Local Search Heuristics Research Articles

Cophenetic Median Trees.

Median tree inference under path-difference metrics has shown great promise for large-scale phylogeny estimation. Similar to these metrics is the family of cophenetic metrics that originates from a classic dendrogram comparison method introduced more than 50 years ago. Despite the appeal of this family of metrics, the problem of computing median trees under cophenetic metrics has not been analyzed. Like other standard median tree problems relevant in practice, as we show here, this problem is also NP-hard. NP-hard median tree problems have been successfully addressed by local search heuristics that are solving thousands of instances of a corresponding (local neighborhood) search problem. For the local neighborhood search problem under a cophenetic metric, the best known (naïve) algorithm has a time complexity that is typically prohibitive for effective heuristic searches. Building on the pioneering work on path-difference median trees, we develop efficient algorithms for Manhattan and Euclidean cophenetic search problems that improve on the naïve solution by a linear and a quadratic factor, respectively. We demonstrate the performance and effectiveness of the resulting heuristic methods in a comparative study using benchmark empirical datasets.

Parallel heuristic local search algorithm on OTIS hyper hexa-cell and OTIS mesh of trees optoelectronic architectures

Heuristic local search algorithms have achieved good results in tackling combinatorial optimization problems, such as Travelling Salesman Problem (TSP). One of the well-known local search algorithms is the 2-opt algorithm. As a local search algorithm, 2-opt has achieved approximate optimal solutions for TSP within a reasonable time, especially for small data instances. However, solving large data instances of TSP using 2-opt requires extensive computation and considerable CPU time. Therefore, this paper presents a parallel version of the 2-opt algorithm, exploiting the features of Optical Transpose Interconnection System (OTIS) in solving the TSP. In this paper, we present the Parallel Repetitive 2-Opt (PRTO) algorithm for solving symmetric TSP on OTIS Hyper Hexa-Cell (OTIS-HHC) and OTIS Mesh of Trees (OTIS-MOT) optoelectronic architectures. We assess the performance of our algorithm analytically in terms of parallel time complexity, speedup, efficiency, cost, and communication cost on both optoelectronic architectures. Furthermore, a set of simulation experiments is conducted on various instances from the standard TSP library. The simulation results confirm that our algorithm is efficient regarding speedup and efficiency. For instance, the PRTO algorithm achieves a speedup of 32.9 for 6880 cities over OTIS-HHC with 36 processors. Moreover, the superiority of PRTO algorithm is shown through solving the TSP on OTIS-HHC and OTIS-MOT; its performance has been compared with the performance of the Parallel Repetitive Nearest Neighbor (PRNN) algorithm in terms of speedup, efficiency, and solution quality. For example, as a best case, the PRTO algorithm has shown 34 times improved speedup over the PRNN algorithm.

Landscape Analysis of a Class of NP-Hard Binary Packing Problems.

This article presents an exploratory landscape analysis of three NP-hard combinatorial optimisation problems: the number partitioning problem, the binary knapsack problem, and the quadratic binary knapsack problem. In the article, we examine empirically a number of fitness landscape properties of randomly generated instances of these problems. We believe that the studied properties give insight into the structure of the problem landscape and can be representative of the problem difficulty, in particular with respect to local search algorithms. Our work focuses on studying how these properties vary with different values of problem parameters. We also compare these properties across various landscapes that were induced by different penalty functions and different neighbourhood operators. Unlike existing studies of these problems, we study instances generated at random from various distributions. We found a general trend where some of the landscape features in all of the three problems were found to vary between the different distributions. We captured this variation by a single, easy to calculate parameter and we showed that it has a potentially useful application in guiding the choice of the neighbourhood operator of some local search heuristics.

The Design and Development of a Modified Artificial Bee Colony Approach for the Traveling Thief Problem

The traveling thief problem (TTP) is a benchmark problem that consists of two well-known problems, the traveling salesman problem (TSP) and the knapsack problem (KP). It was defined to imitate complex real-world applications that comprise different interdependent sub-problems. Various approaches were proposed in the literature to solve such a problem. These approaches mostly focus on local search algorithms, heuristics methods and evolutionary approaches. In addition, some of these approaches concentrated on solving the problem by considering each sub-problem independently. Thus far, limited approaches were proposed to solve the problem using swarm intelligence. In this article, the authors introduce a modified artificial bees colony (ABC) algorithm that addresses the TTP in an interdependent manner. The performance of this approach was compared with various recent approaches in the literature using different benchmark instances. The obtained results demonstrated that it is competitive with the state-of-the-art approaches, especially on small and medium instances.

