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An Attempt to Enhance NSGA-II With a Clustering Approach
This paper models a single allocation multi-commodity hub-and-spoke network problem through a bi-objective mathematical model, considering the congestion in both hubs and connection links. A novel aggregation model is developed based on a general GI/G/c queuing system to evaluate the congestion of the flow of the multiple products in the hubs. The proposed model is then solved using a novel learning-based metaheuristic based on NSGA-II, k-Means clustering method, and an Iterated Local Search (ILS) algorithm. The proposed model and solution algorithm are validated through a set of experiments against optimal solutions, and benchmarked against four existing well-known algorithms.
This paper presents an integrated framework for management of aquifers threatened by saltwater intrusion (SI). In this framework, SEAWAT model is used for simulating the density dependent groundwater flow. Three meta-models based on the artificial neural network (ANN), M5 tree and random subspaces model (RSM) are developed, as surrogate models for SEAWAT to accurately simulate the groundwater response to different pumping and recharge scenarios. Various patterns of recharge to and discharge from aquifer are used to generate a database for training the mentioned surrogate models. To decrease the number of training parameters, the aquifer area is divided into different zones using k-means clustering technique (KMC). Additionally, a conjunctive model (CM) using a combination of the three surrogate models is proposed to enhance the accuracy of the simulation. It is then integrated with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) with the objectives of maximizing pumping rates and minimizing SI length. Next, the socially optimal scenarios are selected from the obtained Pareto-front using the Nash bargaining theory. The performance of the proposed model is evaluated by applying it to the Kahak aquifer, Iran, which is subjected to SI. The results show that the conjunctive model using KMC technique predicts SI length with a comparable accuracy and results in 95% reduction in runtime compared to a simulation-optimization (SO) model.
This study sets out to identify a real-world system by employing binary-coded and real-coded genetic algorithms (GAs). However, in a nascent stage of setting configurations of GAs, it is difficult to determine the feasible boundaries of each parameter of the system. In this paper, both GAs are implemented based on the similar mechanisms of crossover and mutation, and performed on discretized linear, logarithmic, and hybrid search spaces with corresponding encoding methods. Through simple probabilistic analysis, it follows that logarithmic space and hybrid space searches are far more advantageous to general linear space search in wide bound searching. The identification results of a simple electrical circuit support this expectation and confirm that real-coded GA (RCGA) of logarithmic and hybrid space searches are the best way to tackle the real-world problem
Introduction It has become increasingly obvious that the optimization under a single scalar-valued criterion - often a monetary one - fails to reflect the variety of aspects in a world getting more and more complex. Although the mathematical foundations were already laid by V. Pareto [1] about a hundred years ago the existing tools for multiple criteria decision making (MCDM) are still too difficult to be used by non-mathematicians. In order to overcome these difficulties a new method based on evolution strategies has been developed which is capable of giving a good insight into the structure of the Pareto set by computing a finite number of efficient solutions. (A vector f 1 is called efficient if no f 2 exists which is 'better' than f 1 in all its components.) 2 Shortcomings of Conventional Methods Numerous methods have been developed for vector optimization, e.g. linear vector optimizat
Collaboration among logistics companies offers a simple and effective way of increasing logistics operation efficiency. This study designs an optimal collaboration strategy by solving the collaborative logistics pickup and delivery problem with eco-packages (CLPDPE). This problem seeks to minimize the total operational costs by forming collaborative alliances and allocating trucking resources based on time-space (TS) network properties. The synchronization of two-echelon logistics networks is improved by solving this problem. Moreover, this study considers the stability of collaboration (i.e., the willingness of logistics companies to join and remain in collaborative alliances) by comparing different profit allocation strategies in the CLPDPE solving process. A novel methodology that combines multi-objective mixed integer programming, multidimensional K-means clustering, reference point based non-dominated sorting genetic algorithm-II (RP-NSGA-II), forward dynamic programming and improved Shapley value method is developed to formulate and solve CLPDPE. Our results show that the proposed algorithm outperforms most other algorithms in minimizing the total cost, waiting time and number of vehicles. An empirical case study in Chongqing city, China suggests that the proposed collaborative mechanism and transportation resource sharing strategy based on TS network can reduce cost, improve distribution efficiency, and contribute to efficient, smart, intelligent and sustainable urban logistics and transportation systems.
