Adaptive Permutation-Based Genetic Algorithm for Solving VRP with Stochastic Demands

As one of the most popular supply chain management problems, the Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades, most of these studies focus on deterministic problem where the customer demands are known in advance. But the Vehicle Routing Problem with Stochastic Demands (VRPSD) has not received enough consideration. In the VRPSD, the vehicle does not know the customer demands until the vehicle arrive to them. This paper use a hybrid algorithm for solving VRPSD, the hybrid algorithm based on Particle Swarm Optimization (PSO) Algorithm, combines a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, and Variable Neighborhood Search (VNS) algorithm. A real number encoding method is designed to build a suitable mapping between solutions of problem and particles in PSO. A number of computational studies, along with comparisons with other existing algorithms, showed that the proposed hybrid algorithm is a feasible and effective approach for Vehicle Routing Problem with Stochastic Demands.

In this paper we describe an efficient approach for multimodal function optimization using genetic algorithms (GAs). We recommend the use of adaptive probabilities of crossover and mutation to realize the twin goals of maintaining diversity in the population and sustaining the, convergence capacity of the GA. In the adaptive genetic algorithm (AGA), the probabilities of crossover and mutation, p/sub c/ and p/sub m/, are varied depending on the fitness values of the solutions. High-fitness solutions are 'protected', while solutions with subaverage fitnesses are totally disrupted. By using adaptively varying p/sub c/ and p/sub ,/ we also provide a solution to the problem of deciding the optimal values of p/sub c/ and p/sub m/, i.e., p/sub c/ and p/sub m/ need not be specified at all. The AGA is compared with previous approaches for adapting operator probabilities in genetic algorithms. The Schema theorem is derived for the AGA, and the working of the AGA is analyzed. We compare the performance of the AGA with that of the standard GA (SGA) in optimizing several nontrivial multimodal functions with varying degrees of complexity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The vehicle routing problem with stochastic demand (VRPSD) is one of the most important problems in distribution and transportation. The classical models for the vehicle routing problem with stochastic demand are the chance-constrained model and the penalty model. This paper proposes the hybrid model which combines the chance-constrained model and the penalty model. The travel cost of the hybrid model is less than that of the chance-constrained model and the worst case is guaranteed though the hybrid model may have more travel cost than the penalty model. We formulate the VRPSD as a set covering problem and this problem is solved using a column generation approach. We propose the solution methods for the hybrid model. The solution method is based on saving algorithm. In numerical results, we compare the results of the chance-constrained model, the penalty model and the hybrid model.

An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy

This paper presents the methodology for solving the municipal waste collection problem in urban areas.This problem is treated as a vehicle routing problem where the demand in nodes and travel times between all pairs of nodes in a transport network are taken as stochastic quantities, known in the literature as the vehicle routing problem with stochastic demands (VRPSD).This problem is formulated as a chance-constrained programming model with normal distribution.Heuristic and metaheuristic methods, as well as their combinations, are applied to efficiently solve this model.Finally, the paper presents a comparative analysis of the obtained results with real data.

As a classic issue in military operation research, weapon target assignment (WTA) has been of interest to researchers for a long time. The purpose of WTA is to determine the best assignment scheme to gain the largest benefit while satisfying a number of constraints deriving from the capability of available platforms and munitions (or weapons), target characteristics, timings for operation and so on. In order to overcome the drawbacks of easily falling into premature convergence and local optimum of existing heuristic algorithms when they are employed to optimize WTA problems, this paper proposes a hybrid genetic algorithm (HGA) which combines an adaptive genetic algorithm (AGA) with an adaptive variable neighborhood search algorithm (AVNSA) to balance the exploration and exploitation ability. In the framework of HGA, AGA is used for wide scope search in the solution space to avoid premature convergence while AVNSA for local search to jump out of the local optimal space. The simulation result demonstrates the effectiveness and feasibility of the proposed HGA in small-scale WTA optimization problems and through a comparison analysis, advantages of the algorithm over the adaptive genetic algorithm, the immune genetic algorithm and the standard genetic algorithm in large-scale WTA optimization problems are revealed.

An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD) is considered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm. Finally, numerical results are presented for various problem instances to illustrate the ideas.

An improved adaptive genetic algorithm is proposed for the problem of how to plan the assault path of stealth UAVs in a complex battlefield environment. Combined with radar network, terrain obstruction and other threats to simulate the real combat environment, the stealth UAV’s assault path is planned on a three-dimensional map, and in order to improve the real-time and flexibility of the path, the path needs to be re-planned with the addition of emergent obstacles. The improved adaptive genetic algorithm solves the disadvantages of the traditional genetic algorithm such as slow convergence speed and easy to fall into local extremes. The final simulation results show that the improved adaptive genetic algorithm not only converges faster than the standard genetic algorithm and adaptive genetic algorithm, but also the solution results are closer to the optimal solution and the planned paths are more reasonable.

It is now common knowledge that blind search algorithms cannot perform with equal efficiency on all possible optimization problems defined on a domain. This knowledge applies also to Genetic Algorithms when viewed as global and blind optimizers. From this point of view it is necessary to design algorithms capable of adapting their search behavior by making use in a direct fashion of the knowledge pertaining to the search landscape. The paper introduces a novel adaptive Genetic Algorithm where the exploration/exploitation is directly controlled during evolution using a Bayesian decision process. Test cases are analyzed as to how parameters affect the search behavior of the algorithm.

