Problem-specific Heuristics Research Articles

Problem-Specific Heuristics for Diagnosability and Inventory Analysis in a Reconfigurable Manufacturing System

Reconfigurable manufacturing systems are complex systems that are prone to malfunctions and performance decay. Thus, such systems need to be safeguarded against quality issues and decline in production efficiency to ensure the optimal health of machines. The product quality and health of a reconfigurable manufacturing system can be analyzed by using the diagnosability characteristic. This study examines the diagnosability characteristic in a multi-stage reconfigurable manufacturing system. The aim is to understand the impact of time-based diagnostics on the functionality performance of a reconfigurable manufacturing system and the level of inventory used during production. The diagnosability is analyzed regarding product variation and system diagnosability. A mathematical model is proposed, and it is subsequently applied in deterministic and stochastic settings. The deterministic setting is examined through a set of two problem-specific heuristics. The stochastic setting, subject to the gamma process, is examined by using a simulation-based optimization approach. The results suggest that the use of line replacement units can restore a reconfigurable system to optimal functionality, reduce the level of inventory, and complete production in minimum time at the expense of additional cost. Finally, a conclusion and future research avenues are provided.

An analysis of Single-Player Monte Carlo Tree Search performance in Sokoban

We apply the extension of Monte Carlo Tree Search for single player games (SP-MCTS) to Sokoban and compare its performance to a solver integrating Iterative Deepening A* (IDA*) with several problem-specific heuristics. We introduce two extensions of MCTS to deal with some of the challenges that Sokoban poses to MCTS methods, namely, the reduced search space that deadlock situations can cause and the large number of cycles. We also evaluate three domain-independent enhancements that have been shown to improve MCTS performance, namely, UCB1-Tuned, Rapid Action Value Estimation (RAVE), and Node Recycling. We perform a series of experiments to determine the best SP-MCTS configuration and then compare its performance to IDA*. We show that SP-MCTS can solve around 85% of the levels with 1000000 iterations, that is the same performance reached by IDA* with only 10000 nodes. Overall, our results suggest that IDA* is still the best solver for Sokoban, also because it can easily integrate much domain knowledge. At the same time, our results also highlight some interesting directions to design better MCTS solvers for this domain.

Improving service regularity for high-frequency bus services with rescheduling and bus holding

In high-frequency bus services, maintaining the service regularity is a critical issue. The service regularity is directly related to the excessive waiting times (EWT) of passengers at bus stops. In a regular service, the EWT is minimized resulting in even headways between consecutive buses of the same line. In this study, we propose the combined use of rescheduling and bus holding to improve passengers' excessive waiting times. We model the dynamic rescheduling and bus holding problem as an integer nonlinear program (INLP) and we prove its NP-hardness. Our model considers the constraints of the original timetable – an issue that is usually neglected from most dynamic control methods. Given the NP-hardness of our mathematical program, we introduce a problem-specific heuristic to explore efficiently the solution space. The convergence rate of the proposed heuristic is tested against other solution methods, including simulated annealing with linear cooling, hill climbing and branch and bound with multi-start sequential quadratic programming. In addition, simulations with the use of actual operational data from a major bus operator in Asia Pacific demonstrate an up to 35% potential EWT improvement for a minor increase of 6% to the travel times of onboard passengers. • Novel model for the periodic optimization of bus operations. • Combined rescheduling and bus holding decisions. • Up to 35% improvement of the average passenger waiting times. • Proof of NP-Hardness and development of problem-specific heuristics.

Bin packing with lexicographic objectives for loading weight- and volume-constrained trucks in a direct-shipping system

We consider a packing problem that arises in a direct-shipping system in the food and beverage industry: Trucks are the containers, and products to be distributed are the items. The packing is constrained by two independent quantities, weight (e.g., measured in kg) and volume (number of pallets). Additionally, the products are grouped into the three categories: standard, cooled, and frozen (the latter two require refrigerated trucks). Products of different categories can be transported in one truck using separated zones, but the cost of a truck depends on the transported product categories. Moreover, splitting orders of a product should be avoided so that (un-)loading is simplified. As a result, we seek for a feasible packing optimizing the following objective functions in a strictly lexicographic sense: minimize the (1) total number of trucks; (2) number of refrigerated trucks; (3) number of refrigerated trucks which contain frozen products; (4) number of refrigerated trucks which also transport standard products; (5) and minimize splitting. This is a real-world application of a bin-packing problem with cardinality constraints a.k.a. the two-dimensional vector packing problem with additional constraints. We provide a heuristic and an exact solution approach. The heuristic meta-scheme considers the multi-compartment and item fragmentation features of the problem and applies various problem-specific heuristics. The exact solution algorithm covering all five stages is based on branch-and-price using stabilization techniques exploiting dual-optimal inequalities. Computational results on real-world and difficult self-generated instances prove the applicability of our approach.