A new methodology, that combine three different Artificial Intelligence techniques, is proposed in this paper to solve the energy demand planning in Smart Homes. Conceived as a multi-objective scheduling problem, the new method is developed to reach the compromise between energy cost and the user comfort. Using an Elitist Non-dominated Sorting Genetic Algorithm II, the concept of demand-side management is applied taking into account electricity price fluctuations over time, priority in the use of equipment, operating cycles and a battery bank. The demand-side management also considers a forecast of a distributed generation for a day ahead, employing the Support Vector Regression technique. Validated by numerical simulations with real data obtained from a smart home, the user comfort levels were determined by the K-means clustering technique. The efficiency of the proposed Artificial Intelligence combination was proved according to a 51.4% cost reduction, when Smart Homes with and without distributed generation and battery bank are compared.
Collaboration such as resource sharing among logistics participants (LPs) can effectively increase the efficiency and sustainability of logistics operations, especially in the transportation and distribution of fresh and perishable products that require special infrastructure (e.g., refrigerated trucks/vehicles). This study tackles a collaborative multi-center vehicle routing problem with resource sharing and temperature control constraints (CMCVRP-RSTC). Solving the CMCVRP-RSTC by minimizing the total cost and the number of refrigerated vehicles returns a fresh logistics operational strategy that pinpoints how a multi-center fresh logistics distribution network can be reorganized to highlight potential collaboration opportunities. To find the solution to the CMCVRP-RSTC, we develop a hybrid heuristic algorithm that combines the extended k-means clustering and tabu search non-dominated sorting genetic algorithm-II (TS-NSGA-II) to search a large solution space. This hybrid heuristic algorithm ensures that the optimal solution is found efficiently through initial solution filtering and the combination of local and global searches. Furthermore, we explore how to motivate individual LPs to collaborate by analyzing the benefits of collaboration to each LP. Using the minimum costs remaining savings method and the strictly monotonic path rule, a cost saving calculation model is proposed to find the best profit allocation scheme where each collaborating LP keeps benefiting from long-term collaboration. An empirical case study of Chongqing City, China indicates the efficiency of our proposed collaborative mechanism and optimization algorithms. Our study will help improve the efficiency of logistics operation significantly and contribute to the development of more intelligent logistics systems and smart cities.
This paper studies a Green Meal Delivery Routing Problem (GMDRP) which integrates the meal delivery and vehicle routing problem. It focuses on two important issue in the actual meal delivery process: order combination and routing optimization. A multi-objective scheduling model is proposed to maximize customer satisfaction and rider balance utilization, and minimize carbon footprint. Then, Nondominated Sorting Genetic Algorithm II (NSGA-II) is adopted to find an initial rider number at the first stage. Principal Component Analysis (PCA) and k-means way are used to merge the customers’ orders and generate the initial delivery routing. Adaptive Large Neighborhood Search (ALNS) is developed to improve the quality of initial solutions, thus the optimal number of riders and final delivery routing are determined at the second stage. Computational comparison on simulation instances indicate the superiority of the proposed two-stage strategy with Tabu search (TS) and Genetic Algorithm (GA): a) the two-stage strategy could optimize the number of riders, reduce carbon emissions in distribution and ensure high customer satisfaction; b) the obtained results demonstrate the efficiency of the proposed method no matter in convergence rate or solution quality; c) for different scale instances, the proposed method can ensure that all orders are delivered within 45 min, and the average delivery time of each order is no more than 4 min. Hence, this proposed method could both improve the intelligent level of delivery and greatly support the sustainable development for the dispatching system of the meal delivery platform.
In logistics operation, delivery times are often uncertain for customers, and accommodating this uncertainty poses operation challenges as well as extra cost for logistics service providers. The delivery time uncertainty is particularly an issue if there are multiple service providers in a logistics network. To address this issue, we formulate and solve a collaborative multi-depot vehicle routing problem with time window assignment (CMDVRPTWA) to effectively reduce the impact of changing time windows on operating costs. This paper establishes a bi-objective programming model that optimize the total operating cost and the total number of delivery vehicles. A hybrid heuristic algorithm consisting of K-means clustering, Clarke–Wright (CW) saving algorithm and an Extended Non-dominated Sorting Genetic Algorithm-II (E-NSGA-II) is presented to efficiently solve CMDVRPTWA. The clustering and CW saving algorithm are employed to increase the likelihood of finding the optimal vehicle routes by identifying a feasible initial solution. The E-NSGA-II procedure combines partial-mapped crossover (PMC), relocation, 2-opt* exchange and swap mutation operations to find the optimal solution with pre-defined iteration and termination rules. Profit allocation schemes are then analyzed using the Game Quadratic Programming (GQP) method, and the optimal sequences of joining coalitions are obtained based on the principle that coalition participants’ benefits should be non-decreasing when a new participant joins the coalition. We conduct three empirical studies on a small-scale example, on several benchmark datasets and on a large-scale logistics network in Chongqing city, China. Further comparative analysis indicates that E-NSGA-II outperforms most other algorithms in solving CMDVRPTWA. This novel approach identifies profit allocation strategies that ensure the stability and reliability of the collaborative coalitions in the context of flexible customer service time windows, and can be utilized to improve the efficiency of urban logistics and intelligent transportation networks.
