Local Search Problem Research Articles

An Adaptive Cuckoo Algorithm-Based Optimization Method for Tourist Traffic Routes

This paper presents in-depth research and analysis of the optimization method of tourist traffic routes using the adaptive cuckoo algorithm. The traditional cuckoo algorithm has the disadvantages of slow convergence speed and easy falling into local extremes. This paper proposes the iterative adaptive CHSACS algorithm based on iteration. Based on the original CS algorithm, a dynamic adaptive step control amount and a segmented weighted position update formula are introduced to give a class of improved CS algorithms to coordinate the problem of local search and global search of the CS algorithm and speed up the convergence speed at the later stage. To address the problem that the out-of-bounds nests interfere with the convergence of the algorithm, a memory strategy is introduced to relocate the out-of-bounds nests in the search space to improve the stability of the algorithm. Experiments are conducted on the iterative adaptive-based conductive CHSACS algorithm with test function sets. Compared with the original CS algorithm, and ACO algorithm, the CHSACS algorithm has faster convergence, higher search accuracy and a better ability to avoid local optima when dealing with continuous function optimization problems. For the dynamic travel path problem of travel time optimization, the road travel time and sightseeing time of different periods are predicted based on historical data, and the most traveled distance of travel time between two sights is dynamically searched by using the search mechanism based on time windows. The iterative adaptive CHSACS algorithm is used to continuously find the tourist traffic route with the shortest travel time travel path from all combinations of tour sequences. This paper combines the characteristics of bus vehicle scheduling itself, takes into account the interests of both bus companies and tourists, establishes a bus vehicle scheduling model with the departure interval as the independent variable, introduces this hybrid cuckoo algorithm into bus scheduling, verifies the scientific and feasibility of the algorithm through examples, and provides a new idea for solving bus scheduling optimization problems.

Combustion Characteristic Prediction of a Supercritical CO2 Circulating Fluidized Bed Boiler Based on Adaptive GWO-SVM.

The development of a new and efficient supercritical carbon dioxide (S-CO2) power cycle system is one of the important technical ways to break through the bottleneck of coal power development, improve the efficiency of power generation, and realize energy saving and emission reduction. In order to simplify the complicated workload and save the huge time cost of numerical simulations on combustion characteristics, it is of great significance to accurately make the combustion characteristic prediction according to the operating performance of the S-CO2 CFB boiler. This study proposed a combustion characteristic prediction model corresponding to the S-CO2 CFB boiler based on the adaptive gray wolf optimizer support vector machine (AGWO-SVM). The parameters of the gray wolf optimizer algorithm were processed adaptively first combined with the boiler characteristics, and then the adaptive gray wolf optimizer algorithm was integrated with the support vector machine to solve the imbalance of local and global search problems of particles being easy to gather in a certain position in the process of pattern recognition. The novel method effectively predicts the boiler in the scaling process from the aspect of boiler capacity, optimizes the combustion characteristic expression by numerical simulations, greatly saves time cost and applicability of enlarged design by altering complex numerical simulations, and lays the application foundation of the S-CO2 CFB boiler in the industrial field with acceptable operation accuracy.

A new movement strategy of grey wolf optimizer for optimization problems and structural damage identification

In this paper, an improved Grey Wolf Optimizer (GWO) algorithm, termed LGWO, is introduced. The enhanced version is interesting and complementary in terms of the direction of movement of the leader wolf, and a special parameter that allows the faster wolves to prey position. The Lévy flight is employed as a special navigation solution for alpha, beta, and delta wolf. In this way, the leader wolf equips a powerful tool to deal with the local search problem. A new principle illustrates the behaviour of omega wolf in hunting is also added to enhance the convergence speed of this algorithm. To investigate the performance of LGWO, a series of problems, namely 23 classical benchmarks, a set of CEC 2019 functions, and three engineering problems, is investigated. Furthermore, LGWO is employed to study structural damage identification in high-dimensional problems. The research appears to show that the performance of LGWO is substantially increased.

