Эвристика для решения задачи маршрутизации тягачей с прицепами, возникающей в реальной практике
In this paper we introduce a new pattern-based approach within the Linear Assignment Model with the purpose to design heuristics for a combinatorial optimization problem (COP). We assume that the COP has an additive (separable) objective function and the structure of a feasible (optimal) solution to the COP is predefined by a collection of cells (positions) in an input file. We define a pattern as a collection of positions in an instance problem represented by its input file (matrix). We illustrate the notion of pattern by means of some well known problems in COP among them the Linear Ordering Problem, Cell Formation Problem (CFP) just to mention a couple. The CFP is defined on a Boolean input matrix which rows represent machines and columns - parts. The CFP consists in finding three optimal objects: a block-diagonal collection of rectangles, a rows (machines) permutation, and a columns (parts) permutation such that the grouping efficacy is maximized. The suggested heuristic combines two procedures: the pattern-based procedure to build an initial solution and an improvement procedure to obtain a final solution with high grouping efficacy for the CFP. Our computational experiments with the most popular set of 35 benchmark instances show that our heuristic outperforms all well known heuristics and returns either the best known or improved solutions to the CFP.
In this paper we suggest a multi-start greedy heuristic for a real-life truck and trailer routing problem. The considered problem is a site dependent heterogeneous fleet truck and trailer routing problem with soft and hard time windows and split deliveries. This problem arises in delivering goods from a warehouse to stores of a big retail company. There are about 400 stores and 100 vehicles for one warehouse. Our heuristic is based on sequential greedy insertion of a customer to a route with further improvement of the solution. The computational experiments are performed for real-life data. We also provide a mixed integer linear programming formulation for precise and clear description of the problem.
Graph coloring problem is one of the classical combinatorial optimization problems. This problem consists in finding the minimal number of colors in which it is possible to color vertices of a graph so that any two adjacent vertices are colored in different colors. The graph coloring problem has a wide variety of applications including timetabling problems, processor register allocation problems, frequency assignment problems, data clustering problems, traffic signal phasing problems, maximum clique problem, maximum independent set problem, minimum vertex cover problem and others. In this paper a new efficient heuristic algorithm for the graph coloring problem is presented. The suggested algorithm builds the same coloring of a graph as does the widely used greedy sequential algorithm in which at every step the current vertex is colored into minimal feasible color. Computational experiments show that the presented algorithm performs graph coloring much faster in comparison with the standard greedy algorithm. The speedup reaches 5,6 times for DIMACS graphs.
This paper investigates the coordinated scheduling problem of production and transportation in a two-stage supply chain, where the actual job processing time is a linear function of its starting time. During the production stage the jobs are first processed in serial batches on a bounded serial batching machine at the manufacturer's site. Then, the batches are delivered to a customer by a single vehicle with limited capacity during the transportation stage, and the vehicle can only deliver one batch at one time. The objective of this proposed scheduling problem is to make decisions on job batching and batch sequencing so as to minimize the makespan. Moreover, we consider two different models. With regards to the scheduling model with a buffer for storing the processed batches before transportation, we develop an optimal algorithm to solve it. For the scheduling model without buffer, we present some useful properties and develop a heuristic H for solving it. Then a novel lower bound is derived and two optimal algorithms are designed for solving two special cases. Furthermore, computational experiments with random instances of different sizes are conducted to evaluate the proposed heuristic H, and the results show that our proposed algorithm is superior to other four approaches in the literature. Besides, heuristic H in our experiments can effectively and efficiently solve both small-size and large-size problems in a reasonable time.
In our paper, we consider the Cell Formation Problem in Group Technology with grouping efficiency as an objective function. We present a heuristic approach for obtaining high-quality solutions of the CFP. The suggested heuristic applies an improvement procedure to obtain solutions with high grouping efficiency. This procedure is repeated many times for randomly generated cell configurations. Our computational experiments are performed for popular benchmark instances taken from the literature with sizes from 10×20 to 50×150. Better solutions unknown before are found for 23 instances of the 24 considered. The preliminary results for this paper are available in Bychkov et al. (Models, algorithms, and technologies for network analysis, Springer, NY, vol. 59, pp. 43–69, 2013, ).