A heuristic method for the supplier selection and order quantity allocation problem

Purpose Marine transportation has been faced with an increasing demand for containerized cargo during the past decade. Marine container terminals (MCTs), as the facilities for connecting seaborne and inland transportation, are expected to handle the increasing amount of containers, delivered by vessels. Berth scheduling plays an important role for the total throughput of MCTs as well as the overall effectiveness of the MCT operations. This study aims to propose a novel island-based metaheuristic algorithm to solve the berth scheduling problem and minimize the total cost of serving the arriving vessels at the MCT. Design/methodology/approach A universal island-based metaheuristic algorithm (UIMA) was proposed in this study, aiming to solve the spatially constrained berth scheduling problem. The UIMA population was divided into four sub-populations (i.e. islands). Unlike the canonical island-based algorithms that execute the same metaheuristic on each island, four different population-based metaheuristics are adopted within the developed algorithm to search the islands, including the following: evolutionary algorithm (EA), particle swarm optimization (PSO), estimation of distribution algorithm (EDA) and differential evolution (DE). The adopted population-based metaheuristic algorithms rely on different operators, which facilitate the search process for superior solutions on the UIMA islands. Findings The conducted numerical experiments demonstrated that the developed UIMA algorithm returned near-optimal solutions for the small-size problem instances. As for the large-size problem instances, UIMA was found to be superior to the EA, PSO, EDA and DE algorithms, which were executed in isolation, in terms of the obtained objective function values at termination. Furthermore, the developed UIMA algorithm outperformed various single-solution-based metaheuristic algorithms (including variable neighborhood search, tabu search and simulated annealing) in terms of the solution quality. The maximum UIMA computational time did not exceed 306 s. Research limitations/implications Some of the previous berth scheduling studies modeled uncertain vessel arrival times and/or handling times, while this study assumed the vessel arrival and handling times to be deterministic. Practical implications The developed UIMA algorithm can be used by the MCT operators as an efficient decision support tool and assist with a cost-effective design of berth schedules within an acceptable computational time. Originality/value A novel island-based metaheuristic algorithm is designed to solve the spatially constrained berth scheduling problem. The proposed island-based algorithm adopts several types of metaheuristic algorithms to cover different areas of the search space. The considered metaheuristic algorithms rely on different operators. Such feature is expected to facilitate the search process for superior solutions.

In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are implemented, has been introduced to boost the empirical performance. In this paper, we first propose to combine the variants of PSO or DE by modularizing each algorithm and incorporating the variants thereof as different options of the corresponding modules. Then, considering the similarity between the inner workings of PSO and DE, we hybridize the algorithms by creating two populations with variation operators of PSO and DE respectively, and selecting individuals from those two populations. The resulting novel hybridization, called PSODE, encompasses most up-to-date variants from both sides, and more importantly gives rise to an enormous number of unseen swarm algorithms via different instantiations of the modules therein. In detail, we consider 16 different variation operators originating from existing PSO- and DE algorithms, which, combined with 4 different selection operators, allow the hybridization framework to generate 800 novel algorithms. The resulting set of hybrid algorithms, along with the combined 30 PSO- and DE algorithms that can be generated with the considered operators, is tested on the 24 problems from the well-known COCO/BBOB benchmark suite, across multiple function groups and dimensionalities.

Metaheuristic algorithms are computational intelligence paradigms especially used for solving different optimization issues. Metaheuristics examine a collection of solutions otherwise really be wide to be thoroughly addressed or discussed in any other way. Metaheuristics can be applied to a wide range of problems because they make accurate predictions in any optimization situation. Natural processes such as the fact of evolution in Natural selection behavioral genetics, ant behaviors in genetics, swarm behaviors of certain animals, annealing in metallurgy, and others motivate metaheuristics algorithms. The big cluster search algorithm is by far the most commonly used metaheuristic algorithm. The principle behind this algorithm is that it begins with an optimal state and then uses heuristic methods from the community search algorithm to try to refine it. Many metaheuristic algorithms in diverse environments and areas are examined, compared, and described in this article. Such as Genetic Algorithm (GA), ant Colony Optimization Algorithm (ACO), Simulated Annealing (SA), Particle Swarm Optimization (PSO) algorithm, Differential Evolution (DE) algorithm and etc. Finally, show the results of each algorithm in various environments were addressed.