Diabetes mellitus is a medical condition examined by data miners for reasons such as significant health complications in affected people, the economic impact on healthcare networks, and so on. In order to find the main causes of this disease, researchers look into the patient's lifestyle, hereditary information, etc. The goal of data mining in this context is to find patterns that make early detection of the disease and proper treatment easier. Due to the high volume of data involved in therapeutic contexts and disease diagnosis, provision of the intended treatment method become almost impossible over a short period of time. This justifies the use of pre-processing techniques and data reduction methods in such contexts. In this regard, clustering and meta-heuristic algorithms maintain important roles. In this paper, a method based on the k-means clustering algorithm is first utilized to detect and delete outliers. Then, in order to select significant and effective features, four bi-objective meta-heuristic algorithms are employed to choose the least number of significant features with the highest classification accuracy using support vector machines (SVM). In addition, the 10-fold cross validation (CV) method is used to validate the constructed model. Using real case data, it is concluded that the multi-objective firefly (MOFA) and multi-objective imperialist competitive algorithm (MOICA) with a 100% classification accuracy outperform the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) with the accuracies of 98.2% and 94.6%, respectively.
The adoption of collaboration strategies among logistics facilities and the formation of one or multiple coalitions constitute a sustainable approach to vehicle routing network optimization. This paper introduces a collaborative multiple centers vehicle routing problem with simultaneous delivery and pickup (CMCVRPSDP) to minimize operating cost and the total number of vehicles in the network. Distribution and pickup centers are allowed to share vehicles and customers in order to increase the entire network’s efficiency and maximize profit. To provide the coalition coordinators with good routing solutions, we propose a hybrid heuristic algorithm which properly combines k-means and Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Based on clustering solutions, the proposed Hybrid NSGA-II (HNSGA-II) first generates a real coded population to bind our mathematical model constraints and to obtain a large number of feasible solutions which converge to optimality. Chromosomes are divided for genetic operations with partial mapped crossover and swap mutation algorithms, before their recombination to ensure the quality of our results. Comparisons with the traditional NSGA-II and the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm indicate better performances of HNSGA-II in terms of objective function values. We also apply Cost Gap Allocation method (CGA) and the strictly monotonic path selection principle to examine profit allocation schemes. Numerical analyses on part of Chongqing city’s logistics network show the superiority of HNSGA-II over MOPSO and NSGA-II on the practical case study, as well that of CGA over the Minimum Costs-Remaining Savings (MCRS), Shapley and Game Quadratic Programming (GQP) methods. In addition, the proposed profit allocation approach has supported the establishment of a grand coalition instead of two sub-coalitions. CMCVRPSDP optimization reduces long-haul transportation, improves the vehicle loading rate and facilitates sustainable development. Through the rational allocation of profits, the proposed solution methodology assures the stability and fairness among coalition members. The implementation is also important to design sustainable urban transportation networks.
The two-echelon collaborative multiple centers vehicle routing problem (2E-CMCVRP) integrates collaboration mechanism and the vehicle routing problem. Combining k-means clustering algorithm and an improved Non-dominated Sorting Genetic Algorithm-II (Im-NSGA-II), this paper proposes a three-phase approach to simultaneously minimize the aggregate operating cost and reduce carbon dioxide emission. To ensure the initial population's quality, the sweep algorithm is integrated as modification of the standard NSGA-II. The chromosome population consists of multiple depots and corresponding customer nodes independently assessed to find local solutions, and latterly combined to yield suboptimal routes. The nodes scan principle of the sweep algorithm is employed to enforce optimization constraints, and the non-dominated sorting of the population efficiently improves the solution search accuracy. Further, the Minimum Cost-Remaining Savings (MCRS) method is used to determine appropriate profit distribution schemes, and the selection of the optimal sequential coalition is executed on the basis of the strictly monotonic path principle. Computational comparisons on benchmark instances indicate the superiority of Im-NSGA-II over NSGA-II and MOGA, and an empirical study in Chongqing, China confirms the practicability of our solution approach. The evaluation of MCRS solution's stability displays outperformance over other methods including the Shapley value model, CGA and GQP, and suitable coalition sequences are selected and assessed to improve the efficiency of logistics network optimization as well as the achievement of environment-friendly objectives.
