An LP-based heuristic procedure for the generalized assignment problem with special ordered sets

French, Alan; Wilson, John

doi:10.1016/j.cor.2005.09.008

Cited by 10 publications

(4 citation statements)

References 16 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hybrid approaches, which are combinations of LP and metaheuristics, have been proposed for various combinatorial optimization problems [AlvarezValdes et al 2002;Feltl and Raidl 2004;French and Wilson 2007;Klose 1999;Sridhar et al 2000;Umetani et al 2003;Vasquez and Hao 2001]. In these approaches, the fractional solutions of LP are rounded into integral solutions by some rounding techniques, and the integral solutions guide heuristic procedures.…”

Section: Hybrid Lp-based Approachesmentioning

confidence: 99%

See 1 more Smart Citation

Local search starting from an LP solution

Avdil

Weihe

2009

ACM J. Exp. Algorithmics

View full text Add to dashboard Cite

We present and evaluate a specific way to generate good start solutions for local search. The start solution is computed from a certain LP, which is related to the underlying problem. We consider three optimization problems: the directed MAX-CUT problem with a source and a sink and two variations of the MAX-k-SAT problem with k = 2 and k = 3. To compare our technique, we run local search repeatedly with random start solutions.Our technique produces, consistently, final solutions whose objective values are not too far from the best solutions from repeated random starts. The surprising degree of stability and uniformity of this result throughout all of our experiments on various classes of instances strongly suggests that we have consistently achieved nearly optimal solutions. On the other hand, the runtime of our technique is rather small, so the technique is very efficient and probably quite accurate. ACM Reference Format:Avdil, A. and Weihe, K. 2009. Local search starting from an LP solution: Fast and quite good. ACM

show abstract

Section: Hybrid Lp-based Approachesmentioning

confidence: 99%

“…French and Wilson [2007] proposed an LP-based heuristic algorithm for generalized assignment problem (GAP) with special ordered sets of type [Beale and Tomlin 1970], the extension of GAP. The algorithm is an extensive adaptation of heuristic algorithm for GAP.…”

Section: Hybrid Lp-based Approachesmentioning

confidence: 99%

Local search starting from an LP solution

Avdil

Weihe

2009

ACM J. Exp. Algorithmics

View full text Add to dashboard Cite

show abstract

“…A detailed survey of sequential algorithms for solving GAP can be found in [17]. Canonical work on GAP heuristic algorithms include genetic algorithms [22,23,24,25,26], simulated annealing [27], tabu search [28], and hybrid search that combines heuristics and local search strategies [29,30,31]. Previous work on GA approach to GAP showed that standard GA operations (i.e., selection, crossover, mutation, and replacement) often produce infeasible solutions that violate the capacity constraint of GAP, therefore needs additional processing.…”

Section: Related Workmentioning

confidence: 99%

A scalable parallel genetic algorithm for the Generalized Assignment Problem

Liu

Wang

2015

Parallel Computing

View full text Add to dashboard Cite

Known as an effective heuristic for finding optimal or near-optimal solutions to difficult optimization problems, a genetic algorithm (GA) is inherently parallel for exploiting high performance and parallel computing resources for randomized iterative evolutionary computation. It remains to be a significant challenge, however, to devise parallel genetic algorithms (PGAs) that can scale to massively parallel computer architecture (also known as the mainstream supercomputer architecture) primarily because: 1) a common PGA design adopts synchronized migration, which becomes increasingly costly as more processor cores are involved in global synchronization in each iteration; and 2) asynchronous PGA design and associated performance evaluation are intricate due to the fact that PGA is a type of stochastic algorithm and the amount of computation work needed to solve a problem is not simply dependent on the problem size. To address the challenge, this paper describes a scalable coarse-grained PGA -PGAP, for a well-known NP -hard optimization problem: Generalized Assignment Problem (GAP). Specifically, an asynchronous migration strategy is developed to enable efficient deme interactions and significantly improve the overlapping of computation and communication. Buffer overflow and its relationship with migration parameters were investigated to resolve the issues of observed message buffer overflow and the loss of good solutions obtained from migration. Two algorithmic conditions were then established to detect these issues caused by communication delays and improper configuration of migration parameters and, thus, guide the dynamic tuning of PGA parameters to detect and avoid these issues. A set of computational experiments is designed to evaluate the scalability and numerical performance of PGAP. These experiments were conducted for large GAP instances on multiple supercomputers as part of the National Science Foundation Extreme Science and Engineering Discovery Environment. Results showed that, PGAP exhibited desirable scalability by achieving low communication cost when using up to 16,384 processor cores. Near-linear and super-linear speedups on large GAP instances were obtained in strong scaling tests. Desirable scalability to both population size and the number of processor cores were observed in weak scaling tests. The design strategies applied in PGAP are applicable to general asynchronous PGA development.

show abstract

“…Since the GAP problem is an NPhard problem, it is quite common to use heuristic algorithms that gives the near optimal solution in a short time [11]. In the studies using heuristic algorithms, tabu search algorithm [12][13][14], genetic algorithm [15], bees algorithm [16], a heuristic based on Lagrangian relaxation [17,18], LP-based heuristic [19], a hybrid heuristic based on scatter search [20], improved differential evolution algorithm [21], a parallel genetic algorithm [22] and simulated annealing algorithm [14] were used. Degroote et al [23], poposed a methodology for selection the most suitable algorithm for GAP.…”

Section: Introductionmentioning

confidence: 99%

A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

Bektur¹

2019

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

View full text Add to dashboard Cite

In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model.

show abstract

An LP-based heuristic procedure for the generalized assignment problem with special ordered sets

Cited by 10 publications

References 16 publications

Local search starting from an LP solution

Local search starting from an LP solution

A scalable parallel genetic algorithm for the Generalized Assignment Problem

A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

Contact Info

Product

Resources

About