Local Search Algorithm Research Articles

Heuristic Approaches for Using an Exact Model to Obtain the Placement of a Set of Rectangles on a Half-Strip

There is considered the problem of the compact orthogonal placement, which consists in placing of the set of rectangles on the half-strip and its solution by constructing an optimization model that reduces to solving a high-dimensional linear partial Boolean programming problem. The main method of solving the problem is the algorithm of branches and boundaries, providing consistent fiXation of the Boolean variables. The direct use of this algorithm represents significant computational difficulties and is used only for the small size of the initial set of rectangles. In this paper are proposes approaches that reduce the computational complexity of the solution of this optimization model by using heuristic approaches to fix individual Boolean variables. Most of the variables responsible for the relative arrangement of all pairs of rectangles relative to each other are fixed on the basis of generating the permutation of rectangles and special code that determines the direction by which the intersection of the location of the rectangles should be monitored. Thus, the direct computing complexity of the method of branches and the boundaries of solving the problem becomes insignificant. To generate pre-fixation of the Boolean variables, genetic algorithms and local search algorithms are used. Computational experiments showed that the used techniques of fixing the Boolean variables allowed to reduce the volume of calculations and the quality of the resulting approximate solution, in general, it turns out acceptable.

A hybrid local search algorithm for the continuous energy-constrained scheduling problem

AbstractWe consider the continuous energy-constrained scheduling problem (CECSP). A set of jobs has to be processed on a continuous, shared resource. A schedule for a job consists of a start time, completion time, and a resource consumption profile. The goal is to find a schedule such that each job does not start before its release time, is completed before its deadline, satisfies its full resource requirement, and respects its lower and upper bounds on resource consumption during processing. The objective is to minimize the total weighted completion time. We present a hybrid local search approach, using simulated annealing and linear programming, and compare it to a mixed-integer linear programming (MILP) formulation. We show that the hybrid local search approach matches the MILP formulation in solution quality for small instances and is able to find a feasible solution for larger instances in reasonable time.

Energy-Aware Camera Location Search Algorithm for Increasing Precision of Observation in Automated Manufacturing

Visual servoing technology is well developed and applied in many automated manufacturing tasks, especially in tools’ pose alignment. To access a full global view of tools, most applications adopt an eye-to-hand configuration or an eye-to-hand/eye-in-hand cooperation configuration in an automated manufacturing environment. Most research papers mainly put efforts into developing control and observation architectures in various scenarios, but few have discussed the importance of the camera’s location in the eye-to-hand configuration. In a manufacturing environment, the quality of camera estimations may vary significantly from one observation location to another, as the combined effects of environmental conditions result in different noise levels of a single image shot in different locations. In this paper, we propose an algorithm for the camera’s moving policy so that it explores the camera workspace and searches for the optimal location where the image’s noise level is minimized. Also, this algorithm ensures the camera ends up at a suboptimal (if the optimal one is unreachable) location among the locations already searched with the limited energy available for moving the camera. Unlike a simple brute-force approach, the algorithm enables the camera to explore space more efficiently by adapting the search policy by learning the environment. With the aid of an image-averaging technique, this algorithm, in the use of a solo camera, achieves observation accuracy in eye-to-hand configurations to a desirable extent without filtering out high-frequency information in the original image. An automated manufacturing application was simulated, and the results show the success of this algorithm’s improvement in observation precision with limited energy.

A reinforcement learning-based multiobjective heuristic algorithm for multiple-truck routing problems with heterogeneous drones

