Reactive Tabu Search Algorithm Research Articles

Reactive tabu search and mixed-integer linear programming for multi-day assignment, scheduling, and routing problems of specialised education and home-care services

In this paper, we address the Multi-Day Assignment, Scheduling, and Routing Problem for Specialized Education and Home Care Services (SEHCS-MASRP), which involves heterogeneous employees and missions, posing a complex optimisation challenge. To tackle this, we propose a novel Mixed-Integer Linear Programming (MILP) model that considers employee qualifications, service requirements, scheduling constraints, routing decisions, and multiple objectives across the planning horizon. Additionally, we develop two metaheuristic approaches: a Reactive Tabu Search (RTS) algorithm incorporating either a Probabilistic Greedy Heuristic (PGH) or a Greedy Randomized Adaptive Search Procedure (GRASP) for initial solutions and a tailored genetic algorithm (GA). The three approaches aim to minimise wasted and overtime hours, total travel distances, and the number of assignments with an unsatisfied specialty while balancing wasted hours, overtime hours, and travel distances among the employees. Gurobi uses the proposed MILP model to find the optimal solutions, which are then compared with RTS and GA results across various instance sizes based on real-life SEHCS scenarios. Experimental results demonstrate the efficiency of MILP, RTS, and GA. MILP achieves proven optimal solutions for smaller to large instances. For huge instances, RTS generates high-quality solutions within reasonable computing times, outperforming GA performance. Notably, RTS consistently finds solutions within 5% of optimality for most instances.

Labeling-Based Recipient Identification with Low-Order Modulation

Labeling-Based Recipient Identification (LABRID) brings the possibility of representing the destination station address in a Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) system by a signal labeling rule. Low-order modulations, such as BPSK or QPSK, pose a general problem for BICM-ID due to a limited convergence of iterative decoding. In the context of LABRID, they have one more drawback—a small number of different labeling rules in general; the number of the optimal ones, which exhibit the maximal asymptotic coding gain, is reduced even further. Meanwhile, LABRID needs a sizable collection of different optimal labeling rules to serve many users in large wireless networks. In this paper, the author suggests the use of hypercube BPSK or QPSK labeling to overcome all these challenges. By means of the Reactive Tabu Search (RTS) algorithm, more than 1500 equivalent optimal hypercube labeling rules are found. Analytical error bounds of the system are developed and supported by simulation experiments. Then, the focus is moved to the criterion to determine the frame destination at the LABRID receiver; a simple threshold-based method is proposed to keep the incorrect decision probability below 10−5. Finally, it is shown that LABRID outperforms a reference BICM-ID system in terms of computational complexity.

Type-2 Assembly Line Balancing Using Reactive Tabu Search

This study focusses on a two objective type-2 simple assembly line balancing problem. Its primary objective is minimizing the cycle time, or equivalently, maximizing the production rate of the line. Minimization of the workload imbalance among workstations is considered as the secondary objective. Since the problem is known to be intractable, a reactive tabu search algorithm is proposed for the solution. Although tabu search is a well-known meta-heuristic search procedure, based on the detailed literature survey, there is not a reactive tabu search algorithm to solve the investigated problem. Furthermore, the algorithm utilizes a sequence oriented solution representation which is usually applied by population heuristics such as genetic algorithms and differential evolution algorithms. The performance of the algorithm is tested on several benchmark problems taken from the open literature by comparing both objective values with those of previously developed four particle swarm optimization (PSO) algorithms and two multi-objective genetic algorithms (MOGA). The computational results show that the proposed approach presents a quite encouraging success over the existing meta-heuristics.

Range-based truck-state transition modeling method for foldable container drayage services

Manufacturing technologies of foldable containers have almost matured. The use of foldable containers might save transportation costs; however, incorporating them into drayage services also creates great challenges. The foldable container drayage (FCD) problem is formulated as a sequence-dependent multiple traveling salesman problem with time windows using a range-based truck state transition method. An improved reactive tabu search algorithm is designed and validated to solve the FCD problem. The methodology is evaluated extensively on the basis of randomly generated instances. Compared to the use of standard containers, the use of four-in-one foldable containers can save approximately 10% on transportation costs.

A Low Complexity Reactive Tabu Search Based Constellation Constraints in Signal Detection

For Massive multiple-input multiple output (MIMO) systems, many algorithms have been proposed for detecting spatially multiplexed signals, such as reactive tabu search (RTS), minimum mean square error (MMSE), etc. As a heuristic neighborhood search algorithm, RTS is particularly suitable for signal detection in systems with large number of antennas. In this paper, we propose a strategy to reduce the neighborhood searching space of the traditional RTS algorithms. For this, we introduce a constellation constraints (CC) structure to determine whether including a candidate vector into the RTS searching neighborhood. By setting a pre-defined threshold on the symbol constellation, the Euclidean distance between the estimated signal and its nearest constellation points are calculated, and the threshold and distance are compared to separate the reliable estimated signal from unreliable ones. With this structure, the proposed CC-RTS algorithm may ignore a significant number of unnecessary candidates in the RTS neighborhood searching space and greatly reduce the computational complexity of the traditional RTS algorithm. Simulation results show that the BER performance of the proposed CC-RTS algorithm is very close to that of the traditional RTS algorithm, and with about 50% complexity reduction with the same signal-to-noise (SNR) ratio.

