An empirical comparison of heuristic methods for creating maximally diverse groups

Weitz, Rob R.; Lakshminarayanan, S.

doi:10.1057/palgrave.jors.2600510

Cited by 71 publications

(13 citation statements)

References 16 publications

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“…, c p , respectively. This problem has many applications ranging from final exam scheduling to VLSI design (see [12] and the references therein). ΔCPR 2 may be useful in some of these applications where we only want to put an upper bound on the sizes of the connected components in the output cluster subgraph.…”

Section: Previous Results On Cpr K and Related Problemsmentioning

confidence: 99%

Approximation Algorithms for Bounded Degree Phylogenetic Roots

Chen

2007

Algorithmica

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The DEGREE-Δ CLOSEST PHYLOGENETIC kTH ROOT PROBLEM (ΔCPR k ) is the problem of finding a (phylogenetic) tree T from a given graph G = (V , E) such that (1) the degree of each internal node in T is at least 3 and at most Δ, (2) the external nodes (i.e. leaves) of T are exactly the elements of V , and (3) the number of disagreements, i.e., |E ⊕ {{u, v} : u, v are leaves of T and (u, v) denotes the distance between u and v in tree T . This problem arises from theoretical studies in evolutionary biology and generalizes several important combinatorial optimization problems such as the maximum matching problem. Unfortunately, it is known to be NP-hard for all fixed constants Δ, k such that either both Δ ≥ 3 and k ≥ 3, or Δ > 3 and k = 2. This paper presents a polynomial-time 8-approximation algorithm for ΔCPR 2 for any fixed Δ > 3, a quadratic-time 12-approximation algorithm for 3CPR 3 , and a polynomialtime approximation scheme for the maximization version of ΔCPR k for any fixed Δ and k.

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Section: Previous Results On Cpr K and Related Problemsmentioning

confidence: 99%

Approximation Algorithms for Bounded Degree Phylogenetic Roots

Chen

2007

Algorithmica

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“…Weitz and Lakshminarayanan (1996) have remarked that the Lotfi-Cerveny algorithm at each step explores only a portion of the pairwise interchange neighbourhood. They proposed a variation of this algorithm, which checks all pairwise interchanges of elements belonging to different groups (see also Weitz and Lakshminarayanan, 1998). Arani and Lotfi (1989) developed another improvement heuristic for solving the MDGP.…”

Section: Introductionmentioning

confidence: 99%

Maximally diverse grouping: an iterated tabu search approach

Palubeckis

Ostreika

Rubliauskas

2015

Journal of the Operational Research Society

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The maximally diverse grouping problem (MDGP) consists of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. In this paper, we propose an iterated tabu search (ITS) algorithm for solving this problem. We report computational results on three sets of benchmark MDGP instances of size up to 960 elements and provide comparisons of ITS to five state-of-the-art heuristic methods from the literature. The results demonstrate the superiority of the ITS algorithm over alternative approaches. The source code of the algorithm is available for free download via the internet.

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“…Apart from some early greedy and stingy heuristics (Glover et al 1996, Weitz andLakshminarayanan 1998), nearly all heuristic approaches to the MDP adopt the greedy randomized adaptive search procedure methodology (GRASP). For a survey, see Festa and Resende (2002).…”

Section: Introductionmentioning

confidence: 99%

Tabu Search versus GRASP for the maximum diversity problem

Aringhieri

Cordone

Melzani

2007

4OR

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Description: The Maximum Diversity Problem consists in determining a subset M of given cardinality from a set N of elements, in such a way that the sum of the pairwise differences between the elements of M is maximum. This problem, introduced by Glover, Hersh and McMillian, has been deeply studied using the GRASP methodology. GRASPs are often characterized by a strong design effort dedicated to the randomized generation of high quality starting solutions, while the subsequent improvement phase is usually performed by a standard local search technique. The purpose of this paper is to explore a somewhat opposite approach, that is to refine the local search phase, by adopting a Tabu Search methodology, while keeping a very simple initialization procedure. Extensive computational results show that Tabu Search achieves both better results and much shorter computational times with respect to those reported for GRASP.

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An empirical comparison of heuristic methods for creating maximally diverse groups

Cited by 71 publications

References 16 publications

Approximation Algorithms for Bounded Degree Phylogenetic Roots

Approximation Algorithms for Bounded Degree Phylogenetic Roots

Maximally diverse grouping: an iterated tabu search approach

Tabu Search versus GRASP for the maximum diversity problem

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