Yard Crane Scheduling for container storage, retrieval, and relocation

This paper introduces a novel optimization problem resulting from the combination of two major existing problems arising at storage yards in container terminals. The Yard Crane Scheduling Problem is typically concerned with routing the crane given a sequence of storage and retrieval requests to perform, while the Container Relocation Problem tackles the minimization of relocations when retrieving containers in a simpler setting. This paper is the first to consider a model that integrates these two problems by scheduling storage, retrieval and relocations requests and deciding on storage and relocation positions. We formulate this problem as an integer program that jointly optimizes current crane travel time and future relocations. Based on the structure of the proposed formulation and the linear programming relaxation of subproblems, we propose a heuristic local search scheme. Finally, we show the value of our solutions on both simulated instances as well as real data from a port terminal.

The Dynamic Dispatch Waves Problem for same-day delivery

We study same-day delivery (SDD) systems by formulating the Dynamic Dispatch Waves Problem (DDWP). The DDWP models an order dispatching problem faced by a distribution center, where orders arise dynamically throughout a service day and must be delivered by day’s end. At each decision epoch (wave), the system’s operator chooses whether or not to dispatch a single vehicle loaded with orders ready for service in order to minimize vehicle travel costs and penalties for unserved requests. We formulate an arc-based integer programming model and design local search heuristics to solve a deterministic DDWP where order arrival times are known in advance. We use the deterministic variant to design an a priori solution approach, and provide two approaches to obtain dynamic policies using the a priori solution. We test and compare solution approaches on two sets of instances with different geography scenarios, size, information dynamism, and order timing variability. The computational results suggest that our best dynamic policy can reduce the average cost of an a priori policy by 9.1% and substantially improves the fraction of orders delivered (order coverage), demonstrating the importance of reactive optimization for dynamic SDD services. We also analyze the tradeoff between two common SDD objectives: total cost minimization versus order coverage maximization. We find structural differences in the dispatch frequency and route duration of solutions for the two different objectives, and demonstrate empirically that small increases in order coverage may require substantial increases in vehicle travel cost.

Meta-Lamarckian learning in multi-objective optimization for mobile social network search

Mobile Social Networks (MSNs) have recently brought a revolution in socially-oriented applications and services for mobile phones. In this paper, we consider the search problem in a MSN that aims at simultaneously maximizing the user's search outcome (recall) and mobile phone performance (battery usage). Because of the conflicting nature of these two objectives, the problem is dealt within the context of Multi-Objective Optimization (MOO). Our proposed approach hybridizes a Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) with a Meta-Lamarckian (ML) learning strategy that learns from the problem's properties and objective functions. The ML strategy is devised for adaptively select the best performing local search heuristic for each case, from a pool of general-purpose heuristics, so as to locally optimize the solutions during the evolution. We evaluated our propositions on a realistic multi-objective MSN search problem using trace-driven experiments with real mobility and social patterns. Extensive experimental studies reveal that the proposed method successfully learns the behaviour of individual local search heuristics during the evolution, adaptively follows the pattern of the best performing heuristics at different areas of the objective space and offers better performance in terms of both convergence and diversity than its competitors.The proposed Meta-Lamarckian based MOEA does not utilize any problem-specific heuristics, as most cases in the literature do, facilitating its applicability to other combinatorial MOO problems. To test its generalizability the proposed method is also evaluated on various test instances of the well-studied multi-objective Permutation Flow Shop Scheduling Problem.