A Surrogate-Based Optimization Method with Dynamic Adaptation for High-Dimensional Mixed-Integer Problems

• SODA-AD and its two variants are proposed to address HMIO-B under limited computational resources. • SODA-AD and its two variants can well balance global and local search. • SODA-AD and its two variants outperform other counterpart algorithms. This study develops a Surrogate-based Optimization algorithm with Dynamic Adaptation of perturbation search of All Dimensions (SODA-AD) to address high-dimensional mixed-integer optimization problems with a black-box objective function (HMIO-B). SODA-AD improves dynamic coordinate search (DCS) in two ways, i.e., with a new way of sampling candidate points and a new adaptive scaling method, which help to balance global and local search and address high-dimensional problems. Additionally, two variants of SODA-AD are described. One is SODA-AD with a modified infill strategy (SODA-ADM), which uses the prediction scoring criterion to replace the weighted scoring criterion when the budgeted computation resources are going to run out. The second method first employs SODA-ADM and then carries out a sequential dimensioned perturbation search for each iteration periodically to continue the local search, and this is named SODA-ADM-DP. In numerical experiments, we compare SODA-AD and its two variants with other well-known counterparts using one complex real-world engineering problem and eight 100-dimensional (100-D) benchmark problems. It is concluded that SODA-AD and its two variants outperform the other counterparts on most of the test problems and are promising for solving high-dimensional mixed-integer optimization problems with black-box objective functions or nonlinear and nonconvex objective functions.

Applying topological data analysis to local search problems

<p style='text-indent:20px;'>We present an application of topological data analysis (TDA) to discrete optimization problems, which we show can improve the performance of the 2-opt local search method for the traveling salesman problem by simply applying standard Vietoris-Rips construction to a data set of trials. We then construct a simplicial complex which is specialized for this sort of simulated data set, determined by a stochastic matrix with a steady state vector <inline-formula><tex-math id="M1">\begin{document}$ (P,\pi) $\end{document}</tex-math></inline-formula>. When <inline-formula><tex-math id="M2">\begin{document}$ P $\end{document}</tex-math></inline-formula> is induced from a random walk on a finite metric space, this complex exhibits similarities with standard constructions such as Vietoris-Rips on the data set, but is not sensitive to outliers, as sparsity is a natural feature of the construction. We interpret the persistent homology groups in several examples coming from random walks and discrete optimization, and illustrate how higher dimensional Betti numbers can be used to classify connected components, i.e. zero dimensional features in higher dimensions.</p>

Decentralized Intelligent Search of Tourist Routes Based on Check-In Data

The location social network generates a large amount of data; these dada reflect the user's preferences and the popularity of the route, and a new model is provided for travel route search. Based on this demand, a problem of local distributed travel route search is proposed for group users. In this problem, the personal preferences of group users are combined, and an access route is found with partial POI (point of interest) and the largest group profit. The check-in data are used to generate a POI transfer relationship diagram based on the user's transfer between POIs, and route search is performed on the relationship diagram. In order to improve the search efficiency, a two-layer transfer relationship diagram is designed according to the popularity and transfer relationship of POI, the POI is generalized, and a hierarchical query is realized. A branch and bound search strategy optimization algorithm is designed, and the control relationship between nodes is used for pruning; the search efficiency of the algorithm is further improved.

Local Search with Dynamic-Threshold Configuration Checking and Incremental Neighborhood Updating for Maximum k-plex Problem

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamic-threshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V|⋅ΔG) to O(k · Δ‾G). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.

A Multiobjective, Lion Mating Optimization Inspired Routing Protocol for Wireless Body Area Sensor Network Based Healthcare Applications.

The importance of body area sensor networks (BASNs) is increasing day by day because of their increasing use in Internet of things (IoT)-enabled healthcare application services. They help humans in improving their quality of life by continuously monitoring various vital signs through biosensors strategically placed on the human body. However, BASNs face serious challenges, in terms of the short life span of their batteries and unreliable data transmission, because of the highly unstable and unpredictable channel conditions of tiny biosensors located on the human body. These factors may result in poor data gathering quality in BASNs. Therefore, a more reliable data transmission mechanism is greatly needed in order to gather quality data in BASN-based healthcare applications. Therefore, this study proposes a novel, multiobjective, lion mating optimization inspired routing protocol, called self-organizing multiobjective routing protocol (SARP), for BASN-based IoT healthcare applications. The proposed routing scheme significantly reduces local search problems and finds the best dynamic cluster-based routing solutions between the source and destination in BASNs. Thus, it significantly improves the overall packet delivery rate, residual energy, and throughput with reduced latency and packet error rates in BASNs. Extensive simulation results validate the performance of our proposed SARP scheme against the existing routing protocols in terms of the packet delivery ratio, latency, packet error rate, throughput, and energy efficiency for BASN-based health monitoring applications.

