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This paper presents a hybrid grasshopper optimization algorithm using a novel decoder and local search to solve instances of the open vehicle routing problem with capacity and distance constraints. The algorithm’s decoder first defines the number of vehicles to be used and then it partitions the clients, assigning them to the available routes. The...
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... is relevant to notice that this decodification/codification method can lead to infeasible solutions. In Figure 3, an example of an infeasible solution is presented. The violation is made over the capacity and maximum distance constraints since for s-route Whenever a solution is infeasible after decoding, it enters the feasibility recovery procedure. ...
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Finding the shortest route between a pair of origin and destination is known to be a crucial and challenging task in intelligent transportation systems. Current methods assume fixed travel time between any pairs, thus the efficiency of these approaches is limited because the travel time in reality can dynamically change due to factors including the...
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... There are, of course, a very large number of other algorithms that could have been used, such as social engineering optimizer (SEO) [40], ant inspired algorithm [41], grasshopper optimization algorithm [42], red deer algorithm (RDA) [43], quantum fruit fly optimization algorithm [44] and beetle antennae search (NABAS) algorithm [45] to name only a small fraction of the possibilities. Our experiment relied heavily on a random number generator; therefore, we used the well-tested Mersenne Twister Random Number Generator [46]. ...
Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research deals with measuring the performance of stochastic optimization algorithms, as well as the confidence intervals of the empirically obtained statistics. Traditionally, the arithmetic mean is used for measuring average performance, but we propose quantiles for measuring average, peak and bad-case performance, and give their interpretations in a relevant context for measuring the performance of the metaheuristics. In order to investigate the differences between arithmetic mean and quantiles, and to confirm possible benefits, we conducted experiments with 7 stochastic algorithms and 20 unconstrained continuous variable optimization problems. The experiments showed that median was a better measure of average performance than arithmetic mean, based on the observed solution quality. Out of 20 problem instances, a discrepancy between the arithmetic mean and median happened in 6 instances, out of which 5 were resolved in favor of median and 1 instance remained unresolved as a near tie. The arithmetic mean was completely inadequate for measuring average performance based on the observed number of function evaluations, while the 0.5 quantile (median) was suitable for that task. The quantiles also showed to be adequate for assessing peak performance and bad-case performance. In this paper, we also demonstrated how to useproposed a bootstrap method to calculate the confidence intervals of the probability of the empirically obtained quantiles. Considering the many advantages of using quantiles, including the ability to calculate probabilities of success in the case of multiple executions of the algorithm and the practically useful method of calculating confidence intervals, we recommend quantiles as the standard measure of peak, average and bad-case performance of stochastic optimization algorithms.
... Mendoza et al. (2020) used a combination grasshopper headway computation to deliver the VRP to perceive the ideal courses. 3 Alinaghian and Shokouhi (2017) analyzed the coordinating issue with propel where the split movement cannot be recognized and only one vehicle should be used to pass on the things. 4 PSO is used to smooth out the capacitated vehicle directing issue; without a doubt, the waste arrangement viability, eco-benevolence, and full scale cost are used as issue constraints (Hannan et al. 2018). ...
One of the research problems is the vehicle routing problem (VRP) in smart cities for smooth movement of the vehicles and less traffic in the smart cities. The dynamic vehicle routing structure is a problem where a time frame is given for each vehicle to reach the destination, and this is classified as VRP with time windows. The Solomon’s datasets are utilized for this vehicle routing problem with time windows (VRPTW). The goal is to calculate the least number of vehicles using two variants of multiverse optimizer. The two variants of multiverse optimizer are compared with the other techniques in terms of the travelled distances, the number of vehicles and the computational time are analyzed, and the effectiveness is calculated for all the proposed models for the VRPTW problem.
... A generalization of the Travelling Salesman Problem is the Vehicle Routing Problem (VRP) [9,[63][64][65][66] where a desired quantity of goods needs to be delivered from a central depot to customers by vehicles of a certain capacity. ...