Exact algorithms for bi-objective ring tree problems with reliability measures

We introduce bi-objective models for ring tree network design with a focus on network reliability within telecommunication applications. Our approaches generalize the capacitated ring tree problem (CRTP) which asks for a partially reliable topology that connects customers with different security requirements to a depot node by combined ring and tree graphs. While the CRTP aims at optimizing the edge installation costs, we propose four alternative, reliability-oriented objective functions. We study the case of service interruptions due to single-edge failures, and consider the overall number of tree customers and tree edges, the maximal number of subtree customers, and the maximal number of tree hops from rings as additional measures. To model the corresponding novel bi-objective problems, we develop mathematical multi-commodity flow formulations and identify relationships between the new objectives. For identifying the Pareto fronts, we apply an ϵ-constraint method based on integer programming. The computational efficiency is increased by employing local search heuristics in order to tighten upper bounds and by valid inequalities to strengthen lower bounds in the subproblems. In a computational study we report results, illustrate solution network topologies and extensively analyze the algorithm performance for instances from the literature.

A Genetic Algorithm for a Green Vehicle Routing Problem

We propose a Genetic Algorithm (GA) to address a Green Vehicle Routing Problem (G-VRP). Unlike classic formulations of the VRP, this study aims to minimise the CO2 emissions per route. The G-VRP is of interest to policy makers who wish to reduce greenhouse gas emissions. The GA is tested on a suite of benchmark, and real-world instances which include road speed and gradient data. Our solution approach incorporates elements of local and population search heuristics. Solutions are compared with routes currently used by drivers in a courier company. Reductions in emissions are achieved without incurring additional operational costs.

On the use of local search heuristics to improve GES-based Bayesian network learning

Bayesian networks learning is computationally expensive even in the case of sacrificing the optimality of the result. Many methods aim at obtaining quality solutions in affordable times. Most of them are based on local search algorithms, as they allow evaluating candidate networks in a very efficient way, and can be further improved by using local search-based metaheuristics to avoid getting stuck in local optima. This approach has been successfully applied in searching for network structures in the space of directed acyclic graphs.Other algorithms search for the networks in the space of equivalence classes. The most important of these is GES (greedy equivalence search). It guarantees obtaining the optimal network under certain conditions. However, it can also get stuck in local optima when learning from datasets with limited size. This article proposes the use of local search-based metaheuristics as a way to improve the behaviour of GES in such circumstances. These methods also guarantee asymptotical optimality, and the experiments show that they improve upon the score of the networks obtained with GES.

Tool path optimisation method for large thin-wall part of spacecraft

Roughing tool path of panel machining, which is a bottleneck of spacecraft production, should be optimised rapidly to shorten process time. This problem has a large solution space, and surface quality should be taken into account. The decision variables are cavity machining order, feed point and cutting direction of each cavity. Our problem is presented as an asymmetric general travelling salesman problem (AGTSP). A cluster optimisation-based hybrid max–tmin ant system (CO-HMMAS) is proposed, which solves two sub-problems as a whole. The oriented pheromone and dynamic heuristic information calculating methods are designed. We analyse the differences between one-stage and two-stage AGTSP local search heuristics and combine CO-HMMAS with them properly. An improved Global 3-opt heuristic suitable for both symmetric and asymmetric cases is proposed with sharply reduced time complexity. Comparison experiments verified that, two-stage local search heuristics decrease solution error significantly and rapidly when the error is great, and one-stage ones improve a near-optimal solution costing much more computing time. Benchmarks tests show that, CO-HMMAS outperforms the state-of-the-art algorithm on several technical indexes. Experiments on typical panels reveal that all algorithm improvements are effective, and CO-HMMAS can obtain a better tool path than the best algorithm within less CPU time.

The MADLA planner: Multi-agent planning by combination of distributed and local heuristic search

Real world applications often require cooperation of multiple independent entities. Classical planning is a well established technique solving various challenging problems such as logistic planning, factory process planning, military mission planning and high-level planning for robots. Multi-agent planning aims at solving similar problems in the presence of multiple independent entities (agents). Even though such entities might want to cooperate in order to fulfill a common goal, they may want to keep their internal information and processes private. In such case, we talk about privacy-preserving multi-agent planning.So far, multi-agent planners based on heuristic search used either a local heuristic estimating the particular agent's local subproblem or a distributed heuristic estimating the global problem as a whole. In this paper, we present the Multi-Agent Distributed and Local Asynchronous (MADLA) Planner, running a novel variant of a distributed state-space forward-chaining multi-heuristic search which combines the use of a local and a distributed heuristic in order to combine their benefits. In particular, the planner uses two variants of the well known Fast-Forward heuristic. We provide proofs of soundness and completeness of the search algorithm and show how much and what type of privacy it preserves. We also provide an improved privacy-preserving distribution scheme for the Fast-Forward heuristic.We experimentally compare the newly proposed multi-heuristic scheme and the two used heuristics separately. The results show that the proposed solution outperforms classical (single-heuristic) distributed search with either one of the heuristics used separately. In the detailed experimental analysis, we show limits of the planner and of the used heuristics based on particular properties of the benchmark domains. In a comprehensive set of multi-agent planning domains and problems, we show that the MADLA Planner outperforms all contemporary state-of-the-art privacy-preserving multi-agent planners using a compatible planning model.

