Given a set of @math elements separated by a pairwise distance matrix, the minimum differential dispersion problem (Min-Diff DP) aims to identify a subset of m elements (m < n) such that the difference between the maximum sum and the minimum sum of the inter-element distances between any two chosen elements is minimized. We propose an effective iterated local search (denoted by ILS_MinDiff) for Min-Diff DP. To ensure an effective exploration and exploitation of the search space, the proposed ILS_MinDiff algorithm iterates through three sequential search phases: a fast descent-based neighborhood search phase to find a local optimum from a given starting solution, a local optima exploring phase to visit nearby high-quality solutions around a given local optimum, and a local optima escaping phase to move away from the current search region. Experimental results on six data sets of 190 benchmark instances demonstrate that ILS_MinDiff competes favorably with the state-of-the-art algorithms by finding 130 improved best results (new upper bounds).
Three-phase search proposed in @cite_18 follows and generalizes the basic ILS scheme. TPS iterates through three distinctive and sequential search phases. The basic idea of TPS is described as follows. Starting from an initial solution, a descent-based neighborhood search procedure is first employed to find a local optimal solution. Then, a local optima exploring phase is triggered with the purpose of discovering nearby local optima of better quality. When the search stagnates in the current search zone, TPS turns into a diversified perturbation phase, which strongly modifies the current solution to jump into a new search region. The process iteratively runs the above three phases until a given stopping condition is met. Compared to BLS, TPS further divides the perturbation phase into a local optima exploring phase (to discover more local optima within a given region) and a diversified perturbation phase (to displace the search to a new and distant search region). TPS has been successfully used to solve several optimization problems, as shown in the right column of Table . The general framework of TPS is outlined in Algorithm . Actually, the ILS algorithm proposed in this work follows the TPS framework.
@cite_18
1881940886 2121456571 2395540747 2766201361
Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum cost. QMSTP is useful to model many real-life network design applications. We propose a three-phase search approach named TPS for solving QMSTP, which organizes the search process into three distinctive phases which are iterated: (1) a descent neighborhood search phase using two move operators to reach a local optimum from a given starting solution, (2) a local optima exploring phase to discover nearby local optima within a given regional area, and (3) a perturbation-based diversification phase to jump out of the current regional search area. TPS also introduces a pre-estimation criterion to significantly improve the efficiency of neighborhood evaluation, and develops a new swap-vertex neighborhood (as well as a swap-vertex based perturbation operator) which prove to be quite powerful for solving a series of special instances with particular structures. Computational experiments based on 7 sets of 659 popular benchmarks show that TPS produces highly competitive results compared to the best performing approaches in the literature. TPS discovers improved best known results (new upper bounds) for 33 open instances and matches the best known results for all the remaining instances. Critical elements and parameters of the TPS algorithm are analyzed to understand its behavior. HighlightsQMSTP is a general model able to formulate a number of network design problems.We propose a three phase search heuristic (TPS) for this problem.TPS is assessed on 7 groups of 659 representative benchmarks of the literature.TPS finds improved best solutions for 33 challenging instances.TPS finds all the optimal solutions for the 29 instances transformed from the QAP. In this paper, we address the approximate nearest neighbor (ANN) search problem over large scale visual descriptors. We investigate a simple but very effective approach, neighborhood graph search, which constructs a neighborhood graph to index the data points and conducts a local search, expanding neighborhoods with a best-first manner, for ANN search. Our empirical analysis shows that neighborhood expansion is very efficient, with O(1) cost, for a new NN candidate location, and has high chances to locate true NNs and hence it usually performs well. However, it often gets sub-optimal solutions since local search only checks the neighborhood of the current solution, or conducts exhaustive and continuous neighborhood expansions to find better solutions, which deteriorates the query efficiency. In this paper, we propose a query-driven iterated neighborhood graph search approach to improve the performance. We follow the iterated local search (ILS) strategy, widely-used in combinatorial optimization, to find a solution beyond a local optimum. We handle the key challenge in making neighborhood graph search adapt to ILS, Perturbation, which generates a new pivot to restart a local search. To this end, we present a criterion to check if the local search over a neighborhood graph arrives at the local solution. Moreover, we exploit the query and search history to design the perturbation scheme, resulting in a more effective search. The major benefit is avoiding unnecessary neighborhood expansions and hence more efficiently finding true NNs. Experimental results on large scale SIFT matching, similar image search, and shape retrieval with non-metric distance measures, show that our approach performs much better than previous state-of-the-art ANN search approaches. In this paper, we propose the first heuristic approach for the vertex separator problem (VSP), based on Breakout Local Search (BLS). BLS is a recent meta-heuristic that follows the general framework of the popular Iterated Local Search (ILS) with a particular focus on the perturbation strategy. Based on some relevant information on search history, it tries to introduce the most suitable degree of diversification by determining adaptively the number and type of moves for the next perturbation phase. The proposed heuristic is highly competitive with the exact state-of-art approaches from the literature on the current VSP benchmark. Moreover, we present for the first time computational results for a set of large graphs with up to 3000 vertices, which constitutes a new challenging benchmark for VSP approaches. This work proposes a process for efficiently searching over combinations of individual object 6D pose hypotheses in cluttered scenes, especially in cases involving occlusions and objects resting on each other. The initial set of candidate object poses is generated from state-of-the-art object detection and global point cloud registration techniques. The best-scored pose per object by using these techniques may not be accurate due to overlaps and occlusions. Nevertheless, experimental indications provided in this work show that object poses with lower ranks may be closer to the real poses than ones with high ranks according to registration techniques. This motivates a global optimization process for improving these poses by taking into account scene-level physical interactions between objects. It also implies that the Cartesian product of candidate poses for interacting objects must be searched so as to identify the best scene-level hypothesis. To perform the search efficiently, the candidate poses for each object are clustered so as to reduce their number but still keep a sufficient diversity. Then, searching over the combinations of candidate object poses is performed through a Monte Carlo Tree Search (MCTS) process that uses the similarity between the observed depth image of the scene and a rendering of the scene given the hypothesized pose as a score that guides the search procedure. MCTS handles in a principled way the tradeoff between fine-tuning the most promising poses and exploring new ones, by using the Upper Confidence Bound (UCB) technique. Experimental results indicate that this process is able to quickly identify in cluttered scenes physically-consistent object poses that are significantly closer to ground truth compared to poses found by point cloud registration methods.