Optimizing Parameters for Uncertain Execution and Rescheduling Robustness

We describe use of Monte Carlo simulation to optimize schedule parameters for execution and rescheduling robustness in the face of execution uncertainties. We search in the activity input parameter space where a) the onboard scheduler is a one shot non-backtracking scheduler and b) the activity input priority determines the order in which activities are considered for placement in the schedule. We show that simulation driven search for activity parameters outperforms static priority assignment. Our approach can be viewed as using simulation feedback to determine problem specific heuristics e.g. Squeaky Wheel Optimization. These techniques are currently baselined for use in the ground operations of NASA’s next planetary rover, the Mars 2020 rover.

A Hybrid Iterated Greedy Algorithm for a Crane Transportation Flexible Job Shop Problem

In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The flexible job shop scheduling problem (FJSP) can be extended and applied to many types of practical manufacturing processes. Many realistic production processes should consider the transportation procedures, especially for the limited crane resources and energy consumptions during the transportation operations. This study models a realistic production process as an FJSP with crane transportation, wherein two objectives, namely, the makespan and energy consumptions, are to be simultaneously minimized. This study first considers the height of the processing machines, and therefore, the crane lift operations and lift energy consumptions are investigated. A hybrid iterated greedy algorithm is proposed for solving the problem considered, and several problem-specific heuristics are embedded to balance the exploration and exploitation abilities of the proposed algorithm. In addition, the proposed algorithm can be generalized to solve other types of scheduling problems with crane transportations.

Extending an Integer Formulation for the Guillotine 2D Bin Packing Problem

We employ a state-of-the-art Mixed-Integer Linear Programming (MILP) formulation of the literature, and our enhanced version of it, to solve a classical instance dataset for the Guillotine 2D variants of both the Knapsack Problem (G2KP) and the Bin Packing Problem (G2BPP). The results with the G2KP allow us to establish our reimplementation as fair to the original implementation (not available). As far as we know, before this work the considered instances have never been optimally solved for the considered variant of the G2BPP, i.e., the unlimited stages variant, only for the simpler two-staged variant. We also believe this work is the first to gather empirical results of a pure MILP formulation for the G2BPP, even considering the possibility of adaptation was previously known. As we focus on pure and adaptable formulations, we do not employ pricing frameworks or problem-specific heuristics in this short paper. We examine the differences in the running times caused by the change of problems, formulations, number of threads, and, for a subset of the runs, the solver random seed. Some of our findings follow: except for a few G2BPP instances, our enhanced formulation has better timings; 8 of the 30 considered instances have better solutions for unlimited stages G2BPP than for the two-staged G2BPP; the speed-up with 12 threads is smaller than expected and, for the G2BPP, the solver random seed may have a larger effect than the number of threads.

An effective chaos-driven differential evolution for multi-objective unbalanced transportation problem considering fuel consumption

This paper focuses on a special multi-objective unbalanced transportation problem (MOUTP) considering fuel consumption. MOUTP involves finding a transportation decision to minimize the supply–demand deviation (SDD) and the total transportation cost, which is different from conventional transportation problems. In this paper, the mathematical model of MOUTP is established, in which a new mechanism model of the fuel consumption based on the automobile theory is presented. To solve MOUTP, we propose an effective chaos-driven differential evolution (chaos-driven DE, CdDE). In CdDE, the solution representation and problem-specific heuristics based on the solution structures of MOUTP are presented first. Then, a decomposition-based multi-objective search framework integrating with DE is developed to execute the global exploration. Thereafter, a chaos-driven local search procedure based on the well-known Logistic map is proposed to enhance the local exploitation ability of CdDE. Numerical results and comparisons on 100 random instances and a real-life case study verify the effectiveness and practical values of the proposed CdDE.