Rearrangement moves on rooted phylogenetic networks.

Phylogenetic tree reconstruction is usually done by local search heuristics that explore the space of the possible tree topologies via simple rearrangements of their structure. Tree rearrangement heuristics have been used in combination with practically all optimization criteria in use, from maximum likelihood and parsimony to distance-based principles, and in a Bayesian context. Their basic components are rearrangement moves that specify all possible ways of generating alternative phylogenies from a given one, and whose fundamental property is to be able to transform, by repeated application, any phylogeny into any other phylogeny. Despite their long tradition in tree-based phylogenetics, very little research has gone into studying similar rearrangement operations for phylogenetic network—that is, phylogenies explicitly representing scenarios that include reticulate events such as hybridization, horizontal gene transfer, population admixture, and recombination. To fill this gap, we propose “horizontal” moves that ensure that every network of a certain complexity can be reached from any other network of the same complexity, and “vertical” moves that ensure reachability between networks of different complexities. When applied to phylogenetic trees, our horizontal moves—named rNNI and rSPR—reduce to the best-known moves on rooted phylogenetic trees, nearest-neighbor interchange and rooted subtree pruning and regrafting. Besides a number of reachability results—separating the contributions of horizontal and vertical moves—we prove that rNNI moves are local versions of rSPR moves, and provide bounds on the sizes of the rNNI neighborhoods. The paper focuses on the most biologically meaningful versions of phylogenetic networks, where edges are oriented and reticulation events clearly identified. Moreover, our rearrangement moves are robust to the fact that networks with higher complexity usually allow a better fit with the data. Our goal is to provide a solid basis for practical phylogenetic network reconstruction.

Bad Clade Deletion Supertrees: A Fast and Accurate Supertree Algorithm.

Supertree methods merge a set of overlapping phylogenetic trees into a supertree containing all taxa of the input trees. The challenge in supertree reconstruction is the way of dealing with conflicting information in the input trees. Many different algorithms for different objective functions have been suggested to resolve these conflicts. In particular, there exist methods based on encoding the source trees in a matrix, where the supertree is constructed applying a local search heuristic to optimize the respective objective function. We present a novel heuristic supertree algorithm called Bad Clade Deletion (BCD) supertrees. It uses minimum cuts to delete a locally minimal number of columns from such a matrix representation so that it is compatible. This is the complement problem to Matrix Representation with Compatibility (Maximum Split Fit). Our algorithm has guaranteed polynomial worst-case running time and performs swiftly in practice. Different from local search heuristics, it guarantees to return the directed perfect phylogeny for the input matrix, corresponding to the parent tree of the input trees, if one exists. Comparing supertrees to model trees for simulated data, BCD shows a better accuracy (F1 score) than the state-of-the-art algorithms SuperFine (up to 3%) and Matrix Representation with Parsimony (up to 7%); at the same time, BCD is up to 7 times faster than SuperFine, and up to 600 times faster than Matrix Representation with Parsimony. Finally, using the BCD supertree as a starting tree for a combined Maximum Likelihood analysis using RAxML, we reach significantly improved accuracy (1% higher F1 score) and running time (1.7-fold speedup).

AN EVOLUTIONARY APPROACH FOR CMS DESIGN

Cellular Manufacturing Systems (CMS) have been widely considered as the most efficient manufacturing systems in the case of medium variety and medium volume of production. The main advantage of CMS lies in the effective grouping of parts into families and machines in to corresponding groups as it results in minimizing the number of intercellular moves. Over the years, a number of efficient approaches have been developed by researchers to handle the Cell Formation Problem (CFP). Among these, a large number of approaches consist of Artificial Intelligence (AI) based techniques. The main advantage of such approaches is their ability to handle the CFP effectively both in terms of accuracy and computational effort. Following the same trend an evolutionary algorithm has been developed during this research by combining Standard Genetic Algorithm with a very effective Local Search Heuristic (LSH). The results show that it is efficient both in terms accuracy and speed of convergence (CPU time).

