algorithms.

A hybrid multi-objective evolutionary algorithm for open vehicle routing problem through cluster primary-route secondary approach

ABSTRACT This study focuses on the cluster primary-route secondary approach to solve the multi-objective open green vehicle routing problem under a sustainable environment. An open green vehicle routing problem involves distributing products or services from a single depot to several customers placed at different geographical locations using third-party logistics to reduce pollution. The proposed model considers two conflicting realistic objectives: minimizing the operating costs and minimizing the carbon emission due to fuel consumption by the service vehicles. Unlike existing multi-objective problems, this multi-objective model chooses an optimal route based on the decision maker’s choice from the set of alternative solutions. Initially, it clusters all the customers by applying a modified -means algorithm. Each cluster is served by one vehicle only. Then a multi-objective evolutionary algorithm is employed to search for the best subroute to cover all the customers belonging to a cluster. We employ the extended Strength Pareto Evolutionary Algorithm (SPEA2) and Non-dominated Sorting-based Genetic Algorithm (NSGA-II) separately to obtain different approximate fronts. The VIKOR method is used to identify the decision maker’s choice-based solution for each cluster. In the next step, all the compromise solutions are combined to produce the final result of the proposed problem. Some statistical analyses are performed to compare the performance of SPEA2 and NSGA-II. SPEA2 has shown better results compared to NSGA-II.

Hybrid multi-objective evolutionary algorithm for solving RALB-II problem

Hybrid multi-objective evolutionary algorithm for solving RALB-II problem

Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems.

Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi-Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: the Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.

Shape optimization of free-form grid structures based on the sensitivity hybrid multi-objective evolutionary algorithm

In this paper, a novel shape optimization method is proposed to improve the mechanical performance of the free-form grid structures while satisfying the architectural requirements. The height of control points are considered as the optimization variables, the structural strain energy and the comprehensive quantitative index are considered as optimization objectives. The sensitivity hybrid multi-objective evolutionary algorithm (referred to as SH-MOEA) is developed and the shape optimization of the free-form grid structures is carried out based on the developed algorithm. The optimization results are compared with those based on NGSA-II, SPEA2 and MOEA/D algorithms. The results demonstrate that the developed algorithm not only can obtain the Pareto optimal solution set with better accuracy and uniformity, but also indicates higher computational efficiency than other three algorithms. The similarity of surface, the fluence and regularity of free-form grids are effectively improved by considering the geometric comprehensive quantitative index as the optimization objective.

Multi‐objective hybrid decomposition and local dominance based meter placement for distribution system state estimation

The study proposes a new hybrid multi-objective evolutionary optimisation algorithm based on decomposition and local dominance for meter placement in distribution system state estimation. The evenly distributed qualitative and diverse solutions on the Pareto front are required for a decision-maker for selecting a final optimal solution. Such a Pareto front can be achieved by obtaining the balance between convergence and diversity of multi-objective optimisation algorithm. Therefore, the proposed method combined dominance and decomposition techniques, modelled meter placement as a constrained combinatorial multi-objective optimisation. The meter placement is designed as a trade-off between three objectives that are minimising the cost of the meters, average relative percentage error (ARPE) of voltage magnitude and ARPE of voltage angle. As the meter placement problem is a combinatorial optimisation, the binomial distribution-based Monte Carlo method is utilised to initialise the population, which aims to improve the diversity, as a consequence it improves the convergence, which is a by-product of this method. The results of the proposed method are compared with multi-objective evolutionary algorithm based on decomposition, non-dominated sorting genetic algorithm-II and with multi-objective hybrid particle swarm optimisation-krill herd algorithm, multi-objective hybrid estimation of distribution algorithm-interior point method and demonstrated on PG&E 69-bus distribution system and Practical Indian 85-bus distribution system.

Multi-objective optimization based on decomposition for flexible job shop scheduling under time-of-use electricity prices

To decrease the load of electricity grid during the peak period, time-of-use electricity price has been implemented in industries to shift the production activities from the peak to the off-peak period. This paper addresses the flexible job shop scheduling under time-of-use electricity prices (FJSPTOUEP) to minimize both makespan and total electricity cost (TEC) simultaneously. We present the mixed integer programming model and propose a hybrid multi-objective evolutionary algorithm based on decomposition (HMOEA/D) to solve the problem. To generate an initial population with certain quality and diversity, several rules are used together. In the framework of MOEA/D, a cooperative search operator is designed to generate new solutions by exchanging information of neighbours. To improve the quality of solutions, two local intensification operators are designed by analysing the critical path of the schedule. An adaptive selection strategy is designed based on the reference point for well using the local search operators to enhance exploitation ability. Moreover, according to the characteristics of time-of-use electricity prices, an adjustment strategy is proposed to reduce electricity cost for further improving solutions. Computational results and statistical comparisons show that both the local intensification and adjustment strategy are effective. It also shows that the proposed HMOEA/D is more effective than other optimization algorithms in solving the FJSPTOUEP.

Hybrid multi-objective opposite-learning evolutionary algorithm for integrated production and maintenance scheduling with energy consideration

While conventional scheduling researches take production efficiency, cost and quality as objectives, increasingly serious ecological problems and energy shortage have turned scholars’ attention to energy-efficient scheduling. Meanwhile, maintenance activities are of great importance to equipment availability and production continuity. This paper addresses an energy-efficient multi-objective scheduling problem of a serial production line (SPSP) integrating production and maintenance, with the criteria of minimizing the makespan and the total energy consumption simultaneously. The impact of integrating preventive maintenance (PM) is analyzed, and the better interval mode is picked out. An energy-saving strategy combining shutdown windows of PM and energy-saving windows on idle machines is designed to cut down the total energy consumption. In order to tackle this NP-hard problem, a hybrid multi-objective opposite-based learning evolutionary algorithm (HMOLEA) is developed, in which the opposite-based learning and IGD indicator-based evolutionary mechanism are combined together and a special rank assignment is designed to improve the computational efficiency. Furthermore, a self-adaptive weighted mutation operator is fused into the framework of HMOLEA to enhance the exploration of the algorithm. Extensive computational experiments are carried out to verify the effectiveness and superiority of HMOLEA in solving the SPSP.

Hydrodynamic Optimization for Design of a Submersible Axial-Flow Pump with a Swept Impeller

Submersible pumps are now in high demand due to the sporadic occurrence of recent torrential rains. The current study was carried out to investigate the hydraulic characteristics of a submersible axial-flow pump with a swept impeller and to optimize the impeller and diffuser shapes of the pump to enhance the hydraulic performance. Three-dimensional Reynolds-averaged Navier–Stokes equations were solved with the shear stress transport turbulence model. The governing equations were discretized using the finite volume method, and unstructured tetrahedral and hexahedral meshes were used in the grid system. The optimal grid system was selected through a grid dependency test. A performance test for the submersible axial-flow pump was carried out experimentally, and the results of the numerical analysis were validated against the experimental results. The hydraulic efficiency and the total head were used as objective functions. For the first optimization, a multi-objective optimization was carried out to simultaneously improve the objective functions through a hybrid multi-objective evolutionary algorithm coupled with a response surface approximation by varying the swept angle and pitch angle of the blades of the rotating impeller. The second multi-objective optimization was performed using two design variables, i.e., the inlet angle and the length of the diffuser vanes, to simultaneously increase the objective functions. Clustered optimum designs in the Pareto optimal solutions yielded significant increases in the objective function values as compared with the reference design.