Assessment of U.S. chassis supply models on drayage productivity and air emissions

A new drayage scheduling model is developed to assess the effectiveness of different U.S. chassis supply models. It extends previous drayage models by incorporating these features: (1) treating tractor, container, and chassis as separate resources which are provided in different locations, (2) ensuring that container and chassis are of the same size and type, and (3) considering the possibility that drayage companies can subcontract the work to independent owner-operators whose trucks will originate from and terminate at different locations. The resulting model is a mixed-integer quadratic programming model that solves the scheduling of tractor, loaded container, empty container and chassis in drayage operation in an integrated manner. The mathematical model is an extension of the multiple traveling salesman problem with time windows (m-TSPTW). To efficiently solve the developed model, a reactive tabu search (RTS) algorithm combined with an insertion heuristic is developed. The model and algorithm are used to evaluate the effectiveness of different chassis supply models currently in use in the U.S. The results indicated that among the U.S. chassis models the co-op pool, terminal pool and rental pool with chassis yard inside the terminal yield the lowest drayage operation time, percentage of empty movements, and air emissions.

Performance Evaluation of Heuristic Methods in Solving Symmetric Travelling Salesman Problems

Background and Objective: The Travelling Salesman Problem (TSP) is a challenging problem in combinatorial optimization whose main purpose is to find the shortest path reaching all interconnected cities by straight lines.In spite of many available heuristic methods for solving TSPs, no attempts have been made to evaluate and compare their performances. The purpose of this study is to carry out a comparative evaluation study on Simulated Annealing (SA) and several variation of Tabu Search (TS).Materials and Method: This study considers four heuristic methods, i.e., Simulated Annealing (SA), conventional Tabu Search (TS), Improved Tabu Search (ITS) and modified Reactive Tabu Search (RTS) to solve symmetric TSPs.The algorithms were tested on five chosen benchmark problems. Their performances were compared and the appropriate algorithm for solving TSPs was then identified. The solution quality was evaluated using empirical testing, benchmark solutions and probabilistic analyses. Results: The analysis of computational results showed that the modified RTS algorithm provided a better solution quality in terms of minimizing the objective function of TSPs, while the SA algorithm was useful for obtaining instant solutions for TSPs with a large number of cities. The modified RTS algorithm also performed better compared to the existing heuristic methods. Conclusion: This study has explored the most effective heuristic method for solving TSPs based on the intended solution quality. The algorithms proposed in this study should be considered in solving symmetric travelling salesman problems.

Multi-size container transportation by truck: modeling and optimization

This paper investigates a multi-size container truck transportation (MSCTT) problem in which a truck can carry one 40 ft or two 20 ft containers. This problem considers both fixed and flexible drayage orders. A state-transition-based method is presented to formulate the MSCTT problem. The problem is modeled as a sequence-dependent multiple-traveling salesman problem with social constraints in which the distances between cities depend on the sequence of cities visited before. Three tree search procedures and an improved reactive tabu search (IRTS) algorithm are designed to solve the MSCTT problem. They are validated and evaluated based on randomly generated instances extensively. The IRTS algorithm can solve small instances to optimality within less than 1 min. Furthermore, it outperforms the existing reactive tabu search algorithm and can solve realistic-sized instances efficiently. Several interesting findings about the MSCTT problem are presented. Finally, the IRTS algorithm is also applied to a real-world data set.

An analysis of parameter adaptation in reactive tabu search

On-line parameter adaptation schemes are widely used in metaheuristics. They are sometimes preferred to off-line tuning techniques for two main reasons. First, they promise to achieve good performance even on new instance families that have not been considered during the design or the tuning phase of the algorithm. Second, it is assumed that an on-line scheme could adapt the algorithm's behaviour to local characteristics of the search space. This paper challenges the second hypothesis by analysing the contribution of the parameter adaptation to the performance of a state-of-the-art reactive tabu search () algorithm for the maximum clique problem. Our experimental analysis shows that this on-line parameter adaptation scheme converges to good instance-specific settings for the parameters, and that there is no evidence that it adapts to the local characteristics of the search space. The insights gained from the analysis are confirmed by further experiments with an algorithm for the quadratic assignment problem. Together, the results of the two algorithms shed some new light on the reasons behind the effectiveness of .