The usefulness of the genetic algorithm (GA) as judged by numerous applications in engineering and other contexts cannot be questioned. However, to make the application successful, often considerable effort is needed to customise the GA to suit the problem or class of problems under consideration. Perhaps the most basic decision which the designer of a GA makes, is whether to use binary or real coding. If the variable of the parameter space of an optimisation problem is continuous, a real coded GA is possibly indicated. Real numbers have a floating-point representation on a computer and the decision space is always discretised; it is not immediately evident that real coding should be the preferred method for encoding this particular problem. We re-visit this, and other decisions, which GA designers need to make. We present simulations on a standard test function, which show the result that no one GA performs best on every test problem. Perhaps the initial choice to code a problem using a real or binary coding is a false dichotomy. What counts are the algorithms for implementing the genetic operators and these algorithms are a consequence of the coding.
References D. Rani and M. M. Moreira. Simulation--optimization modeling: A survey and potential application in reservoir systems operation. Water Resources Management . Springer Netherlands, 2009. http://www.springerlink.com/content/p61p535r2277r852/ John H. Holland. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control and artificial intelligence. Ann Arbor: University Michigan Press, 1975. http://mitpress.mit.edu/catalog/author/default.asp?aid=3235 Z. Michalewicz. Genetic algorithms + data structures = evolution programs. 3rd edition, New York: Springer--Verlag. http://www.springer.com/computer/ai/book/978-3-540-60676-5 D. Fogel. Evolutionary computation: toward a new philosophy of machine intelligence. 3 rd edition, IEEE Press, 2006. http://ebooks.ebookmall.com/ebook/232338-ebook.htm C. Macnish. Towards unbiased benchmarking of evolutionary and hybrid algorithms for real-valued optimisation. Connection Science , 19:4 , 2007, 361--385. http://www.springerlink.com/content/2446104674981574/
Point predictions of wind speed can hardly be reliable and accurate when the uncertainty level increases in data. Prediction intervals (PIs) provide a solution to quantify the uncertainty associated with point predictions. In this paper, we adopt radial basis function (RBF) neural networks to perform interval forecasting of the future wind speed. A two-step method is proposed to determine the RBF connection weights in a multi-objective optimization framework. In the first step, the centers of the RBF are determined using the K-means clustering algorithm and the hidden-output weights of the RBF are pre-trained using the least squares algorithm. In the second step, the hidden-output weights are further adjusted by the non-dominated sorting genetic algorithm-II (NSGA-II), which aims at concurrently minimizing the width and maximizing the coverage probability of the constructed intervals. We test the performance of the proposed method on three real data sets, which are collected from different wind farms in China. The experimental results indicate that the proposed method can provide higher quality PIs than the conventional multi-layer perceptron (MLP) based methods.
It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for
2^{b}
quanta,
b=1,2, \cdots, 7
, are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.
In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.
Multi-objective evolutionary algorithms (MOEAs) that use
non-dominated sorting and sharing have been criticized mainly for: (1)
their O(MN3) computational complexity (where M is the number
of objectives and N is the population size); (2) their non-elitism
approach; and (3) the need to specify a sharing parameter. In this
paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II
(Non-dominated Sorting Genetic Algorithm II), which alleviates all of
the above three difficulties. Specifically, a fast non-dominated sorting
approach with O(MN2) computational complexity is presented.
Also, a selection operator is presented that creates a mating pool by
combining the parent and offspring populations and selecting the best N
solutions (with respect to fitness and spread). Simulation results on
difficult test problems show that NSGA-II is able, for most problems, to
find a much better spread of solutions and better convergence near the
true Pareto-optimal front compared to the Pareto-archived evolution
strategy and the strength-Pareto evolutionary algorithm - two other
elitist MOEAs that pay special attention to creating a diverse
Pareto-optimal front. Moreover, we modify the definition of dominance in
order to solve constrained multi-objective problems efficiently.
Simulation results of the constrained NSGA-II on a number of test
problems, including a five-objective, seven-constraint nonlinear
problem, are compared with another constrained multi-objective
optimizer, and the much better performance of NSGA-II is observed
Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters neccessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historial perspective rooted in mathematics, statistics and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters in unsupervised learning and the resulting system represents a data concept. From a practicual perspective clustering plays an outstanding role in data mining applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition and machine learning. This survery focuses on clustering in data ming. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique computational requirements on relevant clustering algorithms. A variety of algorithms have recently emerged that meet these requirements and were successfully applied to real-life data mining problems. They are subject of the survey.
Genetic algorithms in search, optimization and machine learning
- D E Goldenberg