Particle Swarm Optimization or Differential Evolution—A comparison

Biomedical image analysis based on metaheuristic algorithms is one of the most important research areas encountered in recent years. Due to the low contrast differences between the diseased areas and the image background in high-contrast biomedical images, effective methods are required to diagnose diseases with high accuracy. To overcome the difficulties encountered in this field, metaheuristic approaches may offer effective solutions due to their advantages such as the ability of converging to the global optimum, higher convergence rate, and having few control parameters. In this work, Jellyfish Search (JS), Marine Predators (MPA), Tunicate Swarm (TSA), Mayfly Optimization (MA), Chimp Optimization (ChOA), Slime Mould Optimization (SMA), Archimedes Optimization (AOA), and Equilibrium Optimizer (EO) algorithms, which are the most recently proposed metaheuristic algorithms in the literature, have been improved as clustering based in order to achieve vessel segmentation with high precision. Also, a detailed performance comparison of these algorithms has been realized for the rate of convergences, error values reached, CPU time, standard deviation, sensitivity, specificity, accuracy, F-score, and Wilcoxon rank sum-test. In order to present the compatibility of the results obtained with the literature, the performances of these novel algorithms have also been compared to that of Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Differential Evolution (DE) algorithms. The simulation results represent that each algorithm produces similar convergence and error performance. Also, it can be emphasized from the statistical analyses that the stability and robustness of each metaheuristic approach are quite adequate in separating the vessel pixels and the background pixels of a retinal image. In general, this paper proves that although having fewer number of control parameters, the JS, MPA, TSA, MA, ChOA, SMA, AOA, and EO algorithms produce similar but a bit better results in terms of image segmentation when compared to PSO, GWO, and DE algorithms.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Comparison of computational intelligence algorithms for loadability enhancement of restructured power system with FACTS devices

SUMMARYIn this paper, we present a new type of hybrid methods for global optimization with particle swarm optimization (PSO) and differential evolution (DE), which have been attracting interest as heuristic and global optimization methods. Concretely, “p‐best solutions” as the targets of PSO's particles are actuated by DE's evolutional mechanism in order to promote PSO's global searching ability. The presented hybrid method works effectively because PSO acts as a local optimizer and DE plays a role as a global optimizer. To evaluate performance of the hybridization, our method is applied to some benchmarks and is compared with the separated PSO and DE. Through computer simulations, it is demonstrated that the proposed hybrid method performs rather better than the component algorithms separately.

The research and development of metaheuristic methods are critical issues in computer science. In the past decade, metaheuristic algorithms have been used in many engineering applications such as optimization of engineering problems, telecommunications, information security, and image processing. Many metaheuristic algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and genetic algorithm (GA) are recently becoming very popular.There are many studies conducted in the literature on the comparison of PSO with other metaheuristic algorithms. In this chapter, various studies carried out between the years of 2010 and 2020 about the comparison of PSO with the other metaheuristic algorithms will be examined. The metaheuristic algorithms to be considered are simulated annealing (SA), genetic algorithm (GA), differential evolution (DE), ant colony optimization (ACO), artificial bee colony (ABC) algorithm, particle swarm optimization (PSO), tabu search (TS), harmony search (HS), firefly algorithm (FF), cuckoo search (CS), bat-inspired algorithm (BA), water wave optimization (WWO), clonal selection algorithm (CLONALG), chemical reaction optimization (CRO), sine cosine algorithm (SCA), glowworm swarm optimization (GSO), and grey wolf optimizer (GWO). This study aims to evaluate and analyze the covered papers according to several criteria such as (a) rates of studies according to publishing years, (b) the metaheuristic algorithms that are compared to PSO, (c) performance evaluation of compared algorithms, (d) the metaheuristic algorithms with their inspirational approaches and their initial proposed studies and years, (e) the field of subjects where the algorithms are applied in the reviewed studies, and (f) used databases in the examined studies.This study is a comprehensive literature review of the comparison of PSO with the most popular metaheuristic algorithms. The intention of this review is to be useful for researchers who want to conduct a survey on this area of the subject as this chapter will cover the essential and helpful analysis of the related research.

A differential evolution algorithm with intersect mutation operator

Network reconfiguration for loss reduction in a distribution system is a very important way to save the electrical energy. This article proposes a hybrid evolutionary algorithm to solve the distribution feeder reconfiguration problem. The algorithm combines a fuzzy adaptive particle swarm optimization with a differential evolution algorithm, called the fuzzy adaptive particle swarm optimization–differential evolution. The fuzzy adaptive particle swarm optimization includes two parts. The first part is fuzzy adaptive binary particle swarm optimization, which determines the status of tie switches (open or closed), and the second part is fuzzy adaptive discrete particle swarm optimization, which determines the sectionalizing switch number. In the proposed algorithm, due to the results of binary particle swarm optimization and discrete particle swarm optimization algorithms that highly depend on the values of their parameters (such as the inertia weight and learning factors), a fuzzy system is employed to adaptively adjust the parameters during the search process. The differential evolution algorithm is combined with the fuzzy adaptive particle swarm optimization algorithm to improve its performance. The proposed algorithm is tested on two distribution test feeders. The results of simulation show that the proposed method is very powerful and is guaranteed to obtain the global optimization.

Objective: In this paper, an improved hybrid differential evolution (IHDE) algorithm based on differential evolution (DE) algorithm and particle swarm optimization (PSO) has been proposed to solve the optimal power flow (OPF) problem of power system which is a multi-constrained, large-scale and nonlinear optimization problem. Method: In IHDE algorithm, the DE is employed as the main optimizer; and the three factors of PSO, which are inertia, cognition, and society, are used to improve the mutation of DE. Then the learning mechanism and the adaptive control of the parameters are added to the crossover, and the greedy selection considering the value of penalty function is proposed. Furthermore, the replacement mechanism is added to the IHDE for reducing the probability of falling into the local optimum. The performance of this method is tested on the IEEE30-bus and IEEE57-bus systems, and the generator quadratic cost and the transmission real power losses are considered as objective functions. Results: The simulation results demonstrate that IHDE algorithm can solve the OPF problem successfully and obtain the better solution compared with other methods reported in the recent literatures.

