An Effective Lagrangian Heuristic For The Generalized Assignment Problem

A path relinking approach with ejection chains for the generalized assignment problem

“…For each instance, the time limit of PREC was set to the minimum of the following two: (i) 15 (resp., 30) seconds for n = 100 (resp., 200), and (ii) a tenth of the execution time reported in [14]. The results are shown in Table 4.…”

“…Since some recent papers [3,14] reported computational results for the instances from set MED-IUM using smaller computation time than in Table 2, we also tested our algorithm PREC with a shorter time limit. For each instance, the time limit of PREC was set to the minimum of the following two: (i) 15 (resp., 30) seconds for n = 100 (resp., 200), and (ii) a tenth of the execution time reported in [14].…”

“…The results are shown in Table 4. Column HO is the result by the Lagrangian heuristic algorithm by Haddadi and Ouzia [14], and column APT is the result by the path-relinking approach by Alfandari et al [3]. Column Ôbest costÕ shows the cost of the best solution obtained within the time limit, column Ôtime to bestÕ shows the CPU seconds when the best solution was found first, column Ôtime limitÕ is the time limit, and column Ôexecution timeÕ is the CPU time when the algorithm stopped (algorithms HO and APT did not use CPU time for the stopping criteria).…”

“…The proposed algorithm is compared with many existing heuristic algorithms including the recent path relinking approach by Alfandari et al [2,3], tabu search by Díaz and Fernández [6], a Lagrangian heuristic algorithm by Haddadi and Ouzia [14], tabu search by Yagiura et al [33], variable depth search algorithms by Yagiura et al [34,35], another variable depth search algorithm by Racer and Amini [26], tabu search by Laguna et al [18], MAX-MIN ant system by Lourenço and Serra [20], genetic algorithm by Chu and Beasley [4] and a mixed integer programming solver CPLEX 6.5. The results show that our GAP method is highly effective, especially for instances of types D and E, which have been established as the most difficult problem classes.…”

A Lagrangian Approach for Multiple Personalized Campaigns

“…There have been a number of papers that studied the Lagrangian method for discrete problems [10], [15], [18], [26], [30], [35]. Most of them focused on the problems with a linear objective function called integer programming problems.…”