... Finally, GAMS for the kroA100.tsp benchmark stopped the computation at 1000.02 s by exceeding the time limit, but the intermediate result of the path length 21282 and its traversal through positions 1, 47,93,28,67,58,61,51,87,25,81,69,64,40,54,2,44,50,73,68,85,82,95,13,76,33,37,5,52,78,96,39,30,48,100,41,71,14,3,43,46,29,34,83,55,7,9,57,20,12,27,86,35,62,60,77,23,98,91,45,32,11,15,17,59,74,21,72,10,84,36,99,38,24,18,79,53,88,16,94,22,70,66,26,65,4,97,56,80,31,89,42,8,92,75,19,90,49,6,63, 1 corresponds to the known optimal solution for this benchmark. The optimal route is in Figure 5. ...
The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software’s applicability.
... Performance (solution accuracy and computation time) of the metaheuristic algorithms vary one with respect to another, and are truly dependent on tuning common and specific parameters of algorithms [59,60]. The metaheuristic algorithms are developed with common features, such as [63]: (a) search mechanisms employed with basic principles, namely velocity, force, and acceleration, and (b) mimic the social behavior of a group of animals. Grasshopper optimization algorithms (GOA) have proven their potential in solving many recent problems (engineering design, energy, image processing, and so on), namely, optimization [64,65]. ...
In India, a densely populated country, fossil fuel depletion affects the energy sector that fulfils the industrial and human needs. Concerning greenhouse gas emissions and pollutants, and sustainability, there is a great demand to search for alternate feedstocks to produce alternate fuels at a low cost. The present work focuses on waste coconut and fish oil as potential inexpensive feedstock for biodiesel production. Two-stage transesterification processes for biodiesel production from hybrid oils mixed in a 1:1 volume ratio by employing solid nano-catalyst Magnesium Oxide (MgO). Response surface methodology (RSM) was used to analyze the effects of the physics of transesterification variables, such as methanol-to-oil molar ratio (M:O), MgO catalyst concentration (MgO CC), and reaction temperature (RT), on biodiesel yield, based on experimental data gathered in accordance with the matrices of central composite design (CCD). MgO CC showed the highest contribution, followed by M:O and RT, to maximize biodiesel yield. All interaction factors showed a significant effect except the M:O with RT. Grasshopper optimization algorithm (GOA) determined optimal conditions (M:O: 10.65; MgO CC: 1.977 wt.%; RT: 80 °C) based on empirical equations, resulting in maximum biodiesel yield conversion experimentally equal to 96.8%. The physical stability of the MgO nano-catalyst and reactivity up to 5 successive cycles can yield 91.5% biodiesel yield, demonstrating its reusability for sustainable biodiesel production at low cost. The optimized biodiesel yield showed better physicochemical properties (tested according to ASTM D6751-15C) to use practically in diesel engines.
... The search agents are urged to move quickly during exploration, while they tend to move slowly during exploitation. However, GOA is not adopted in combinatorial t-way testing problem, even though it is accepted in some areas of optimization including multiobjective problems [151], routing problems [152], scheduling problem [153], and so on. ...
The metaheuristic algorithm is a very important area of research that continuously improves in solving optimization problems. Nature-inspired is one of the metaheuristic algorithm classifications that has grown in popularity among researchers over the last few decades. Nature-inspired metaheuristic algorithms contribute significantly to tackling many standing complex problems (such as the combinatorial t-way testing problem) and achieving optimal results. One challenge in this area is the combinatorial explosion problem, which is always intended to find the most optimal final test suite that will cover all combinations of a given interaction strength. As such, test case generation has been selected as the most active research area in combinatorial t-way testing as Non-deterministic Polynomial-Time Hardness (NP-hard). However, not all metaheuristics are effectively adopted in combinatorial t-way testing, some proved to be effective and thus have been popular tools selected for optimization, whilst others were not. This research paper outlines a hundred and ten (110) outstanding nature-inspired metaheuristic algorithms for the last decades (2001 and 2021), such as the Coronavirus Optimization Algorithm, Ebola Optimization Algorithm, Harmony Search, Tiki-Taka Algorithm, and so on. The purpose of this review is to revisit and carry out an up-to-date review of these distinguished algorithms with their respective current states of use. This is to inspire future research in the field of combinatorial t-way testing for better optimization. Thus, we found that all metaheuristics have a simple structure that can be adopted in different areas to become more efficient in optimization. Finally, we suggested some future paths of investigation for researchers who are interested in the combinatorial t-way testing field to employ more of these algorithms by tuning their parameters settings to achieve an optimal solution.
