Djordje Dugošija

Genetic algorithms for solving the discrete ordered median problem

In this paper we present two new heuristic approaches to solve the Discrete Ordered Median Problem (DOMP). Described heuristic methods, named HGA1 and HGA2 are based on a hybrid of genetic algorithms (GA) and a generalization of the well-known Fast Interchange heuristic (GFI). In order to investigate the effect of encoding on GA performance, two different encoding schemes are implemented: binary encoding in HGA1, and integer representation in HGA2. If binary encoding is used (HGA1), new genetic operators that keep the feasibility of individuals are proposed. Integer representation keeps the individuals feasible by default, so HGA2 uses slightly modified standard genetic operators. In both methods, caching GA technique was integrated with the GFI heuristic to improve computational performance. The algorithms are tested on standard ORLIB p-median instances with up to 900 nodes. The obtained results are also compared with the results of existing methods for solving DOMP in order to assess their merits.

GA Inspired Heuristic for Uncapacitated Single Allocation Hub Location Problem

In this article, the results achieved by applying GA-inspired heuristic on Uncapacitated Single Allocation Hub Location Problem (USAHLP) are discussed. Encoding scheme with two parts is implemented, with appropriate objective functions and modified genetic operators. The article presents several computational tests which have been conducted with ORLIB instances. Procedures described in related work round distance matrix elements to few digits, so rounding error is significant. Due to this fact, we developed exact total enumeration method for solving subproblem with fixed hubs, named Hub Median Single Allocation Problem (HMSAP). Computational tests demonstrate that GA-inspired heuristic reach all best solutions for USAHLP that are previously obtained and verified branch-and-bound method for HMSAP. Proposed heuristic successfully solved some instances that were unsolved before.

A mixed integer linear programming formulation of the maximum betweenness problem

This paper considers the maximum betweenness problem. A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on randomly generated instances from the literature. The results of CPLEX solver, based on the proposed MILP formulation, are compared with results obtained by total enumeration technique. The results show that CPLEX optimally solves instances of up to 30 elements and 60 triples in a short period of time.

Variable neighborhood search for Multiple Level Warehouse Layout Problem

Abstract In this paper we present a variable neighborhood search algorithm (VNS) for solving Multiple Level Warehouse Layout Problem (MLWLP). The algorithm deals with a specific representation of the solution, enabling the effective application of the shaking and local search procedures. System of neighborhoods changes the assignment ordering for an increasing number of items, while local search procedure tries to locally improve the solution by swapping the assignment ordering for pairs of items. Numerical experiments are performed on instances known in the literature. Computational results show that the proposed VNS achieves all optimal solutions for smaller instances, while for larger instances it finds rather better solutions than previously known method.

The modification of genetic algorithms for solving the balanced location problem

In this paper is described the modification of the existing evolutionary approach for Discrete Ordered Median Problem (DOMP), in order to solve the Balanced Location Problem (LOBA). Described approach, named HGA1, includes a hybrid of Genetic Algorithm (GA) and a well-known Fast Interchange Heuristic (FIH). HGA1 uses binary encoding schema. Also, new genetic operators that keep the feasibility of individuals are proposed. In proposed method, caching GA technique was integrated with the GFI heuristic to improve computational performance. The algorithm is tested on standard instances from the literature and on large-scale instances, up to 1000 potential facilities and clients, which is generated by generator described in [5]. The obtained results are also compared with the existing heuristic from the literature.

Two Hybrid Genetic Algorithms for Solving the Super-Peer Selection Problem

The problem that we will address here is the Super-Peer Selection Problem (SPSP). Two hybrid genetic algorithm (HGA) approaches are proposed for solving this NP-hard problem. The new encoding schemes are implemented with appropriate objective functions. Both approaches keep the feasibility of individuals by using specific representation and modified genetic operators. The numerical experiments were carried out on the standard data set known from the literature. The results of this test show that in 6 out of 12 cases HGAs outreached best known solutions so far, and that our methods are competitive with other heuristics.