A Particle Swarm Optimisation for Vehicle Routing Problem with Time Windows

A heuristic based on Particle Swarm Optimisation (PSO) algorithm for solving VRPTW, which is an extension of PSO application for the Capacitated Vehicle Routing Problem (CVRP) (Ai and Kachitvichyanukul,2007), is presented in this paper. A computational experiment is carried out by running the proposed algorithm with the VRPTW benchmark data set of Solomon (1987). The results show that the proposed algorithm is able to provide VRPTW solutions that are very close to its optimal solutions for problems with 25 and 50 customers within reasonably short of computational tim

A survey on computational intelligence approaches for predictive modeling in prostate cancer

Predictive modeling in medicine involves the development of computational models which are capable of analysing large amounts of data in order to predict healthcare outcomes for individual patients. Computational intelligence approaches are suitable when the data to be modelled are too complex forconventional statistical techniques to process quickly and eciently. These advanced approaches are based on mathematical models that have been especially developed for dealing with the uncertainty and imprecision which is typically found in clinical and biological datasets. This paper provides a survey of recent work on computational intelligence approaches that have been applied to prostate cancer predictive modeling, and considers the challenges which need to be addressed. In particular, the paper considers a broad definition of computational intelligence which includes evolutionary algorithms (also known asmetaheuristic optimisation, nature inspired optimisation algorithms), Artificial Neural Networks, Deep Learning, Fuzzy based approaches, and hybrids of these,as well as Bayesian based approaches, and Markov models. Metaheuristic optimisation approaches, such as the Ant Colony Optimisation, Particle Swarm Optimisation, and Artificial Immune Network have been utilised for optimising the performance of prostate cancer predictive models, and the suitability of these approaches are discussed

A Particle Swarm Optimization for the Vehicle Routing Problem with Clustered Customers

This paper presented a particle swarm optimization algorithm (PSO) sor solving vehicle routing problem (VRP) which involves single depot and clustered customers. Three different solution representations and decoding methods are proposed for solving VRP using PSO. Thisrepresentations are similari the use of particle with 2m dimension to represent m vehicles. In the decoding step, these particle dimensions are transforming to a priority matrix of vehicle to serve each customer. These representations are different on how to create customer priority list: the first representations directly uses the customer list data as the customer priority list; the second preprocesses the customer list data according to its polar angle as the customer priority list; the third uses random-key to build the costomer priority list. The customer priority list and vehicle matrix are utilized for constructing vehicle routes at the end of the decoding step. A computational experiment is conducted by applying the proposed algoritmn on the benchmark data set of capacitated vehicle routing problem(CVRP) and the vehicle routing problem with time windows (VRPTW). The result showed that the proposed algorithm with the third representation isthe most effective to solve CVRP and VRPTW problem

A particle swarm optimization for the capacitated vehicle routing problem

This paper proposed a random-key based solution representaion and decoding metdod for solving the Capacitated Vehicle Routing Problem (CVRP) using Particle Swarm Optimization (PSO). The Solution CVRP with n customers and m vehicles. The decoding method start with transforming the particle to a priority list of customer to enterroute and priority matrix of vehicle to serve each customer. The vehicle routes are constructed based on the costumer representation is applied using GLNPSO, a PSO algorithm with multiple social learning structures. The proposed algorithm is tested using the benchmark data set provided by Christofides. The computational result shows that representation ang decoding method is promising to be applied for CVRP

A Particle Swarm Optimization for the Heterogeneous Fleet Vehicle Routing Problem

This paper present an application of particle swarm optimization (PSO) for solving the heterogenous fleet vehicle routing problem (HVRP). HVRP is a vehicle routing problem (VRP) vriant that takes different types of vehicle in each type, there are two types of HVRP in the literature: the vehicle fleet mix problem (VFM) that deals with unlimited number of vehicles and the fixed fleet version of HVRP that deals with fixed number of vehicle. This paper focus only on the latter since normally the number avaible vehicle is know in advance in theactual operations. A PSO algorithm, solution representations and decoding methods that have beensuccessfully applied to the basic variant of VRP are re-utilized as the basicsolution technique. In order to arquire the nature of heterogenous type of vehicles in to the technique, aspecial preprocessing method is incorporated to the vehicle list, so that a vehicle with lower relative routing cost is given higher priotity over the bigger one. The proposed algorithm is tested using benchmark data set and the computational result shows that the proposed method is competitive with other published result for solving HVRP

A Study on Adaptive Particle Swarm Optimization for Solving Vehicle Routing Problems

This paper presents a study on an adaptive version of particle swarm optimization (PSO) algorithmfor solving vehicle routing problems (VRPs). Recently, PSO has been showing promising results in solvingmany optimization problems include VRP. There are some parameters that need to be set in order to obtain agood performance of the PSO algorithm. However, finding the best set of parameters that is good for allproblem cases is not an easy task. Many experiments must be performed to set the parameters and yet there isno guarantee that the best obtained parameter set will provide consistently good algorithm performance whenit is applied to a new problem cases. Hence, a novel idea to have a self-adaptive PSO, that can adapt itsparameters automatically whenever it is applied to solve a problem instance, is an alternative way toovercome this situation. The adaptive version of PSO proposed in this paper has additional capability to selfadaptits inertia weight (w), one of the key PSO parameter, based on the velocity index of the swarm, thesearching agents in PSO. The inertia weight is controlled so that the balance between exploration andexploitation phases of the swarm is maintained, since a better balance of these phases is often mentioned asthe key to a good performance of PSO. The performance of this adaptive PSO is evaluated for solving VRPinstances and is compared with the existing application of PSO for VRP. The computational experiment showsthat the adaptive version of PSO is able to provide better solution than the existing non-adaptive PSO withslightly slower computational time

Computer Generation of Poisson, Binomial, and Hypergeometric Random Variates

This research is focused on the development of exact, uniformly fast computer algorithms for generating random variates from the Poisson, binomial, and hypergeometric distributions. All four fundamental approaches to random variate generation, i.e., inverse transformation, composition, acceptance/rejection, and special properties, are used in the formulation of the new algorithms. The algorithms developed are implemented in FORTRAN and comparisons are made against comparable existing algorithms. All three algorithms developed dominate comparable existing algorithms in terms of execution speed. The one-sided approximations for the Poisson, binomial, and hypergeometric probabilities, which may be useful in a more general context, are given the appendices along with the computer codes