To enable agents negotiate more efficiently in multilateral multi-issue cooperative negotiations in multi-agent based on e-commerce, a hybrid genetic algorithm (HGA) is presented and applied in the negotiation. After compare of 1000 times of experiments for four kinds of genetic algorithm, the result shows that standard genetic algorithm (SGA) averagely needs negotiation 185 times, genetic algorithm based on Metropolis rule (MGA) averagely needs 176 times, adaptive genetic algorithm (AGA) averagely needs 169 times, while the HGA averagely needs only 153 times. The HGA can gain optimal negotiation result more efficiently than the other three kinds of genetic algorithms in multi-lateral multi-issue cooperation negotiation.

In this paper, the Vehicle Routing Problem with Stochastic Demands (VRPSD) is considered where customer demands are normally distributed. We propose a new model for computing the expected length of a tour. Monte Carlo simulation is used to demonstrate the accuracy of the model on randomly generated test problems. It is assumed that the service policy is non-divisible, meaning that the entire demand at each customer must be served in a single visit by a unique vehicle.

The multiple Unmanned Aerial Vehicles (UAVs) reconnaissance problem with stochastic observation time (MURSOT) is modeled by modifying the typical vehicle routing problem with stochastic demand (VRPSD). The objective consists in optimizing mission duration, total time and the quantity of UAVs. This multi-objective optimization problem is solved using a steady-state multi-objective evolutionary algorithm MOEA with e - dominance conception. In this paper, we propose a heuristic evolutionary operation (HEO) using Insert-to-Nearest Method (INM). Route Simulation Method (RSM) is presented in details to estimate the expected cost of each route and this method is designed especially for our MURSOT. The developed algorithm is further validated on a series of test problems adapted from Solomon's vehicle routing problems. Experimental results show that the INM is capable of finding better solutions in contrast and its advantage is more remarkable as the size of the problem become larger.

This paper was targeted at minimizing the expectation of traveling distance maximizing the expectation of customers' degree satisfaction, a multi-objective vehicle routing problem with stochastic demand (VRPSD) model based on soft time window was proposed. In order to solve the problem, a hybrid PSO algorithm based on Pareto optimization method was designed in this paper. The paper made the standard PSO algorithm discrete by re-defining operators and employing swap recon, utilized challenge tournament method to construct Pareto optimal solution set, applied an external archive to keep the diversity of solutions. Ultimately, a standard example is used to verify the validity of the algorithm.

Various factors in the stock market are intricate and complex, and changes in the primary and secondary relationship are uncertain. The investigation found that the stock price is affected by factors such as buyers and sellers, stock policies, investors and other factors. Considering these factors, it is easy to draw a conclusion: stock price changes are random. After understanding the most obvious characteristics of stock prices, I found that there are very few high-precision stock price prediction models in the market. Under this background, it is necessary to study high-precision stock price prediction models. After looking up information from multiple parties, the method chosen by the author is a new method formed by the combination of BP neural network and genetic algorithm. The investigation found that the random initial weight of BP neural network and genetic algorithm will enter an infinite loop due to the local optimal solution. The author made some improvements, because adaptive genetic algorithm can solve the problem of initial weight of BP neural network, so BP The neural network is improved by an adaptive genetic algorithm, and a high-precision stock prediction model can be obtained. Heterogeneous processors are increasingly used in the field of high-performance computing, especially in the application of processor cores, which provides huge potential for parallel computing, but it also brings huge challenges. Higher accuracy requires a large knowledge system and a more advanced programming model. People need to master a more advanced programming model. Because for most programmers, this requirement is almost impossible to complete, so I thought of another way, using parallel compilation to complete the work. At present, the parallel compilation technology for heterogeneous architecture has achieved fruitful research results, but there are still many problems that need to be analyzed and solved. For these problems, the author proposes to create a new data area that transfers data to the nested external calculation, so the data transfer only occurs before and after the loop calculation, thereby avoiding the internal parallel loop in the iterative calculation process. Multiple copies of external serial loop data. Experiments show that these storage optimization methods can optimize the transmission, storage and access of different levels and different granularities of data, thereby improving the performance of the generated parallel programs to varying degrees.

A hybrid diagnostic method utilizing Extended Kalman Filter (EKF) and Adaptive Genetic Algorithm (AGA) is presented for performance degradation estimation and sensor anomaly detection of turbofan engine. The EKF is used to estimate engine component performance degradation for gas path fault diagnosis. The AGA is introduced in the integrated architecture and applied for sensor bias detection. The contributions of this work are the comparisons of Kalman Filters (KF)-AGA algorithms and Neural Networks (NN)-AGA algorithms with a unified framework for gas path fault diagnosis. The NN needs to be trained off-line with a large number of prior fault mode data. When new fault mode occurs, estimation accuracy by the NN evidently decreases. However, the application of the Linearized Kalman Filter (LKF) and EKF will not be restricted in such case. The crossover factor and the mutation factor are adapted to the fitness function at each generation in the AGA, and it consumes less time to search for the optimal sensor bias value compared to the Genetic Algorithm (GA). In a word, we conclude that the hybrid EKF-AGA algorithm is the best choice for gas path fault diagnosis of turbofan engine among the algorithms discussed.