Biased Random-key Genetic Algorithm Research Articles

A biased random-key genetic algorithm for the knapsack problem with forfeit sets

AbstractThis work addresses the Knapsack Problem with Forfeit Sets, a recently introduced variant of the 0/1 Knapsack Problem considering subsets of items associated with contrasting choices. Some penalty costs need to be paid whenever the number of items in the solution belonging to a forfeit set exceeds a predefined allowance threshold. We propose an effective metaheuristic to solve the problem, based on the Biased Random-Key Genetic Algorithm paradigm. An appropriately designed decoder function assigns a feasible solution to each chromosome, and improves it using some additional heuristic procedures. We show experimentally that the algorithm outperforms significantly a previously introduced metaheuristic for the problem.

Obtaining the Grundy chromatic number: How bad can my greedy heuristic coloring be?

Given a simple undirected graph G, its Grundy chromatic number Γ(G) (or Grundy number) defines the worst-case behavior for the well-known and widely-used greedy first-fit coloring heuristic. Specifically, Γ(G) is the largest k for which a k-coloring can be obtained with the first-fit heuristic. In this paper, we address the Grundy coloring problem, the optimization problem consisting of obtaining the Grundy number of a graph. First, we propose a new combinatorial upper bound for the problem. Second, we describe a standard integer programming formulation and a formulation by representatives. The latter attempts to overcome the symmetries in the problem and relies on the idea that a subset of the vertices in the graph can be represented by one of its vertices, denoted as a representative. Finally, as integer programming approaches can struggle to tackle instances of the problem, we devise a biased random-key genetic algorithm (BRKGA) to obtain heuristic solutions in low computational times. Computational experiments show that our new upper bound can improve over well-established combinatorial bounds available in the literature for several instances. The results also indicate that the formulation by representatives has an overall superior performance than the standard formulation, achieving better results for the denser instances while slightly underperforming on the sparser ones. Furthermore, the BRKGA can find high-quality solutions and can be used with confidence in large instances where the formulations fail.

Heuristic approaches for scheduling of a two-machine flowshop with outsourcing lead-time

This article studies a scheduling problem of a two-machine flowshop , considering outsourcing lead-time, where outsourcing a job incurs outsourcing cost as well as outsourcing lead-time. Each job has an option of being outsourced, i.e. the first operation of the outsourced job is handled by an external subcontractor while the second operation must be processed in-house after its delivery. The objective is to find a schedule for minimizing the weighted sum of the outsourcing costs and the total completion time. For the problem, the subset of jobs to be outsourced and the processing order of jobs are interwoven, implying that decisions have to be made simultaneously. This study examines the properties of the optimal solution and proposes various heuristics based on iterative local search and the biased random-key genetic algorithm. Extensive computational experiments are carried out in various settings.

Two hybrid flow shop scheduling lines with assembly stage and compatibility constraints.

Two hybrid flow shop scheduling lines must be coordinated to assemble batches of terminated products at their last stage. Each product is thus composed of two jobs, each produced in one of the lines. The set of jobs is to be processed in a series of stages to minimize the makespan of the scheduling, but jobs forming a product must arrive at the assembly line simultaneously. We propose a mixed integer linear programming model. Then, based on the model, we propose a pull-matheuristic algorithm. Finally, we present two metaheuristics, a greedy randomized adaptive search procedure and a biased random key genetic algorithm, and compare all the methodologies with real-based instances of a production scheduling problem in the automobile manufacturing industry. The greedy algorithm yields high-quality solutions, while the genetic one offers the best computational times.