As a result of new technological developments, drone usage has become common in last-mile logistics activities. Owing to the limited flight range of drones, drones may service customers by using trucks as hubs. Although the truck routing problem with drones (TRP-D) has been studied frequently, studies that have addressed this problem in a multiobjective manner are rare. In this study, multiobjective TRP-D is discussed. In this problem, multiple trucks are considered. Each truck is equipped with multiple heterogeneous drones. A multiobjective mixed-integer linear programming (MILP) model is proposed. Since the problem is NP-hard, a reinforcement learning (RL)-based multiobjective heuristic algorithm is proposed to obtain solutions in large-scale cases. A three-phase heuristic feasible-solution-generation algorithm is proposed. The variable neighbourhood descent (VND) algorithm with RL is proposed as a local search algorithm for the multiobjective optimization problem. The results of the proposed heuristic algorithm are compared with the Pareto optimal solutions for small-sized test problems via the augmented ε-constraint (AUGMECON) method and the CPLEX solver. The proposed algorithm is also compared with state-of-the-art multiobjective heuristic algorithms for large-scale problems. According to the results, the proposed algorithm is an efficient multiobjective heuristic algorithm for the addressed problem.

Scheduling of Earth observing satellites using distributed constraint optimization

Earth observation satellites (EOS) are satellites equipped with optical sensors that orbit the Earth to take photographs of particular areas at the request of users. With the development of space technology, the number of satellites has increased continuously. Yet still, the number of satellites cannot meet the explosive growth of applications. Thus, scheduling solutions are required to satisfy requests and obtain high observation efficiency. While the literature on multi-satellite scheduling is rich, most solutions are centralized algorithms. However, due to their cost, EOS systems are often co-funded by several agents (e.g., countries, companies, or research institutes). Central solutions require that these agents share their requests for observations with others. To date, there has yet to be a solution for EOS scheduling that protects the private information of the interested parties. In this study, we model the EOS scheduling problem as a distributed constraint optimization problem (DCOP). This modeling enables the generation of timetables for the satellites in a distributed manner without a priori sharing users’ private information with some central authority. For solving the resulting DCOP, we use and compare the results of two different local search algorithms—Distributed Stochastic Algorithm and Maximum Gain Message—which are known to produce efficient solutions in a timely manner. The modeling and solving of the resulting DCOP constitute our new solution method, which we term Distributed Satellite Timetable Solver (DSTS). Experimental evaluation reveals that the DSTS method provides solutions of higher quality than a commonly used centralized greedy algorithm and is comparable to an additional centralized algorithm that we propose.

Lot Sizing and Scheduling Problem in Distributed Heterogeneous Hybrid Flow Shop and Learning-Driven Iterated Local Search Algorithm

Lot Sizing and Scheduling Problem in Distributed Heterogeneous Hybrid Flow Shop and Learning-Driven Iterated Local Search Algorithm

Set Packing Optimization by Evolutionary Algorithms with Theoretical Guarantees.

The set packing problem is a core NP-complete combinatorial optimization problem which aims to find the maximum collection of disjoint sets from a given collection of sets, S, over a ground set, U. Evolutionary algorithms (EAs) have been widely used as general-purpose global optimization methods and have shown promising performance for the set packing problem. While most previous studies are mainly based on experimentation, there is little theoretical investigation available in this area. In this study, we analyze the approximation performance of simplified versions of EAs, specifically the (1+1) EA, for the set packing problem from a theoretical perspective. Our analysis demonstrates that the (1+1) EA can provide an approximation guarantee in solving the k-set packing problem. Additionally, we construct a problem instance and prove that the (1+1) EA beats the local search algorithm on this specific instance. This proof reveals that evolutionary algorithms can have theoretical guarantees for solving NP-hard optimization problems.

IOHexperimenter: Benchmarking Platform for Iterative Optimization Heuristics.

We present IOHexperimenter, the experimentation module of the IOHprofiler project. IOHexperimenter aims at providing an easy-to-use and customizable toolbox for benchmarking iterative optimization heuristics such as local search, evolutionary and genetic algorithms, and Bayesian optimization techniques. IOHexperimenter can be used as a stand-alone tool or as part of a benchmarking pipeline that uses other modules of the IOHprofiler environment. IOHexperimenter provides an efficient interface between optimization problems and their solvers while allowing for granular logging of the optimization process. Its logs are fully compatible with existing tools for interactive data analysis, which significantly speeds up the deployment of a benchmarking pipeline. The main components of IOHexperimenter are the environment to build customized problem suites and the various logging options that allow users to steer the granularity of the data records.