A study of the loops control for reconfigurable computing with OpenCL in the LABS local search problem

In this article, we study the steepest descent local search (SDLS) algorithm that is used as the improvement step in the memetic algorithms for the search of low autocorrelation binary sequences (LABS). We address the method of reconfigurable computing, as the algorithm is of the field programmable gate array (FPGA) type as it features the integer operations, bit-wise data representation, regular execution flow, and huge computational complexity. It contains four levels of nested loops, but its direct parallel implementation as a custom processor leads to typical problems because the loops expose a dynamic range and too many iterations. This inhibits a simple parallel data path that is typically produced by the method of the loop unrolling. We have examined the four architectures that mitigate the found obstacles, and we provide the results of their implementation. The solutions take advantages of the loop pipelining, reordering of the loops, and dynamic reconfiguration. The recently available development tool was involved in our study as we have used the OpenCL (OCL) platform for FPGAs to draw practical conclusions. The given proposals are characterized by their performance and capacity for a problem size. Consequently, the speed/size trade-off is highlighted, as an FPGA size is a design constraint. The performance of the FPGA-based solutions is compared to the CPU speed, and the maximum reported speed-up is 750. Readers can further develop and/or use the presented OCL solutions for efficient LABS discovery as we provide the corresponding software repository.

Distributed onboard mission planning for multi-satellite systems

The increasing number of satellites for specific space missions is hindering efficient control from the ground stations. In addition, the risk of failing or deteriorating elements in a multi-satellite system (MSS) leads to the uncertainty in its operating environment which challenges traditional centralized planning algorithms. Centralized algorithms depend on one coordinator to overview entire system, which is a single poitn of failure, so if it malfunctional, the MSS may go down. To overcome this problem, a distributed onboard mission planning algorithm based on the Hybrid Dynamic Mutation Genetic Algorithm (HDMGA) is proposed for such MSS. The satellites are considered as autonomous agents which can communicate and negotiate with other satellites. The mission objective is decomposed through the team negotiation procedures, and the local goals are dispatched to the participant satellite. The local planning procedure on each satellite is modeled as local search problems, while the planning problem for entire team is formulated as strongly-coupled distributed optimization problem. The verification shows that the proposed distributed approach can achieve the same results as the centralized approach. The simulation results illustrate that the proposed approach shows superior performance on both computation time and success rate, as compared with other two state-of-the-art distributed mission planning approaches.

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.

Computing Manhattan Path-Difference Median Trees: A Practical Local Search Approach.

Median tree problems are powerful tools for inferring large-scale phylogenetic trees that hold enormous promise for society at large. Such problems seek a median tree for a given collection of input trees under some problem-specific distance. Here, we introduce a median tree problem under the classic Manhattan path-difference distance. We show that this problem is NP-hard, devise an ILP formulation, and provide an effective local search heuristic that is based on solving a local search problem exactly. Our algorithm for the local search problem improves asymptotically by a factor of $n$n on the best-known (naïve) solution, where $n$n is the overall number of taxa in the input trees. Finally, comparative phylogenetic studies using considerably large empirical data and an accuracy analysis for smaller phylogenetic trees reveal the ability of our novel heuristic.

Modified genetic algorithms for solving facility layout problems

A facility layout design is one of the most commonly faced problems in the manufacturing sectors. The problem is mixed-integer in nature and usually an NP-hard problem. Due to mixed-integer nature of the problem, it is difficult to solve the problem using classical optimization techniques. The classical optimization techniques are better for local search of the optimal solution. However, these algorithms are not efficient when there are multiple optimal solutions and alternate optimal solutions. To overcome these limitations, this paper proposed a new interactive evolutionary algorithm based local search algorithm for solving static facility layout problems with unequal compartments. This is an iterative based two steps algorithm. The evolutionary algorithm creates the new solutions for the local search algorithm to obtain a local optimal solution. The designer can interact between these processes to derive the best possible solution of the problem. The objective function of the problem is non-linear one in which the sum of the material handling cost has been minimized. Apart from the conventional evolutionary operators, i.e. selection, crossover, mutation and elitism, this paper has also proposed exchange and rotation operators. The rotation operator is used to avoid mixed-integer formulation of the problem for the local search problem. The use of rotation operator has also reduced the number of variables of the problem significantly. The performance of the model is tested over previously solved problems selected from the literature. The evaluation of the results shows that the performance of the proposed model is better than many existing algorithms and has the potential for real-world applications.

On the [formula omitted]-complexity of maximum constraint assignment

In this paper, we investigate the complexity of computing locally optimal solutions for the local search problem Maximum Constraint Assignment (MCA). For our investigation, we use the framework of PLS, as defined by Johnson et al. (1988) [9]. In a nutshell, the MCA-problem is a local search version of weighted, generalized MaxSat on constraints (functions mapping assignments to integers) over variables with higher valence; additional parameters in (p,q,r)- MCA simultaneously limit the maximum length p of each constraint, the maximum appearance q of each variable and its valence r. We focus on hardness results and show PLS-completeness of (3,2,3)-MCA and (2,3,6)-MCA using tight reductions from Circuit/Flip. Our results are optimal in the sense that (2,2,r)- MCA is solvable in polynomial time for every r∈N. We also pay special attention to the case of binary variables and show that (6,2,2)- MCA is tight PLS-complete. For our results, we extend and refine a technique from Krentel (1989) [10].