Biased random-key genetic algorithm for the job sequencing and tool switching problem with non-identical parallel machines

We address the job sequencing and tool switching problem associated with non-identical parallel machines – a variation of the well-known sequencing and switching problem (SSP) better adapted to reflect the challenges in modern production environments. The NP-hard problem is approached by considering two isolated objective functions: the minimization of the makespan and the minimization of the total flow time. We present two versions of a parallel biased random-key genetic algorithm hybridized with tailored local search procedures that are organized using variable neighborhood descent. The proposed methods are compared with state-of-the-art methods by considering 640 benchmark instances from literature. For both objective functions considered, the proposed methods consistently outperform the compared methods. All known optimal values for both objectives are achieved, and a substantial gap is reported for all instance groups when compared with the best previously published solution values.

Optimizing job shop scheduling with speed‐adjustable machines and peak power constraints: A mathematical model and heuristic solutions

AbstractThis paper addresses a job shop scheduling problem with peak power constraints, in which jobs can be processed once or multiple times on either all or a subset of the machines. The latter characteristic provides additional flexibility, nowadays present in many manufacturing systems. The problem is complicated by the need to determine both the operation sequence and starting time as well as the speed at which machines process each operation. Due to the adherence to renewable energy production and its intermittent nature, manufacturing companies need to adopt power‐flexible production schedules. The proposed power control strategies, that is, adjusting processing speed and timing to reduce peak power requirements may impact production time (makespan) and energy consumption. Therefore, we propose a bi‐objective approach that minimizes both objectives. A linear programming model is developed to provide a formal statement of the problem, which is solved to optimality for small‐sized instances. We also proposed a multi‐objective biased random key genetic algorithm framework that evolves several populations in parallel. Computational experiments provide decision and policymakers with insights into the implications of imposing or negotiating power consumption limits. Finally, the several trade‐off solutions obtained show that as the power limit is lowered, the makespan increases at an increasing rate and a similar trend is observed in energy consumption but only for very small makespan values. Furthermore, peak power demand reductions of about 25% have a limited impact on the minimum makespan value (4–6% increase), while at the same time allowing for a small reduction in energy consumption.

Airfreight forwarder’s shipment planning: Shipment consolidation and containerization

This study focuses on an airfreight forwarder's shipment planning problem, while considering shipment consolidation and containerization in the international supply chain. Items belonging to different shipments from supplier's manufacturing warehouses are consolidated and loaded into Unit Loading Devices (ULDs) at outbound logistics hubs and to inbound logistics hubs by air transportation, where items are unloaded from the ULDs and distributed to the corresponding retailers by parcel delivery. A three-dimensional multiple bin size bin packing problem is considered, where items are consolidated and orthogonally loaded into ULDs of heterogeneous irregular shapes, where each item has a required latest allowable delivery time. A mixed integer programming model is formulated for the problem, which aims to determine the optimal route planning and feasible packing scheme for the transported items. This study develops a biased random-key genetic algorithm combining a three-dimensional bin packing heuristic to solve the problem. A two-phase greedy heuristic with a chaotic system is designed for the generation of initial population. Additionally, a catastrophe operator and a self-adaptive neighborhood search are put forward to further improve the performance of the algorithm. A numerical experiment is given to demonstrate the feasibility of formulation and effectiveness of algorithm by comparing with ILOG CPLEX, and managerial insights are provided.

A biased random-key genetic algorithm for the minimum quasi-clique partitioning problem

A biased random-key genetic algorithm for the minimum quasi-clique partitioning problem

A parallel branch-and-cut and an adaptive metaheuristic to solve the Family Traveling Salesman Problem

This paper addresses the Family Traveling Salesman Problem (FTSP), a variant of the Traveling Salesman Problem that group nodes into families. The goal is to select the best route by visiting only a subset of nodes from each family. We developed two methods to solve the FTSP: (i) a parallel branch-and-cut algorithm with an efficient local search procedure (P-B&C) to obtain an optimal solution, and (ii) an adaptive metaheuristic that combines the Biased Random-key Genetic Algorithm (BRKGA) with a reinforcement learning algorithm. In this case, the Q-Learning algorithm controls the parameters of the BRKGA during the evolutionary process. We perform computational experiments on a well-known benchmark dataset with 185 instances. Our P-B&C proves the optimal value for 179 instances, improving the best upper bounds in 19 open instances. The new local search component of the P-B&C finds the best upper bounds for 50% of instances. The BRKGA-QL finds the optimal solution in 131 instances, improving the best upper bounds in 21 open instances. Finally, we compare our results with the best results in the literature, and both methods show robustness and efficiency in solving the FTSP.