On the impact of co-optimizing station locations, trip assignment, and charging schedules for electric buses

As many public transportation systems around the world transition to electric buses, the planning and operation of fleets can be improved via tailored decision-support tools. In this work, we study the impact of jointly locating charging facilities, assigning electric buses to trips, and determining when and where to charge the buses. We propose a mixed integer linear program that co-optimizes planning and operational decisions jointly and an iterated local search heuristic to solve large-scale instances. Herein, we use a concurrent scheduler algorithm to generate an initial feasible solution, which serves as a starting point for our iterated local search algorithm. In the sequential case, we first optimize trip assignments and charging locations. Charging schedules are then determined after fixing the optimal decisions from the first level. The joint model, on the other hand, integrates charge scheduling within the local search procedure. The solution quality of the joint and sequential iterated local search models are compared for multiple real-world bus transit networks. Our results demonstrate that joint models can help further improve operating costs by 14.1% and lower total costs by about 4.1% on average compared with sequential models. In addition, energy consumption costs and contracted power capacity costs have been reduced significantly due to our integrated planning approach.

A fast local search based memetic algorithm for the parallel row ordering problem

The parallel row ordering problem (PROP) is concerned with arranging two groups of facilities along two parallel lines with the goal of minimizing the sum of the flow cost-weighted distances between the pairs of facilities. As the main result of this paper, we show that the insertion neighborhood for the PROP can be explored in optimal time Θ(n2) by providing an O(n2)-time procedure for performing this task, where n is the number of facilities. As a case study, we incorporate this procedure in a memetic algorithm (MA) for solving the PROP. We report on numerical experiments that we conducted with MA on PROP instances with up to 500 facilities. The experimental results demonstrate that the MA is superior to the adaptive iterated local search algorithm and the parallel hyper heuristic method, which are state-of-the-art for the PROP. Remarkably, our algorithm improved best known solutions for six largest instances in the literature. We conjecture that the time complexity of exploring the interchange neighborhood for the PROP is Θ(n2), exactly as in the case of insertion operation.

Fitness landscapes of buffer allocation problem for production lines with unreliable machines

We study the structural properties of the buffer allocation problem from the fitness landscape perspective. We consider manufacturing flow lines with series–parallel network structure. The machines are supposed to be unreliable, their time to failure and repair time are exponentially distributed. Tentative solutions are evaluated by means of an approximate method based on the Markov models aggregation. We carry out computational experiments with local search and genetic algorithms in order to evaluate the fitness landscape properties of previously published instances and their modifications. It turns out that the so-called ‘massif central’ or ‘big valley’ structure of the fitness landscape is present but only partially: The fitness of local optima is negatively correlated with the distance to the best found solution, yet the set of local optima cannot be encompassed by a ball of relatively small size with respect to the size of solution space. Moreover, we show that in many problem instances, several clusters of local optima can be identified. The performance of genetic algorithms is discussed with respect to population clustering and the permanent usage of crossover is recommended.

Augmented multi-agent algorithm utilizing intelligent search range detection heuristic to solve assembly line sequencing problem: A case study in the truck industry

Car sequencing is a widely adopted approach to implicitly enhance the short-term balancing of mixed-model assembly lines in practical applications. In this research, we investigate this problem in the context of a real-world case taken from a truck final assembly line. Our study considers cross-ratio constraints that address limitations related to dependent features of the products. Additionally, to manage the distribution of violation errors in cases where predefined congestion level thresholds (soft rules) exist, we propose a piecewise linear penalty function. To tackle these considerations, we formulate a mathematical programming model aimed at minimizing the total weighted penalty incurred from violating both independent and dependent sequencing rules. As the problem falls into the NP-hard category, we develop a multi-start parallel local search algorithm based on multi-agent approach to efficiently solve it. The algorithm is augmented by incorporating a self-adaptive diversification mechanism and a novel intelligent search range detection heuristic. The proposed heuristic enables the searching agents to intelligently explore the solution space rather than relying on a purely random search. The numerical experiments are conducted using 30 real-world instances from three truck assembly lines to validate the quality of the proposed algorithm. The comparison of the results indicates that our algorithm outperforms state-of-the-art algorithms. Furthermore, computational experiments demonstrate the effectiveness of each proposed mechanism in enhancing the algorithm's performance.