... As the literature review reveals, most hybrid approaches are designed for specific optimization tasks that involve feature selection [15], image segmentation [46], clustering [19], or unique engineering problems [37]. Furthermore, since designing a hybridization strategy that would be able to enhance more than one meta-heuristic is particularly challenging [45], existing solutions often incorporate two algorithms suitable to an optimization problem. ...
The recent proliferation of population-based meta-heuristics designed for solving optimization problems and their successes confirm that more promising techniques inspired by physical phenomena or biological systems are desired. Therefore, in this paper, a novel hybridization approach is proposed to improve the performance of optimization algorithms. The approach replaces a small number of worst solutions obtained by a meta-heuristic with predicted candidates without altering its search operators. Specifically, a target fitness value of the predicted candidate is determined based on the fitness of the population and a search strategy. Then, a calibration problem is solved to infer its decision variables. In this study, the proposed hybridization technique is applied to ten state-of-the-art population-based algorithms. The meta-heuristics and hybrids are evaluated on 82 functions, four engineering problems, and a new challenging problem of estimating a constant in Markov’s inequality using minimal polynomials of different degrees. The experimental results reveal the superiority of the hybrids over their counterparts and confirm the suitability of the proposed approach for improving the efficiency of meta-heuristics.
A model predictive cascade controller is proposed in this article to resolve the actuator saturation problem of underwater human‐occupied vehicle (HOV) trajectory tracking. For the kinematic model, a grasshopper optimization‐based model predictive control (MPC) is developed to obtain control velocities with small fluctuations in allowable regions. Based on the desired velocities obtained from the improved kinematic control, the HOV dynamic model is used to generate the corresponding torques and forces using sliding mode control. With the control velocities and forces given by the cascade control strategy, the elimination of actuator saturation during the HOV trajectory tracking can be realized. The proposed controller is verified by simulations using a numerical example based on a four degrees of freedom (4‐DOFs) HOV.
Abstract
Nowadays organizations outsource transportation of goods or services to reduce cost which
leads to a particular type of problem called open location-routing. Also, each logistic
organization possesses a limited number of specifc vehicles that may not be enough in cer�tain circumstances. This issue indicates the importance of simultaneously considering both
open and closed routs. On the other hand, the growing concerns about the detrimental envi�ronmental impacts of human activities reveal the necessity of paying attention to environ�mental issues in logistics. In this study, a bi-objective mathematical programming model is
proposed for two-echelon close and open location-routing problem (2E-COLRP) including
two echelons of factories, depots and customers to minimize costs and CO2 emissions. The
proposed model fnds the optimal routs, optimal number of vehicles and facilities as well
as the locations of facilities. The augmented epsilon constraint method is used as an exact
method to solve the small-sized problems. Due to complexity of model, two metaheuristic
algorithms named MOGWO and NSGA-II are utilized to tackle the problems. The ef�ciency of two aforementioned algorithms is evaluated in terms of several indices consid�ering 22 problem instances with various sizes. The results show that MOGWO performs
better than NSGA-II.
Keywords Open location routing · Closed location routing · Environmental impact ·
Metaheuristic · MOGWO · NSGA-II
Nowadays organizations outsource transportation of goods or services to reduce cost which
leads to a particular type of problem called open location-routing. Also, each logistic
organization possesses a limited number of specifc vehicles that may not be enough in cer-
tain circumstances. This issue indicates the importance of simultaneously considering both
open and closed routs. On the other hand, the growing concerns about the detrimental envi-
ronmental impacts of human activities reveal the necessity of paying attention to environ-
mental issues in logistics. In this study, a bi-objective mathematical programming model is
proposed for two-echelon close and open location-routing problem (2E-COLRP) including
two echelons of factories, depots and customers to minimize costs and CO2 emissions. The
proposed model fnds the optimal routs, optimal number of vehicles and facilities as well
as the locations of facilities. The augmented epsilon constraint method is used as an exact
method to solve the small-sized problems. Due to complexity of model, two metaheuristic
algorithms named MOGWO and NSGA-II are utilized to tackle the problems. The ef-
ciency of two aforementioned algorithms is evaluated in terms of several indices consid-
ering 22 problem instances with various sizes. The results show that MOGWO performs
better than NSGA-II.