Efficient multi-objective algorithm for the lot-streaming hybrid flowshop with variable sub-lots

Abstract Recent years, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been researched and applied for numerous optimization problems. In this study, we propose an improved version of MOEA/D with problem-specific heuristics, named PH-MOEAD, to solve the hybrid flowshop scheduling (HFS) lot-streaming problems, where the variable sub-lots constraint is considered to minimize four objectives, i.e., the penalty caused by the average sojourn time, the energy consumption in the last stage, as well as the earliness and the tardiness values. For solving this complex scheduling problem, each solution is coded by a two-vector-based solution representation, i.e., a sub-lot vector and a scheduling vector. Then, a novel mutation heuristic considering the permutations in the sub-lots is proposed, which can improve the exploitation abilities. Next, a problem-specific crossover heuristic is developed, which considered solutions with different sub-lot size, and therefore can make a solution feasible and enhance the exploration abilities of the algorithm as well. Moreover, several problem-specific lemmas are proposed and a right-shift heuristic based on them is subsequently developed, which can further improve the performance of the algorithm. Lastly, a population initialization mechanism is embedded that can assign a fit reference vector for each solution. Through comprehensive computational comparisons and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several presented algorithms, both in solution quality and population diversity.

Hybrid Artificial Bee Colony Algorithm for a Parallel Batching Distributed Flow-Shop Problem With Deteriorating Jobs.

In this article, we propose a hybrid artificial bee colony (ABC) algorithm to solve a parallel batching distributed flow-shop problem (DFSP) with deteriorating jobs. In the considered problem, there are two stages as follows: 1) in the first stage, a DFSP is studied and 2) after the first stage has been completed, each job is transferred and assembled in the second stage, where the parallel batching constraint is investigated. In the two stages, the deteriorating job constraint is considered. In the proposed algorithm, first, two types of problem-specific heuristics are proposed, namely, the batch assignment and the right-shifting heuristics, which can substantially improve the makespan. Next, the encoding and decoding approaches are developed according to the problem constraints and objectives. Five types of local search operators are designed for the distributed flow shop and parallel batching stages. In addition, a novel scout bee heuristic that considers the useful information that is collected by the global and local best solutions is investigated, which can enhance searching performance. Finally, based on several well-known benchmarks and realistic industrial instances and via comprehensive computational comparison and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several algorithms in terms of both solution quality and population diversity.

A decomposition-based matheuristic for supply chain network design with assembly line balancing

This paper addresses a supply chain network design problem with assembly line balancing, which considers a three-layer supply chain including manufacturers, assemblers, and customers. By analyzing the characteristics and complexities of the problem, we decompose it into an upper-level problem and two lower-level problems. The upper level problem is to determine the assignment amount of each assembler. The two lower-level problems include the assembly line balancing problem (ALBP) inside each assembler and the transportation problem (TP) between different layers. To solve the problem effectively, a decomposition-based matheuristic (DMAT) is proposed by fusing metaheuristic and model-based approaches. The ALBP is solved by using branch and bound, and a lookup table method is proposed to speed up the computation time. The TP is solved by using mathematical programming. By solving the lower-level problems, the cost function of the upper-level problem can be evaluated. To optimize the upper-level problem, a metaheuristic based on the differential evolution is presented. In population initialization, the problem specific heuristics are designed. To repair and improve the infeasible solutions, reassignment with local intensification is designed. Numerical tests with extensive instances demonstrate the effectiveness of the proposed DMAT.

Revisiting Approximate Linear Programming: Constraint-Violation Learning with Applications to Inventory Control and Energy Storage

Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs). VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost. However, solving ALPs near-optimally remains challenging, for example, when approximating MDPs with nonlinear cost functions and transition dynamics or when rich basis functions are required to obtain a good VFA. We address this tension between theory and solvability by proposing a convex saddle-point reformulation of an ALP that includes as primal and dual variables, respectively, a vector of basis function weights and a constraint violation density function over the state-action space. To solve this reformulation, we develop a proximal stochastic mirror descent (PSMD) method that learns regions of high ALP constraint violation via its dual update. We establish that PSMD returns a near-optimal ALP solution and a lower bound on the optimal policy cost in a finite number of iterations with high probability. We numerically compare PSMD with several benchmarks on inventory control and energy storage applications. We find that the PSMD lower bound is tighter than a perfect information bound. In contrast, the constraint-sampling approach to solve ALPs may not provide a lower bound, and applying row generation to tackle ALPs is not computationally viable. PSMD policies outperform problem-specific heuristics and are comparable or better than the policies obtained using constraint sampling. Overall, our ALP reformulation and solution approach broadens the applicability of approximate linear programming.This paper was accepted by Yinyu Ye, optimization.