Solving continuous quadratic programming for the discrete balanced graph partitioning problem using simulated annealing algorithm hybridized local search and multi-start algorithms

In a discrete balanced graph partitioning problem (DBGPP), a simple undirected weighted graph in that both vertices and edges are weighted is given. The task is dividing vertices into two disjoint subsets such that the sum of the weights of cut edges is minimized and the sum of the weights of vertices in each subset must equal or be as close as possible to each other. Here in order to solve the DBGPP, we first transform the problem into continuous quadratic programming and then show that the new problem has a binary solution, which is the optimal solution for the DBGPP. We also give necessary and sufficient conditions of continuous quadratic programming to identify stationary and local optimal solutions. In addition, we propose a local search to find a binary solution of the continuous quadratic programming. An approximated solution of the DBGPP is obtained using a hybrid simulated annealing algorithm. In our proposed algorithm, the structure of the objective function in a continues problem is considered as the evaluator function. Due to the Dolan–Moré performance profiles and the non-parametric statistical one-sided Wilcoxon signed rank test, we demonstrate the efficiency of our proposed approach in comparison with other available methods.

An Improved Ant Colony Algorithm with Deep Reinforcement Learning for the Robust Multiobjective AGV Routing Problem in Assembly Workshops

Vehicle routing problems (VRPs) are challenging problems. Many variants of the VRP have been proposed. However, few studies on VRP have combined robustness and just-in-time (JIT) requirements with uncertainty. To solve the problem, this paper proposes the just-in-time-based robust multiobjective vehicle routing problem with time windows (JIT-RMOVRPTW) for the assembly workshop. Based on the conflict between uncertain time and JIT requirements, a JIT strategy was proposed. To measure the robustness of the solution, a metric was designed as the objective. Afterwards, a two-stage nondominated sorting ant colony algorithm with deep reinforcement learning (NSACOWDRL) was proposed. In stage I, ACO combines with NSGA-III to obtain the Pareto frontier. Based on the model, a pheromone update strategy and a transfer probability formula were designed. DDQN was introduced as a local search algorithm which trains networks through Pareto solutions to participate in probabilistic selection and nondominated sorting. In stage II, the Pareto frontier was quantified in feasibility by Monte Carlo simulation, and tested by diversity-robust selection based on uniformly distributed weights in the solution space to select robust Pareto solutions that take diversity into account. The effectiveness of NSACOWDRL was demonstrated through comparative experiments with other algorithms on instances. The impact of JIT strategy is analyzed and the effect of networks on the NSACOWDRL is further discussed.

Aggregated planning to solve multi-product multi-period disassembly line balancing problem by considering multi-manned stations: A generic optimization model and solution algorithms

Disassembly lines are crucial in the recovery process of end-of-life (EOL) products, facilitating the systematic extraction of parts to meet predetermined objectives. While previous studies have made significant advancements, they have not addressed the disassembly line planning and balancing problem by focusing on the real-life significance of combining long-term decision-making and short-term operational missions. This study fills this gap by combining multi-product, multi-period, and multi-manned disassembly line concepts into a novel integrated approach. Initially, a generic optimization model is formulated, incorporating the concept of multi-manned stations. Subsequently, genetic algorithm (GA)-based solution approaches are developed to address the problem’s complexity. Three tactical-level policies, including economic disassembly quantity (EDQ), just-in-time (JIT), and random (R) based lot size policies, are explored within the algorithms. Additionally, simulated annealing-based local search algorithms and two crossover operators, CR1 and CR2, are incorporated to enhance solution quality. Through computational analysis, six algorithms are evaluated, with the GACR1-JIT algorithm demonstrating significant cost reductions compared to alternatives. The findings underscore the growing importance of JIT-based lot size policies, particularly with an increasing number of periods. This research bridges theoretical and practical considerations by highlighting the strategic importance of combining long-term disassembly line planning and short-term lot sizing decisions to improve system performance.