Parallel Batch Processing Machine Scheduling Under Two-Dimensional Bin-Packing Constraints

The parallel batch processing machine scheduling problem with two-dimensional bin packing constraints (PBS-2D) has appeared in many industrial environments, but the research on this problem is still not sufficient. In this article, we use the 2-D rectangular packing constraints to describe the spatial geometric layout of jobs more accurately, and propose a mixed integer linear programming (MILP) model to minimize the makespan of PBS-2D. According to the in-depth analysis of the problem properties, PBS-2D is separated into three subproblems, which are job-machine assignment, 2-D job placement, and job sequence optimization. An improved biased random key genetic algorithm (OBRKGA) is proposed to solve job-machine assignment and job sequence optimization. This algorithm generates the initial population based on the idea of orthogonal experimental design, so that the whole solution space can be scanned evenly when generating the initial solution, making the algorithm be more likely to find better solutions for subsequent evolution. At the same time, a bin packing algorithm based on best fit is designed to handle 2-D job placement problem. Finally, the algorithms are tested on a large number of randomly generated instances, the results show that OBRKGA outperformed the original BRKGA, the classical moth-flame optimization algorithm, particle swarm optimization algorithm, gravity search algorithm, and MILP.

Supply Chain Scheduling Method for the Coordination of Agile Production and Port Delivery Operation

The cost-reducing potential of intelligent supply chains (ISCs) has been recognized by companies and researchers. This paper investigates a two-echelon steel supply chain scheduling problem that considers the parallel-batching processing and deterioration effect in the production stage and sufficient vehicles in the port delivery stage. To solve this problem, we first analyze several sufficient and necessary conditions of the optimal scheme. We then propose a heuristic algorithm based on a dynamic programming algorithm to obtain the optimal solution for a special case where the assignment of all ingots to the soaking pits is known. Based on the results of this special case, we develop a modified biased random-key genetic algorithm (BRKGA), which incorporates genetic operations based on the flower pollination algorithm (FPA) to obtain joint production and distribution schedules for the general problem. Finally, we conduct a series of computational experiments, the results of which indicate that BRKGA-FPA has certain advantages in solving quality and convergence speed issues.

Biased Random-Key Genetic Algorithm with Local Search Applied to the Maximum Diversity Problem

The maximum diversity problem (MDP) aims to select a subset with a predetermined number of elements from a given set, maximizing the diversity among them. This NP-hard problem requires efficient algorithms that can generate high-quality solutions within reasonable computational time. In this study, we propose a novel approach that combines the biased random-key genetic algorithm (BRKGA) with local search to tackle the MDP. Our computational study utilizes a comprehensive set of MDPLib instances, and demonstrates the superior average performance of our proposed algorithm compared to existing literature results. The MDP has a wide range of practical applications, including biology, ecology, and management. We provide future research directions for improving the algorithm’s performance and exploring its applicability in real-world scenarios.

Improving Additive Manufacturing production planning: A sub-second pixel-based packing algorithm