This paper investigates the suitability of the Particle Swarm Optimization (PSO) and the Differential Evolution (DE) algorithms in solving expensive optimization problems. Eight PSO variants, and eight DE variants are experimentally compared among each other. The Comparing Continuous Optimizers (COCO) methodology was adopted in comparing these variants on the noiseless BBOB test bed. Based on the results, we provide useful insights regarding the algorithms' relative efficiency and effectiveness under an expensive budget of function evaluations, and draw suggestions about which algorithm should be used depending on what we know about our optimization problem in terms of evaluation budget, dimensionality, and function structure. Furthermore, we propose possible future research directions addressing the algorithms limitations. Overall, DE variants perform well in low dimensions, whereas in higher dimensions, several PSO variants surpass DE algorithms. Among the top performers, JADE and χPSO are the robust algorithms for solving expensive budget problems.

Fuel cells are complex multiphysical systems characterized by a stratified geometry consisting of thin layers of different materials. Their full characterization involves a number of physical parameters, which are important for quantifying and comparing the performance of the materials. The physical parameters are also used in fuel cell models, which allow the fast exploration of different operating scenarios and can be implemented in optimization procedures aimed at achieving the best structural and operating conditions. The system of equations involved in these models, e.g. the Nernst equation, the Butler-Volmer equation and the diffusion equation, are strongly non-linear; thus, the model itself is extremely sensitive to parameter variations. Careful ex-situ measurements of such parameters can be performed by means of a number of diagnostic techniques, whose results are however not completely consistent with fuel cell operation due to several effects, e.g. variable interactions and boundary effects in the thin layers of the fuel cell. Conversely, “in situ” measurements can provide meaningful operational values, but a very few techniques are available to determine a limited number of parameters.A solution can consist in multiple parameter identification from multiple fundamental measurements, such as polarization curve and electrochemical impedance spectroscopy, performed in different conditions, e.g. at different temperature, pressure, concentration, and humidification.If there is only one unknown parameter, the solution is easy, requiring just a statistical interpolating technique. In the case of multiple unknown parameters, which is the most frequent condition, the problem becomes increasingly difficult as the number of parameters increases as duplicity problem emerges, i.e., several groups of parameters may lead to the same performance (e.g. polarization curve).Recently, a number of numerical tools are under development to face this kind of problems, some based on stochastic mathematical models, each presenting specific features in terms of accuracy, convergence, stability, robustness, and calculation speed [1]. Among the most promising methods, some of which have already been applied to multiple fuel cell parameter identification, are the Ishibashi–Kimura method [2], the Lambert W-function method [3], the Levenberg-Marquardt algorithm (LMA), the Gauss-Newton algorithm (GNA), the hybrid artificial bee colony algorithm [4], the trust region method, the current switching method [5], the simulated annealing method [6], and the particle swarm optimization (PSO) [7], and the differential evolution method [8].The presentation will focus on the application of a particular class of stochastic optimization methods to the problem of multiple parameters identification. These methods have already been widely tested and applied successfully to the simultaneous search of sets of optimal parameters with different physical dimensions, making them ideal tools to cope with the present problem. Their recent relevant literature is vast. They are especially suited for multimodal and noisy functions over large search spaces, which makes them particularly appealing for the problem at hand. The main drawback of such methods is the high number of objective function evaluations needed for convergence; however, thanks to a particular formulation of the PEMFC model, such drawback can be of minor impact, i.e. the overall computational times are on the order of a few tens of seconds.We are going to present the application of two of the most well-known metaheuristic methods, namely Particle Swarm Optimization (PSO) and Differential Evolution (DE), developed in previous work and suitably adapted. It should be noted that PSO has already been applied to parameter identification for FCs, while the application of DE is novel in this context. This is somewhat surprising since, as results will show, DE provides better results and offers higher robustness. We will present the implementation details regarding PSO and DE. The optimization algorithms have not been tuned to the specific problem and algorithm control parameters have been chosen from reasonable values suggested in literature.

Thiswork proposes a Differential Evolution (DE) algorithm based energy management system (EMS) to optimize the performance of a microgrid in the presence of renewable energy sources. Various types of distributed generators (DGs), namely Micro Turbine (MT), Phosphoric Acid Fuel Cell (PAFC), Wind Turbine (WT), Photo-voltaic (PV) and battery (batt) are present in the micro-grid. Out of these DGs, WT and PV have a randomized natural behavior. To optimize the micro-grid operation and cover the uncertainty in power generation from the renewable resources, the incentive based demand response programs are incorporated in the EMS. The performance of EMS is optimized by minimizing the operating cost of the micro-grid and by minimizing its pollutant emissions using DE algorithm. The results obtained using DE algorithm are compared with the Particle Swarm Optimization (PSO) based reported results. On comparison the proposed DE algorithm is found to be superior in terms of solution quality and convergence speed.