A novel reduced local search algorithm for optimization of digital filter coefficients

Digital Filtering is an important operation in DSP. Most of the DSP applications demand low power implementations. In CMOS digital circuits, switching from logic 0 to logic 1 and vice-versa decides the dynamic power consumption. This paper proposes and develops a novel algorithm based on mixed integer linear programming to minimize the number of ones (filter cost) in filter coefficients, which in turn minimizes the switching factor of CMOS circuits and the number of additional adders needed for hardware implementation. The search space for finding the optimal value of the coefficient is reduced thereby increasing the speed of execution of the algorithm. The average reduction of 18.02 % in the number of transitions is obtained with the proposed algorithm. The suggested technique results in an 18.72 % decrease in the typical price of digital filters. Also the proposed algorithm works faster than the previously proposed algorithm used for finding the optimized coefficients.

A Graph Multi-separator Problem for Image Segmentation

We propose a novel abstraction of the image segmentation task in the form of a combinatorial optimization problem that we call the multi-separator problem. Feasible solutions indicate for every pixel whether it belongs to a segment or a segment separator, and indicate for pairs of pixels whether or not the pixels belong to the same segment. This is in contrast to the closely related lifted multicut problem, where every pixel is associated with a segment and no pixel explicitly represents a separating structure. While the multi-separator problem is np-hard, we identify two special cases for which it can be solved efficiently. Moreover, we define two local search algorithms for the general case and demonstrate their effectiveness in segmenting simulated volume images of foam cells and filaments.

A fast local search algorithm for minimum sum coloring problem on massive graphs

The minimum sum coloring problem (MSCP) is an important extension of the graph coloring problem with wide real-world applications. Compared to the classic graph coloring problem, where lots of methods have been developed and even massive graphs with millions of vertices can be solved well, few works have been done for the MSCP, and no specialized MSCP algorithms are available for solving massive graphs. This paper explores how to solve MSCP on massive graphs, and then proposes a fast local search algorithm for the MSCP based on three main ideas including a coarse-grained reduction method, two kinds of scoring functions and selection rules as well as a novel local search framework. Experiments are conducted to compare our algorithm with several state-of-the-art algorithms on massive graphs. The proposed algorithm outperforms previous algorithms in almost all the massive graphs and also improves the best-known solutions for some conventional instances, which demonstrates the performance and robustness of the proposed algorithm.

An Effective Local Search Algorithm for Flexible Job Shop Scheduling in Intelligent Manufacturing Systems

As one of the most classical scheduling problems, flexible job shop scheduling problems (FJSP) find widespread applications in modern intelligent manufacturing systems. However, the majority of meta-heuristic methods for solving FJSP in the literature are population-based evolutionary algorithms, which are complex and time-consuming. In this paper, we propose a fast effective single-solution based local search algorithm with an innovative adaptive weighting technique (AWLS) for solving FJSP. The adaptive weighting technique assigns weights to each operation and adaptively updates them during the exploration. AWLS integrates a Tabu Search strategy and the adaptive weighting technique to smooth the landscape of the search space and enhance the exploration diversity. Computational experiments on 313 well-known benchmark instances demonstrate that AWLS is highly competitive with state-of-the-art algorithms in terms of both solution quality and computational efficiency, despite of its simplicity. Specifically, AWLS improves the previous best-known results in the literature on 33 instances and match the best-known results on the remaining ones except for only one under the same time limit of up to 300 s. As a strongly Non-deterministic Polynomia (NP)-hard problem which has been extensively studied for nearly half a century, breaking the records on these classic instances is an arduous task. Nevertheless, AWLS establishes new records on 8 challenging instances whose previous best records were established by a state-of-the-art meta-heuristic algorithm and a famous industrial solver.

A Hybrid Recommendation Model for Tourist Using Evolutionary Algorithm Combined with Local Search Algorithm for Trip Planning

A Hybrid Recommendation Model for Tourist Using Evolutionary Algorithm Combined with Local Search Algorithm for Trip Planning