Universal Golomb–Rice Coding Parameter Estimation Using Deep Belief Networks for Hyperspectral Image Compression

For efficient compression of hyperspectral images, we propose a universal Golomb–Rice coding parameter estimation method using deep belief network, which does not rely on any assumption on the distribution of the input data. We formulate the problem of selecting the best coding parameter for a given input sequence as a supervised pattern classification problem. Simulations on the synthesized data and five hyperspectral image datasets show that we can achieve significantly more accurate estimation of the coding parameters, which can translate to slightly higher compression than three state-of-the-art methods. More extensive simulations on additional images from the 2006 AVIRIS datasets show that the proposed method achieved overall compression bitrates comparable with other estimation methods, as well as the sample-adaptive entropy coder employed by the Consultative Committee for Space Data Systems standard for multispectral and hyperspectral data compression. Regarding computational feasibility, we show how to use transferable deep belief networks to speed up training by about five times. We also show that inferring the best coding parameters using a trained deep belief network offers computational advantages over the brute-force search method. As an extension, we propose a novel side-information free codec, where the intersequence correlations can be learned by a differently trained network based on the current sequence to predict reasonably good parameters for coding the next sequence. As another extension, we introduce a variable feature combination architecture, where problem specific heuristics such as the sample means can be incorporated to further improve the estimation accuracy.

Fix-and-optimize heuristics for capacitated lot sizing with setup carryover and backordering

PurposeThe capacitated lot sizing problem (CLSP) is one of the most important production planning problems which has been widely studied in lot sizing literature. The CLSP is the extension of the Wagner-Whitin problem where there is one product and no capacity constraints. The CLSP involves determining lot sizes for multiple products on a single machine with limited capacity that may change for each planning period. Determining the right lot sizes has a critical importance on the productivity and success of organizations. The paper aims to discuss these issues.Design/methodology/approachThis study focuses on the CLSP with setup carryover and backordering. The literature focusing on this problem is rather limited. To fill this gap, a number of problem-specific heuristics have been integrated with fix-and-optimize (FOPT) heuristic in this study. The authors have compared the performances of the proposed approaches to that of the commercial solver and recent results in literature. The obtained results have stated that the proposed approaches are efficient in solving this problem.FindingsThe computational experiments have shown that the proposed approaches are efficient in solving this problem.Originality/valueTo address the solution of the CLSP with setup carryover and backordering, a number of heuristic approaches consisting of FOPT heuristic are proposed in this paper.

An artificial bee colony algorithm with a Modified Choice Function for the traveling salesman problem

Abstract The Artificial Bee Colony (ABC) algorithm is a swarm intelligence approach which has initially been proposed to solve optimisation of mathematical test functions with a unique neighbourhood search mechanism. This neighbourhood search mechanism could not be directly applied to combinatorial discrete optimisation problems. In order to tackle combinatorial discrete optimisation problems, the employed and onlooker bees need to be equipped with problem-specific perturbative heuristics. However, a large variety of problem-specific heuristics are available, and it is not an easy task to select an appropriate heuristic for a specific problem. In this paper, a hyper-heuristic method, namely a Modified Choice Function (MCF), is applied such that it can regulate the selection of the neighbourhood search heuristics adopted by the employed and onlooker bees automatically. The Lin-Kernighan (LK) local search strategy is integrated to improve the performance of the proposed model. To demonstrate the effectiveness of the proposed model, 64 Traveling Salesman Problem (TSP) instances available in TSPLIB are evaluated. On average, the proposed model solves the 64 instances to 0.055% from the known optimum within approximately 2.7 min. A performance comparison with other state-of-the-art algorithms further indicates the effectiveness of the proposed model.

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.

Two new heuristics for the dominating tree problem

Dominating Tree Problem (DTP) aims to find a dominating tree (d T r e e) of minimum cost on a given connected, undirected and weighted graph in such a way that a vertex in the graph is either in d T r e e or adjacent to a vertex in d T r e e. A solution (d T r e e) to this problem can be used as routing backbone in wireless sensor network. Being a \(\mathcal {NP}\)-Hard problem, several problem-specific heuristics and metaheuristic techniques have been proposed. This paper presents two new heuristics for the DTP. First one is a new problem-specific heuristic that exploits the problem structure effectively, whereas the other is an artificial bee colony (ABC) algorithm. The proposed ABC for the DTP is different from the existing ABC algorithm for the DTP in the literature on its two main components: initial solution generation, and determining a neighboring solution. Computational results show on a set of standard benchmark instances that the proposed problem-specific heuristic and ABC algorithm for the DTP demonstrate the superiority over all existing problem-specific heuristics and metaheuristic techniques respectively in the literature.

