Comparative Benchmarking of Multi-Objective Algorithms for Renewable Energy System Design Using Pareto Front Quality Metrics

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.

Economic Environmental Dispatch (EED) problem is the most serious problem in power operations and management. Taking into consideration transmission losses, power balance constraint, and generator capacity constraint, the EED problem becomes a non convex optimization problem, which is a difficult task that cannot be solved with traditional techniques. Furthermore, with both the environmental issues and economic objectives, the EDD problem can be formulated as a constrained nonlinear multiobjective optimization problem. In the present work, an enhanced multiobjective particle swarm optimization algorithm (EMOPSO) is proposed and applied to solve the EED problem. The proposed approach EMOPSO extends the particle swarm optimization to deal with multiobjective continuous optimization problems, EMOPSO incorporates a crowding distance mechanism for leader selection and deletion in an external archive of non dominated solutions, this mechanism improves the diversity and uniformity of the pareto front. A mutation operator is used in the population to prevent the premature convergence of the algorithm. The simulations have been made on IEEE 30 bus test system with six generators. The results are satisfying, and show that the proposed EMOPSO method was capable of achieving better performance compared with other multiobjective algorithms in the literature.

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.

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.

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.

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.

So far, many performance indicators have been proposed to compare different evolutionary multiobjective optimization algorithms (MOEAs). Among them, the inverted generational distance (IGD) is one of the most commonly used, mainly because it can measure a population’s convergence, diversity, and evenness. However, the effectiveness of IGD highly depends on the quality of the reference set. That is to say, all the reference points should be as close to the Pareto front (PF) as possible and evenly distributed to become ready for a fair performance evaluation. Currently, it is still challenging to generate well-configured reference sets, even if the PF can be given analytically. Therefore, biased reference sets might be a significant source of systematic error. However, in most MOEA literature, biased reference sets are utilized in experiments without an error estimation, which may make the experimental results unconvincing. In this paper, we propose an exact IGD (eIGD) for continuous PF, which is derived from the original IGD under an additional assumption that the reference set is perfect, i.e., the PF itself is directly utilized as an infinite-sized reference set. Therefore, the IGD values produced by biased reference sets can be compared with eIGD so that systematic error can be quantitatively evaluated and analyzed.KeywordsMultiobjective optimizationEvolutionary computationPerformance indicatorReference setDifferential geometry

A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification

Particle Swarm Optimization(PSO) algorithm is population-based and it is effective for multi-objective optimization problems.For the convergence of the swarm makes the classical algorithm easily converge to local pareto front,the convergence and diversity of the solution are not satisfactory.This paper proposed an independent dynamic inertia weights method for multi-objective particle swarm optimization(DWMOPSO).It changed each particle's inertia weight according to the evolution speed which was calculated by the value of each particle's best fitness in the history.It improved the probability to escape from the local optima.In comparison with Coello's MOPSO through five standard test functions,the solution of the new algorithm has great improvement both in the convergence to the true Pareto front and diversity.

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.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

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.

In assembly optimisation, assembly sequence planning and assembly line balancing have been extensively studied because both activities are directly linked with assembly efficiency that influences the final assembly costs. Both activities are categorised as NP-hard and usually performed separately. Assembly sequence planning and assembly line balancing optimisation presents a good opportunity to be integrated, considering the benefits such as larger search space that leads to better solution quality, reduces error rate in planning and speeds up time-to-market for a product. In order to optimise an integrated assembly sequence planning and assembly line balancing, this work proposes a multi-objective discrete particle swarm optimisation algorithm that used discrete procedures to update its position and velocity in finding Pareto optimal solution. A computational experiment with 51 test problems at different difficulty levels was used to test the multi-objective discrete particle swarm optimisation performance compared with the existing algorithms. A statistical test of the algorithm performance indicates that the proposed multi-objective discrete particle swarm optimisation algorithm presents significant improvement in terms of the quality of the solution set towards the Pareto optimal set.

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

The Production Routing Problem (PRP) has been extensively studied in logistics optimization, yet research that explicitly integrates environmental and social sustainability dimensions remains limited. This research proposes a sustainable production routing problem (SU-PRP) as a multi-objective optimization model, minimising the total operating cost, CO₂ emissions cost, and social cost simultaneously. The complex model is addressed using Multi-Objective Particle Swarm Optimization (MOPSO), which has been modified to handle discrete decision variables in a supply chain environment. The algorithm’s performance is benchmarked against NSGA-II using three quality indicators: Spacing Metric (SM), Inverted Generational Distance (IGD), and Hypervolume (HV). Numerical testing was performed using a moderate-sized problem instance comprising two plants, five customers, two products, and a two-period planning horizon, with 663 binary variables and 546 constraints. In the results, it can be observed that MOPSO has reached a larger HV, indicating better coverage of the objective space. Nevertheless, NSGA-II outperforms MOPSO in terms of solution uniformity and convergence, as evidenced by smaller SM and IGD values. The results suggest that MOPSO is more effective in operational planning scenarios where fast computation and solution diversity are crucial, such as real-time production and routing adjustments. In contrast, NSGA-II is more appropriate than MOPSO for strategic planning tasks to obtain more accurate and evenly distributed Pareto solutions.