On the automatic design of multi-objective particle swarm optimizers: experimentation and analysis

In this paper, a multi-objective particle swarm optimization algorithm based on the relative distance strategy is proposed to realize hydrodynamic coefficient identification, which can improve the accuracy of parameter identification without determining the weight manually. Firstly, single-objective particle swarm optimization (PSO) is used to identify the parameters of the model with a low coupling degree. Then, the parameters of the strongly coupled sway and yaw motion model are regarded as multi-objective, and a set of unbiased Pareto optimal solutions are obtained by the multi-objective particle swarm optimization (MOPSO) algorithm. Then the distance function of the Pareto solution is constructed to determine the parametric solution of the model. Finally, experimental identification is carried out by using the data set collected from the real ship. Experimental results show that the accuracy of model parameters obtained by this identification method is about 91.6%, and there is no need to set the weighting coefficient.

A method for designing miniaturized frequency selective surface (FSS) using equivalent circuit model (ECM) and multi-objective particle swarm optimization (MOPSO) algorithm is proposed in this paper. In the proposed method, ECM describing the desired frequency response is established, and parameters of the ECM are determined using the MOPSO algorithm. Combining the ECM analysis and the MOPSO algorithm, the requirements of desired frequency response can be converted into the constraints of equivalent circuit parameters, which simplifies the optimization process of FSS design. For verification, a single-layer bandstop-bandpass FSS composed of convoluted elements with the unit cell size of 0.073λ 0 × 0.073λ 0 is designed. Simulation results show that the −15 dB bandwidth is from 2.62 to 2.83 GHz, and the −0.5 dB bandwidth is from 3.84 to 5 GHz. Meanwhile, the resonant frequency is stable at different incident angles (up to 80°) under TE and TM polarization. Finally, the proposed FSS prototype is fabricated and measured. The measured results agree well with the simulated ones.

An integrated optimization strategy based on Kriging model and multi-objective particle swarm optimization (PSO) algorithm was constructed. As a new surrogate model technology, Kriging model has better fitting precision for nonlinear problem. The Kriging model was adopted to replace computer aided engineering (CAE) simulation as fitness function of multi-objective PSO algorithm, and the computation cost can be reduced greatly. By introducing multi-objective handling mechanism of crowding distance and mutation operator to multi-objective PSO algorithm, the entire Pareto front can be approximated better. It is shown that the multi-objective optimization strategy can get higher solving accuracy and computation efficiency under small sample.

This paper addresses a multi-objective approach for simultaneous dynamic expansion planning of conventional sub-transmission grid and Regional Virtual Power Plant (RVPP). In such a feed-in tariff electricity market, it will assist RVVP’s stakeholders in deciding whether or not they should invest in new equipment’s installation. A Multi-Objective Particle Swarm Optimization (MOPSO) algorithm as a heuristic optimization method is proposed to eliminate the conventional centralized planning, which has led to competition between Regional Electric Company (REC) and RVPP for power delivery in sub-transmission system. Two objective functions are considered for simultaneous expansion planning of these two systems. The first one takes the minimum cost of the REC, as the sub-transmission grid operator, into account while the other one considers profit maximization for RVPP. To achieve the goals, MOPSO algorithm is employed to find the best expansion of REC and best location and capacity of RVPP’s resources. Having solved the proposed multi-objective optimization problem, a Pareto front is determined to show the trade-off between REC and RVPPs' contributions in joint optimal expansion planning of conventional sub-transmission grid and the RVPP. To demonstrate the applicability and effectiveness of the proposed approach, a realistic sub-transmission system in Guilan Province, Iran is used as a test system, and the results are evaluated accordingly.