Two phased hybrid local search for the periodic capacitated arc routing problem

The periodic capacitated arc routing problem (PCARP) is a challenging general model with important applications. The PCARP has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (Fv) and a secondary objective of minimizing the total cost (Fc). In this paper, we propose an effective two phased hybrid local search (HLS) algorithm for the PCARP. The first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space. For both phases, combined local search heuristics are devised to ensure an effective exploration of the search space. Experimental results on 63 benchmark instances demonstrate that HLS performs remarkably well both in terms of computational efficiency and solution quality. In particular, HLS discovers 44 improved best known values (new upper bounds) for the total cost objective Fc while attaining all the known optimal values regarding the objective of the number of vehicles Fv. To our knowledge, this is the first PCARP algorithm reaching such a performance. Key components of HLS are analyzed to better understand their contributions to the overall performance.

Local search heuristics for a surgical case assignment problem

This work is part of an ongoing project with a Portuguese public hospital, where the elective surgeries scheduling problem is studied. The administration of the hospital aims to achieve the targets set by the Portuguese Ministry of Health for surgical production and to ensure a surgical service with a high level of efficiency. However, hospitals do not have an elective surgeries scheduling system, so the surgeries are unsystematically scheduled and without respecting equity criteria, thus disregarding the Ministry’s goals.Three versions of the problem are considered and local search heuristics are developed in order to quickly find good solutions for each version of the problem. The heuristics select patients from a long waiting list for surgery to be scheduled in each week, and define a room, a day and a shift for each selected surgery according to one of three different perspectives of the problem.The heuristics developed are tested in real instances and the values of the solutions are compared with the values of the solutions obtained using mixed integer linear programming models. The solutions obtained by the heuristics are of very good quality and the computational time required is generally quite low, even considering the instances with more surgeries in the waiting list.In addition, a user-friendly interface is created for the hospital, which reads all the relevant data and proposes a weekly surgical schedule in a systematic manner.

Smoothed Analysis of Local Search for the Maximum-Cut Problem

Even though local search heuristics are the method of choice in practice for many well-studied optimization problems, most of them behave poorly in the worst case. This is, in particular, the case for the Maximum-Cut Problem, for which local search can take an exponential number of steps to terminate and the problem of computing a local optimum is PLS-complete. To narrow the gap between theory and practice, we study local search for the Maximum-Cut Problem in the framework of smoothed analysis in which inputs are subject to a small amount of random noise. We show that the smoothed number of iterations is quasi-polynomial, that is, it is bounded from above by a polynomial in n log n and ϕ, where n denotes the number of nodes and ϕ denotes the perturbation parameter. This shows that worst-case instances are fragile, and it is a first step in explaining why they are rarely observed in practice.

A computational comparison of local search heuristics for solving quadratic assignment problems

A computational comparison of local search heuristics for solving quadratic assignment problems

Efficient and Effective Learning of HMMs Based on Identification of Hidden States

The predominant learning algorithm for Hidden Markov Models (HMMs) is local search heuristics, of which the Baum-Welch (BW) algorithm is mostly used. It is an iterative learning procedure starting with a predefined size of state spaces and randomly chosen initial parameters. However, wrongly chosen initial parameters may cause the risk of falling into a local optimum and a low convergence speed. To overcome these drawbacks, we propose to use a more suitable model initialization approach, a Segmentation-Clustering and Transient analysis (SCT) framework, to estimate the number of states and model parameters directly from the input data. Based on an analysis of the information flow through HMMs, we demystify the structure of models and show that high-impact states are directly identifiable from the properties of observation sequences. States having a high impact on the log-likelihood make HMMs highly specific. Experimental results show that even though the identification accuracy drops to 87.9% when random models are considered, the SCT method is around 50 to 260 times faster than the BW algorithm with 100% correct identification for highly specific models whose specificity is greater than 0.06.