Additive Manufacturing (AM), the technology of rapid prototyping directly from 3D digital models, has made a significant impact on both academia and industry. When facing the growing demand of AM services, AM production planning (AMPP) plays a vital role in reducing makespan and costs for AM service companies. This research focuses on the AMPP problem under the unrelated machine environment and two-dimensional irregular packing constraints such that the makespan can be minimized. Since there is no promising sub-second algorithm for solving the 2D irregular packing sub-problems in current literature, the efficiency of checking the packing feasibility of batches is the bottleneck of algorithms of AMPP. Therefore, we propose an efficient pixel-based AM packing algorithm (PAMPA) which can tackle irregular packing sub-problems that allow hole filling and free rotation. In PAMPA, parts are placed one by one in a Bottom-Left (BL) way and the rotation angle is determined by a novel angle selection heuristic. A new codification method and contour-guided method are proposed to accelerate separating overlap. The placement sequence is optimized by a biased random-key genetic algorithm (BRKGA). Furthermore, by adopting PAMPA, we introduce a variable neighbourhood search (VNS) framework to solve the AMPP. Finally, new instances are generated to conduct experiments. Based on the new instances and instances from (ESICUP), the efficiency of PAMPA is analysed and verified. The proposed VNS framework can reduce the makespan by 8 h on average compared with the initial solution, which illustrates that our PAMPA is beneficial for AMPP. Some interesting insights are also revealed and discussed based on the case study.

A biased random-key genetic algorithm for the chordal completion problem

A graph is chordal if all its cycles of length greater than or equal to four contain a chord, i.e., an edge connecting two nonconsecutive vertices of the cycle. Given a graph G = (V, E), the chordal completion problem consists in finding the minimum set of edges to be added to G to obtain a chordal graph. It has applications in sparse linear systems, database management and computer vision programming. In this article, we developed a biased random-key genetic algorithm (BRKGA) for solving the chordal completion problem, based on the strategy of manipulating permutations that represent perfect elimination orderings of triangulations. Computational results show that the proposed heuristic improve the results of the constructive heuristics fill-in and min-degree. We also developed a strategy for injecting externally constructed feasible solutions coded as random keys into the initial population of the BRKGA that significantly improves the solutions obtained and may benefit other implementations of biased random-key genetic algorithms.

A biased random-key genetic algorithm for the two-level hub location routing problem with directed tours

A biased random-key genetic algorithm for the two-level hub location routing problem with directed tours

Energy-efficient job shop scheduling problem with transport resources considering speed adjustable resources

This work extends the energy-efficient job shop scheduling problem with transport resources by considering speed adjustable resources of two types, namely: the machines where the jobs are processed on and the vehicles that transport the jobs around the shop-floor. Therefore, the problem being considered involves determining, simultaneously, the processing speed of each production operation, the sequence of the production operations for each machine, the allocation of the transport tasks to vehicles, the travelling speed of each task for the empty and for the loaded legs, and the sequence of the transport tasks for each vehicle. Among the possible solutions, we are interested in those providing trade-offs between makespan and total energy consumption (Pareto solutions). To that end, we develop and solve a bi-objective mixed-integer linear programming model. In addition, due to problem complexity we also propose a multi-objective biased random key genetic algorithm that simultaneously evolves several populations. The computational experiments performed have show it to be effective and efficient, even in the presence of larger problem instances. Finally, we provide extensive time and energy trade-off analysis (Pareto front) to infer the advantages of considering speed adjustable machines and speed adjustable vehicles and provide general insights for the managers dealing with such a complex problem.

Optimization of Multispacecraft Maneuvers for Mobile Target Tracking from Low Earth Orbit

This paper presents a method of planning spacecraft maneuvers for mobile target tracking. Agile, maneuverable spacecraft have been proposed as a means of modifying satellite orbits to observe discrete targets on the Earth on demand. This work adapts this concept to propose a method of using maneuverable spacecraft to observe a mobile target as it moves across the Earth. Previous work has shown the potential of such an approach to increase persistence of coverage of a moving target. This work applies a suitable optimizer to select possible maneuvers for a spacecraft, or a constellation of spacecraft, to repeatedly observe a moving target. A biased random key genetic algorithm is used, which adjusts the for each maneuver to minimize the total used and maximize target coverage over the full sequence of maneuvers. The developed method is applied to two case studies concerning monitoring of tropical storms. The results indicate that, using relatively small maneuvers, spacecraft orbits can be adjusted to improve the quantity and quality of views of a moving target. In the Typhoon Megi case study, a single spacecraft using less than is shown to double the access time and provide two additional observations of the storm eye compared with a nonmaneuvering spacecraft in an identical initial orbit. Opportunities for observations increase as the number of maneuverable spacecraft are increased, with a three-spacecraft constellation able to provide five complete observations of the storm eye for a total change in velocity of 12 m/s.

