We present a novel variation of the vehicle routing problem (VRP). Single commodity cargo with pickup and delivery service is considered. Customers are labeled as either cargo sink or cargo source, depending on their pickup or delivery demand. This problem is called a single commodity vehicle routing problem with pickup and delivery service (1-VRPPD). 1-VRPPD deals with multiple vehicles and is the same as the single-commodity traveling salesman problem (1-PDTSP) when the number of vehicles is equal to 1. Since 1-VRPPD specializes VRP, it is hard in the strong sense. Iterative modified simulated annealing (IMSA) is presented along with greedy random-based initial solution algorithm. IMSA provides a good approximation to the global optimum in a large search space. Experiment is done for the instances with different number of customers and their demands. With respect to average values of IMSA execution times, proposed method is appropriate for practical applications.
We consider a modification of the well known work function algorithm (WFA) for solving the on-line kserver problem. Our modified WFA is based on a moving window, i. e. on the approximate work function that takes into account only a fixed number of most recent on-line requests. The main motivation for using a moving window is to gain control over the prohibitive computational complexity imposed by the original algorithm. Experimental results are presented, where the performance of the modified WFA has been compared vs. the original WFA.
This paper deals with the work function algorithm (WFA) for solving the on-line k-server problem. The paper is concerned with assessing actual performance of the WFA in terms of its serving costs. First, an efficient implementation of the WFA is briefly described. Next, some experiments are presented, where the performance of the implemented WFA has been measured on very large problem instances. Thereby, the problem instances have been selected from some frequently studied classes where sharp theoretical estimates of performance are available. Finally, the measured performance of the WFA is compared with the corresponding theoretical estimates and with some other algorithms.
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