Miroslaw Blocho

Adaptive memetic algorithm for minimizing distance in the vehicle routing problem with time windows

This paper presents an adaptive memetic algorithm to solve the vehicle routing problem with time windows (VRPTW). It is a well-known NP-hard discrete optimization problem with two objectives—to minimize the number of vehicles serving a set of geographically dispersed customers, and to minimize the total distance traveled in the routing plan. Although memetic algorithms have been proven to be extremely efficient in solving the VRPTW, their main drawback is an unclear tuning of their numerous parameters. Here, we introduce the adaptive memetic algorithm (AMA-VRPTW) for minimizing the total travel distance. In AMA-VRPTW, a population of solutions evolves with time. The parameters of the algorithm, including the selection scheme, population size and the number of child solutions generated for each pair of parents, are adjusted dynamically during the search. We propose a new adaptive selection scheme to balance the exploration and exploitation of the solution space. Extensive experimental study performed on the well-known Solomon’s and Gehring and Homberger’s benchmark sets confirms the efficacy and convergence capabilities of the proposed AMA-VRPTW. We show that it is very competitive compared with other state-of-the-art techniques. Finally, the influence of the proposed adaptive schemes on the AMA-VRPTW behavior and performance is investigated in a thorough sensitivity analysis. This analysis is complemented with the two-tailed Wilcoxon test for verifying the statistical significance of the results.

A Parallel Memetic Algorithm for the Vehicle Routing Problem with Time Windows

A parallel memetic algorithm for the NP-hard vehicle routing problem with time windows (VRPTW) is proposed. The algorithm consists of components which are executed as parallel processes. A process runs either a heuristic algorithm or a hybrid of a genetic algorithm and some local refinement procedures. In order to improve the results, processes co-operate periodically using a novel randomized scheme. During each phase of co-operation processes exploit their best solutions found so far. The purpose of the work is to devise the parallel memetic algorithm which determines the VRPTW solutions of the highest possible quality. The experiments on Gehring and Hombergers (GH) benchmarking tests show that the algorithm achieves very good results. By making use of it the best-known solutions to 171 out of 300 GH tests were improved.

A Parallel Algorithm with the Search Space Partition for the Pickup and Delivery with Time Windows

The pickup and delivery problem with time windows (PDPTW) is an NP-hard optimization problem of serving transportation requests using a limited number of vehicles. Its main objective is to minimize the number of delivering trucks, whereas the secondary objective is to decrease the distance traveled during the service. A feasible routing schedule must satisfy the time window, capacity and precedence constraints. In this paper, we propose to partition the search space in our parallel guided ejection search algorithm (P-GES) to minimize the fleet size in the PDPTW. The introduced techniques help decrease the convergence time of the algorithm without affecting the quality of results. An extensive experimental study (comprising nearly 52,000 CPU hours on an SMP cluster) performed on the Li and Lims benchmark set shows that the parallel algorithm is effective, and is able to retrieve very high-quality results. We report 10 new worlds best solutions obtained using P-GES enhanced with the proposed search space partition approaches.

Co-operation Schemes for the Parallel Memetic Algorithm

This paper presents a study of co-operation schemes for the parallel memetic algorithm to solve the vehicle routing problem with time windows. In the parallel co-operative search algorithms the processes communicate to exchange the up-to-date solutions, which may guide the search and improve the results. The interactions between processes are defined by the content of the exchanged data, timing, connectivity and mode. We show how co-operation schemes influence the search convergence and solutions quality. The quality of a solution is defined as its proximity to the best, currently-known one. We present the experimental study for the well-known Gehring and Homberger’s benchmark. The new world’s best solutions obtained in the study confirm that the co-operation scheme has a strong impact on the quality of final solutions.

A Parallel EAX-based Algorithm for Minimizing the Number of Routes in the Vehicle Routing Problem with Time Windows

A parallel EAX-based algorithm for minimizing the number of routes in the vehicle routing problem with time windows is presented. The main contribution is a novel approach concerning the usage of the edge assembly crossover (EAX) operator during exchanging the best solutions between the processes. The objective of the work is to analyze the speedup, achieved accuracy of solutions and scalability of the MPI implementation. For comparisons the selected Gehring and Hombergers (GH) tests are used. The results of the extensive computational experiments indicate that the new algorithm based on the EAX approach is not only very fast but also very effective. The eight new best-known solutions for the GH benchmarking tests were found by making use of the algorithm.

Enhanced Guided Ejection Search for the Pickup and Delivery Problem with Time Windows

This paper presents an enhanced guided ejection search (GES) to minimize the number of vehicles in the NP-hard pickup and delivery problem with time windows. The proposed improvements decrease the convergence time of the GES, and boost the quality of results. Extensive experimental study on the benchmark set shows how the enhancements influence the GES capabilities. It is coupled with the statistical tests to verify the significance of the results. We give a guidance on how to select a proper algorithm variant based on test characteristics and objectives. We report one new world’s best result obtained using the enhanced GES.

A parallel algorithm for minimizing the number of routes in the vehicle routing problem with time windows

A parallel algorithm for minimizing the number of routes in the vehicle routing problem with time windows (VRPTW) is presented. The algorithm components cooperate periodically by exchanging their best solutions with the lowest number of routes found to date. The objective of the work is to analyze speedup, achieved accuracy of solutions and scalability of the MPI implementation. For comparisons the selected VRPTW tests are used. The derived results justify the proposed parallelization concept. By making use of the parallel algorithm the twelve new best-known solutions for Gehring and Hombergers benchmarking tests were found.

A Parallel Algorithm for Minimizing the Fleet Size in the Pickup and Delivery Problem with Time Windows

In this paper, we propose a parallel guided ejection search algorithm to minimize the fleet size in the NP-hard pickup and delivery problem with time windows. The parallel processes co-operate periodically to enhance the quality of results and to accelerate the convergence of computations. The experimental study shows that the parallel algorithm retrieves very high-quality results. Finally, we report 13 (22% of all considered benchmark tests) new worlds best solutions.

A Parallel Memetic Algorithm for the Pickup and Delivery Problem with Time Windows

Solving the pickup and delivery problem with time windows (PDPTW) is a vital research topic due to its NP-hardness and its numerous practical applications. In this paper, we propose an island-model parallel memetic algorithm for minimizing the distance in the PDPTW. In this algorithm, the processes execute the same memetic algorithm and co-operate to guide the optimization efficiently. An extensive experimental study revealed that the MPI implementation of the proposed approach retrieves very high-quality routing schedules. The analysis is coupled with appropriate statistical tests.

Temporally Adaptive Co-operation Schemes

Selecting an appropriate co-operation scheme in parallel evolutionary algorithms is an important task and it should be undertaken with care. In this paper, we introduce the temporally adaptive schemes, and apply them in our parallel memetic algorithm for solving the vehicle routing problem with time windows. The experimental results revealed that this approach allows for retrieving better solutions in much shorter time compared with other cooperation schemes. The analysis is backed up with the statistical tests, which gave the clear evidence that the results are important. We report one new world’s best solution to the benchmark problem obtained using our adaptive co-operation scheme.