A novel BRKGA for the customer order scheduling with missing operations to minimize total tardiness

We introduce a new variant of the customer order scheduling problem with missing operations to minimize total tardiness. This problem arises in the pharmaceutical industry, more specifically in physical–chemical analysis processes. Since each sample must be processed in some specific machines, we have missing operations. Given the NP-hardness of the problem, we present approximate algorithms to solve large-sized instances. First, we propose an innovative size-reduction matheuristic for a scheduling problem with due dates. This approach is based on partitioning the decision variables considering due dates and a dispatch rule. Furthermore, we develop a novel Biased Random Key Genetic Algorithm (BRKGA) that considers an efficient local search as 2-opt best improvement with swap neighborhood and a parameter-free restart procedure which restarts the search if the quality of the worst and best solutions were equal, minimizing the amount of parameters to be defined by the BRKGA. We perform computational experiments on 640 test instances to evaluate the proposed solution approaches. The results indicate the superiority of BRKGA compared to the competitive algorithms for order scheduling and its recent variants. In all set of instances, the novel BRKGA performed better than benchmarking methods and mathematical programming models, with average relative deviation index regarding best results as lower as 0.15%. Computational results point to the capacity of the proposed approaches to solve large-sized problems. • We introduce the customer order scheduling with missing operations. • We propose mixed-integer linear programming and constraint programming models. • We propose a new matheuristic named size reduction with partitions (SR-Q). • We develop an innovative BRKGA with a robust improvement procedure and a parameter-free restart operator. • We perform extensive computational tests with 640 randomly generated test instances.

Heuristic algorithms for integrated workforce allocation and scheduling of perishable products

We study a problem from a real-world application, in which a daily set of orders must be processed following two stages, consisting of preparing perishable products on benches and allocating them to conveyors to be packed in disposable trays. Daily decisions must be made regarding the number and start time of working shifts, the number of workers and their allocation to machines, and the scheduling of orders in a two-stage flexible flow shop environment. The flow shop environment of the studied problem is common in many industries of perishable products, making the problem very general. The problem involves a number of operational constraints, and three objective functions that are minimised in a lexicographic way. To solve the problem, we implement a constructive heuristic and embed it within three metaheuristics: a Random multi-start algorithm (MR), a Biased random key genetic algorithm (BRKGA), and a Variable neighbourhood search (VNS) based one. We perform computational experiments over a set of realistic instances, and present a lower bound obtained from a constraint programming model for the scheduling counterpart. The results of the experiments show that the BRKGA is the most effective in practice for the integrated problem of workforce allocation and scheduling.

Optimization of Robot-Trajectory Planning with Nature-Inspired and Hybrid Quantum Algorithms

We solve robot trajectory planning problems at industry-relevant scales. Our end-to-end solution integrates highly versatile random-key algorithms with model stacking and ensemble techniques, as well as path relinking for solution refinement. The core optimization module consists of a biased random-key genetic algorithm. Through a distinct separation of problem-independent and problem-dependent modules, we achieve an efficient problem representation, with a native encoding of constraints. We show that generalizations to alternative algorithmic paradigms such as simulated annealing are straightforward. We provide numerical benchmark results for industry-scale data sets. Our approach is found to consistently outperform greedy baseline results. To assess the capabilities of today's quantum hardware, we complement the classical approach with results obtained on quantum annealing hardware, using qbsolv on Amazon Braket. Finally, we show how the latter can be integrated into our larger pipeline, providing a quantum-ready hybrid solution to the problem.