This paper deals with the optimal placement of distributed generation (DG) units in distribution systems via an enhanced multi-objective particle swarm optimization (EMOPSO) algorithm. To pursue a better simulation of the reality and provide the designer with diverse alternative options, a multi-objective optimization model with technical and operational constraints is constructed to minimize the total power loss and the voltage fluctuation of the power system simultaneously. To enhance the convergence of MOPSO, special techniques including a dynamic inertia weight and acceleration coefficients have been integrated as well as a mutation operator. Besides, to promote the diversity of Pareto-optimal solutions, an improved non-dominated crowding distance sorting technique has been introduced and applied to the selection of particles for the next iteration. After verifying its effectiveness and competitiveness with a set of well-known benchmark functions, the EMOPSO algorithm is employed to achieve the optimal placement of DG units in the IEEE 33-bus system. Simulation results indicate that the EMOPSO algorithm enables the identification of a set of Pareto-optimal solutions with good tradeoff between power loss and voltage stability. Compared with other representative methods, the present results reveal the advantages of optimizing capacities and locations of DG units simultaneously, and exemplify the validity of the EMOPSO algorithm applied for optimally placing DG units.

The current paper presents a novel multi-objective particle swarm optimization (MOPSO) algorithm for solving no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, in the algorithm, particles are represented as job permutations and updated directly in the discrete domain. Second, the concept of Pareto dominance is applied to compare different solutions of multi-objective optimization, and a set is employed to hold and to update the obtained non-dominated solutions, where a randomly selected non-dominated solution is assigned as the global best particle to maintain the diversity of the searching direction and to speed up the convergence process to the Pareto front. Third, a new multi-objective heuristic, named the PWQ (Pan—Wang—Qian) heuristic, is proposed to produce a population of initial particles with relatively good performances. Fourth, a simple but effective multi-objective local search algorithm is developed to embed in the MOPSO algorithm for stressing the balance between global exploration and local exploitation. In addition, two speed-up methods are devised to evaluate a job permutation and its insert neighbourhood respectively. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed algorithm is superior to a recently published multi-objective hybrid differential evolution (MHDE) algorithm in terms of searching quality, diversity level, robustness, and efficiency.

Multi-objective particle swarm optimization model for conjunctive use of treated wastewater and groundwater

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

This paper deals with a multi-objective unequal sized dynamic facility layout problem (DFLP) with pickup/drop-off locations. First, a mathematical model to obtain optimal solutions for small size instances of the problem is developed. Then, a multi-objective particle swarm optimisation (MOPSO) algorithm is implemented to find near optimal solutions. Two new heuristics to prevent overlapping of the departments and to reduce ‘unused gaps’ between the departments are introduced. The performance of the MOPSO is examined using some sets of available test problems in the literature and various random test problems in small, medium, and large sizes. The percentage of improvements on the initial solutions is calculated for small, medium and large size instances. Also, the generation metric and the space metric for non-dominated solutions are examined. These experiments show the good performance of the developed MOPSO and sensitivity analysis show the robustness of the obtained solutions.

In order to enhance the convergence and distribution of multi-objective particle swarm algorithm, an improved multi-objective particle swarm optimization algorithm was proposed. Linear decreasing inertia weight was used to update. The method can improve the deficiency that the algorithm falls into local optimal easily. The improved Logistic mapping was used to increase ergodicity of the particles. The method can expand the search scope. At the same time, the elite archiving mechanism and the mutation probability were introduced to increase the disturbance. The method can improve the local optimal. Compared with the real Pareto front, NSGA-II and MOEAD algorithm, the simulation shows that the algorithm proposed in the paper is effective.

This study employs a multi-objective particle swarm optimization (MOPSO) algorithm to address the dual-objective challenge in the robotic polishing of Ti-6Al-4V. The aim is to determine optimal parameters that minimize surface roughness while maximizing the material removal rate (MRR), thereby improving both surface quality and processing efficiency. First, a material removal depth model for end-face polishing is established based on Preston's equation and theoretical analysis, from which the MRR model is derived. Subsequently, orthogonal experiments are conducted to investigate the influence of process parameters and their interactions on surface roughness, followed by the development of a quadratic polynomial roughness prediction model. Analysis of variance (ANOVA) and model validation confirm the model's reliability. Finally, the MOPSO algorithm is applied to obtain the Pareto optimal solution set, yielding the optimal parameter combination. Experimental results demonstrate that at a normal contact force of 7.58 N, a feed rate of 4.52 mm/s, and a spindle speed of 5851 rpm, the achieved MRR and Ra values are 0.2197 mm3/s and 0.291 μm, respectively. These results exhibit errors of only 5.64% and 2.65% compared to model predictions, validating the proposed method's effectiveness.