Automated generation of constructive ordering heuristics for educational timetabling

Construction heuristics play an important role in solving combinatorial optimization problems. These heuristics are usually used to create an initial solution to the problem which is improved using optimization techniques such as metaheuristics. For examination timetabling and university course timetabling problems essentially graph colouring heuristics have been used for this purpose. The process of deriving heuristics manually for educational timetabling is a time consuming task. Furthermore, according to the no free lunch theorem different heuristics will perform well for different problems and problem instances. Hence, automating the induction of construction heuristics will reduce the man hours involved in creating such heuristics, allow for the derivation of problem specific heuristics and possibly result in the derivation of heuristics that humans have not thought of. This paper presents generation construction hyper-heuristics for educational timetabling. The study investigates the automatic induction of two types of construction heuristics, namely, arithmetic heuristics and hierarchical heuristics. Genetic programming is used to evolve arithmetic heuristics. Genetic programming, genetic algorithms and the generation of random heuristic combinations is examined for the generation of hierarchical heuristics. The hyper-heuristics generating both types of heuristics are applied to the examination timetabling and the curriculum based university course timetabling problems. The evolved heuristics were found to perform much better than the existing graph colouring heuristics used for this domain. Furthermore, it was found that the while the arithmetic heuristics were more effective for the examination timetabling problem, the hierarchical heuristics produced better results than the arithmetic heuristics for the curriculum based course timetabling problem. Genetic algorithms proved to be the most effective at inducing hierarchical heuristics.

Revisiting Approximate Linear Programming Using a Saddle Point Based Reformulation and Root Finding Solution Approach

Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs). VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost. However, solving ALPs near-optimally remains challenging, for example, when approximating MDPs with nonlinear cost functions and transition dynamics or when rich basis functions are required to obtain a good VFA. We address this tension between theory and solvability by proposing a convex saddle-point reformulation of an ALP that includes as primal and dual variables, respectively, a vector of basis function weights and a constraint violation density function over the state-action space. To solve this reformulation, we develop a proximal stochastic mirror descent (PSMD) method that learns regions of high ALP constraint violation via its dual update. We establish that PSMD returns a near-optimal ALP solution and a lower bound on the optimal policy cost in a finite number of iterations with high probability. We numerically compare PSMD with several benchmarks on inventory control and energy storage applications. We find that the PSMD lower bound is tighter than a perfect information bound. In contrast, the constraint sampling approach to solve ALPs may not provide a lower bound and applying row generation to tackle ALPs is not computationally viable. PSMD policies outperform problem-specific heuristics and are comparable or better than the policies obtained using constraint sampling. Overall, our ALP reformulation and solution approach broadens the applicability of approximate linear programming.

Bi-level multi-objective fuzzy design optimization of energy supply systems aided by problem-specific heuristics

Multi-objective design and operation optimization of energy supply systems with respect to costs, energy efficiency and environmental indicators is a very important, yet difficult and challenging task. The assumption of cost-optimal operation may impose the necessity for bi-level problems. This paper presents a methodology to formulate and solve multi-objective bi-level optimization problems where upper-level decision makers decide on design and policy, while plant operation is defined at the lower level. It can be used to assess energy consumption or emission reduction potential corresponding to cost-optimal operation. The methodology applies conceptual decomposition to the outer design- and inner operation-optimization problems. The first is solved with the scatter search method and the second using mixed integer linear programming. Scatter search is a metaheuristic method convenient to integrate problem-specific heuristics into the process and systematically take advantage of the designer's knowledge. The fuzzy approach considers multiple design objectives and helps formulate heuristic rules based on the decision criteria satisfaction rates. The case study illustrates the design of a trigeneration system for an urban settlement. The design objectives are: total costs, primary energy and greenhouse gases emission. Cost-optimal operation is presumed. The optimal plant design and operation are realistic and mostly consistent with the literature. Compared to the cost-optimal solution, other objectives might lead to reduced primary energy consumption for 7.21% or lower emission for 91.85% with 43.35% and 83.1% larger costs. The results are compared with the ones obtained with customary methods. It is demonstrated that the methodology is applicable and convenient for the considered class of problems.