Applicability of Genetic and Ant Algorithms in Highway Alignment and Rail Transit Station Location Optimization

The emergence of artificial intelligence (AI)-based optimization heuristics like genetic and ant algorithms is useful in solving many complex transportation location optimization problems. The suitability of such algorithms depends on the nature of the problem to be solved. This study examines the suitability of genetic and ant algorithms in two distinct and complex transportation problems: (1) highway alignment optimization and (2) rail transit station location optimization. A comparative study of the two algorithms is presented in terms of the quality of results. In addition, Ant algorithms (AAs) have been modified to search in a global space for both problems, a significant departure from traditional AA application in local search problems. It is observed that for the two optimization problems both algorithms give almost similar solutions. However, the ant algorithm has the inherent limitation of being effective only in discrete search problems. When applied to continuous search spaces ant algorithm requires the space to be sufficiently discretized. On the other hand, genetic algorithms can be applied to both discrete and continues spaces with reasonable confidence. The application of AA in global search seems promising and opens up the possibility of its application in other complex optimization problems.

Genetic local search the graph partitioning problem under cardinality constraints

For the graph partitioning problem under cardinality constraints, a genetic local search method is developed. At each iteration of the method, there is a set of local optima of the problem. This set is used to search for new local optima with a smaller error. The local search problem with certain polynomially searchable neighborhoods is proved to be tight PLS-complete. It is shown that, in the worst case, number of local improvements can be exponentially large for any pivoting rule. Numerical experiments are performed in the special case of edge weights equal to unity, when local search is a polynomial-time procedure. The results of the experiments indicate that the method is highly efficient and can be applied to large-scale problems.

Nested PLS

In this note we will introduce a class of search problems, called nested Polynomial Local Search (nPLS) problems, and show that definable NP search problems, i.e., $${\Sigma^{b}_{1}}$$ -definable functions in $${T^{2}_{2}}$$ are characterized in terms of the nested PLS.

Robinson-Foulds supertrees.

BackgroundSupertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.ResultsWe introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (naïve) solutions by a factor of Θ(n) and Θ(n2) respectively (where n is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.ConclusionsOur heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.

A robust iterative refinement clustering algorithm with smoothing search space

Iterative refinement clustering algorithms are widely used in data mining area, but they are sensitive to the initialization. In the past decades, many modified initialization methods have been proposed to reduce the influence of initialization sensitivity problem. The essence of iterative refinement clustering algorithms is the local search method. The big numbers of the local minimum points which are embedded in the search space make the local search problem hard and sensitive to the initialization. The smaller number of local minimum points, the more robust of initialization for a local search algorithm is. In this paper, we propose a Top–Down Clustering algorithm with Smoothing Search Space (TDCS3) to reduce the influence of initialization. The main steps of TDCS3 are to: (1) dynamically reconstruct a series of smoothed search spaces into a hierarchical structure by ‘filling’ the local minimum points; (2) at the top level of the hierarchical structure, an existing iterative refinement clustering algorithm is run with random initialization to generate the clustering result; (3) eventually from the second level to the bottom level of the hierarchical structure, the same clustering algorithm is run with the initialization derived from the previous clustering result. Experiment results on 3 synthetic and 10 real world data sets have shown that TDCS3 has significant effects on finding better, robust clustering result and reducing the impact of initialization.

POLYNOMIAL LOCAL SEARCH IN THE POLYNOMIAL HIERARCHY AND WITNESSING IN FRAGMENTS OF BOUNDED ARITHMETIC

The complexity class of [Formula: see text]-polynomial local search (PLS) problems is introduced and is used to give new witnessing theorems for fragments of bounded arithmetic. For 1 ≤ i ≤ k + 1, the [Formula: see text]-definable functions of [Formula: see text] are characterized in terms of [Formula: see text]-PLS problems. These [Formula: see text]-PLS problems can be defined in a weak base theory such as [Formula: see text], and proved to be total in [Formula: see text]. Furthermore, the [Formula: see text]-PLS definitions can be skolemized with simple polynomial time functions, and the witnessing theorem itself can be formalized, and skolemized, in a weak base theory. We introduce a new [Formula: see text]-principle that is conjectured to separate [Formula: see text] and [Formula: see text].