In data center companies, cloud computing can host multiple types of heterogeneous virtual machines (VMs) and provide many features, including flexibility, security, support, and even better maintenance than traditional centers. However, some issues need to be considered, such as the optimization of energy usage, utilization of resources, reduction of time consumption, and optimization of virtual machine placement. Therefore, this paper proposes an alternative multiobjective optimization (MOP) approach that combines the salp swarm and sine-cosine algorithms (MOSSASCA) to determine a suitable solution for virtual machine placement (VMP). The objectives of the proposed MOSSASCA are to maximize mean time before a host shutdown (MTBHS), to reduce power consumption, and to minimize service level agreement violations (SLAVs). The proposed method improves the salp swarm and the sine-cosine algorithms using an MOP technique. The SCA works by using a local search approach to improve the performance of traditional SSA by avoiding trapping in a local optimal solution and by increasing convergence speed. To evaluate the quality of MOSSASCA, we perform a series of experiments using different numbers of VMs and physical machines. The results of MOSSASCA are compared with well-known methods, including the nondominated sorting genetic algorithm (NSGA-II), multiobjective particle swarm optimization (MOPSO), a multiobjective evolutionary algorithm with decomposition (MOEAD), and a multiobjective sine-cosine algorithm (MOSCA). The results reveal that MOSSASCA outperforms the compared methods in terms of solving MOP problems and achieving the three objectives. Compared with the other methods, MOSSASCA exhibits a better ability to reduce power consumption and SLAVs while increasing MTBHS. The main differences in terms of power consumption between the MOSCA, MOPSO, MOEAD, and NSGA-II and the MOSSASCA are 0.53, 1.31, 1.36, and 1.44, respectively. Additionally, the MOSSASCA has higher MTBHS value than MOSCA, MOPSO, MOEAD, and NSGA-II by 362.49, 274.70, 585.73 and 672.94, respectively, and the proposed method has lower SLAV values than MOPSO, MOEAD, and NSGA-II by 0.41, 0.28, and 1.27, respectively.

A novel approach to hybrid dynamic environmental-economic dispatch of multi-energy complementary virtual power plant considering renewable energy generation uncertainty and demand response

In this paper, a multi-objective hybrid firefly and particle swarm optimization (MOHFPSO) was proposed for different multi-objective optimal power flow (MOOPF) problems. Optimal power flow (OPF) was formulated as a non-linear problem with various objectives and constraints. Pareto optimal front was obtained by using non-dominated sorting and crowding distance methods. Finally, an optimal compromised solution was selected from the Pareto optimal set by applying an ideal distance minimization method. The efficiency of the proposed MOHFPSO technique was tested on standard IEEE 30-bus and IEEE 57-bus test systems with various conflicting objectives. Simulation results were also compared with non-dominated sorting based multi-objective particle swarm optimization (MOPSO) and different optimization algorithms reported in the current literature. The achieved results revealed the potential of the proposed algorithm for MOOPF problems.

The selection of variational mode decomposition (VMD) parameters usually adopts the empirical method, trial-and-error method, or single-objective optimization method. The above-mentioned method cannot achieve the global optimal effect. Therefore, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters of VMD, and it is applied to the composite fault diagnosis of the gearbox. The specific steps are: first, symbol dynamic entropy (SDE) can effectively remove background noise, and use state mode probability and state transition to preserve fault information. Power spectral entropy (PSE) reflects the complexity of signal frequency composition. Therefore, the SDE and PSE are selected as fitness functions and then the Pareto frontier optimal solution set is obtained by the MOPSO algorithm. Finally, the optimal combination of VMD parameters (k, a) is obtained by normalization. The improved VMD is used to analyze the simulation signal and gearbox fault signal. The effectiveness of the proposed method is verified by comparing with the ensemble empirical mode decomposition (EEMD).