Comments on “Optimal Constellation Labeling for Iteratively Decoded Bit-Interleaved Space-Time Coded Modulation”

Having developed an optimization criterion, the authors of the commented paper used the Reactive Tabu Search algorithm to find several optimal labeling maps of bit-interleaved space-time coded modulation with iterative decoding, one per each considered system diversity order. However, they might have overlooked the fact that some of the contributed 16-QAM labelings are equivalent to one another. It is shown in this paper by means of spectral analysis and reinforced by computation of the asymptotic coding gain. Thus, there is no need to switch 16-QAM labeling maps when reconfiguring the system from one diversity scheme to another, which makes the results of Huang and Ritcey's contribution even more valuable from a practical point of view.

Primary power distribution systems planning taking into account reliability, operation and expansion costs

In this work, the planning problem of primary distribution networks is formulated as a multi-objective mixed-integer non-linear programming model (MINLP). The objective functions of this model are the expansion and operation investment costs of primary distribution networks as well as the system's reliability costs in the contingency events. The reliability costs are obtained by means of calculating the non-supplied energy because of the repairing and switching operations in the distribution network carried out to isolate and to redistribute loads in the affected sections by permanent faults. In order to solve the expansion problem of the primary network a Multi-objective Reactive Tabu Search algorithm (MO-RTS) is proposed. The concepts of dominance are used to obtain Pareto's optimal frontier in the MO-RTS. The problem of placement of sectionalising switches (automatic or manual) to restore the distribution network and to reduce non-supplied energy costs when permanent faults occur in the network is solved simultaneously with the network expansion planning problem by means of a dedicated genetic algorithm. For testing, the proposed methodology is used as a primary power distribution system, with 180 points of consumption, where 49 already exist and 131 can be added to the system during the planning process.

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

We present a low-complexity algorithm based on reactive tabu search (RTS) for near maximum likelihood (ML) detection in large-MIMO systems. The conventional RTS algorithm achieves near-ML performance for 4-QAM in large-MIMO systems. But its performance for higher-order QAM is far from ML performance. Here, we propose a random-restart RTS (R3TS) algorithm which achieves significantly better bit error rate (BER) performance compared to that of the conventional RTS algorithm in higher-order QAM. The key idea is to run multiple tabu searches, each search starting with a random initial vector and choosing the best among the resulting solution vectors. A criterion to limit the number of searches is also proposed. Computer simulations show that the R3TS algorithm achieves almost the ML performance in 16 × 16 V-BLAST MIMO system with 16-QAM and 64-QAM at significantly less complexities than the sphere decoder. Also, in a 32 × 32 V-BLAST MIMO system, the R3TS performs close to ML lower bound within 1.6 dB for 16-QAM (128 bps/Hz), and within 2.4 dB for 64-QAM (192 bps/Hz) at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> BER.

Joint allocation of measurement points and controllable tooling machines in multistage manufacturing processes

Stream of variations (SoV) modeling of multistage manufacturing process has been studied for the past 15 years and has been used for identification of root causes of manufacturing errors, characterization and optimal allocation of measurements, process-oriented tolerance allocation, fixture design, and operation sequence optimization. Most recently, it was used for optimal in-process adjustments of programmable, controllable tooling (controllable fixtures, CNC machines) in order to enable autonomous minimization of errors in dimensional product quality. However, due to the time and resources needed to take the measurements and the high cost of controllable tooling, it is plausible to strategically position such measurements and controllable devices across a manufacturing system in a way that the ability to mitigate quality problems is maximized. In this article, a distributed stochastic feed-forward control method is devised to optimally (in the least square sense) reduce the variations in dimensional workpiece quality with a limited number of controllable tooling components and measurements distributed across a multistage manufacturing process. Based on this, a reactive tabu search algorithm is proposed to enable joint optimal allocation of measurement points a controllable tooling devices. Theoretical results are evaluated and demonstrate using the SoV model of an actual industrial process for automotive cylinder head machining.

Alocação otimizada de dispositivos de controle e proteção em redes de distribuição

A Alocação e/ou realocação otimizada de dispositivos de controle e proteção em redes de distribuição de energia elétrica melhora a qualidade do serviço de fornecimento de energia e os índices de confiabilidade do sistema. Neste trabalho apresenta-se um modelo de programação não linear binário (PNLB) para o problema de alocação e/ou realocação de chaves seccionadoras e dispositivos de proteção em alimentadores radiais aéreos de distribuição. As restrições consideradas no modelo refletem limitações técnicas e econômicas, tais como problemas de coordenação de dispositivos de proteção em série, número de equipamentos disponíveis, importância do alimentador sob análise, topologia do circuito, qualidade do fornecimento de energia e limitações físicas do sistema. Para solução desse problema propõe-se um algoritmo de Busca Tabu Reativo (RTS). São apresentados os resultados obtidos através de testes realizados com a implementação computacional da metodologia proposta, utilizando-se um alimentador de distribuição radial real com 134 barras.

Optimized Allocation of Control and Protective Devices in Electric Distribution Systems

Optimized allocation and/or reallocation of control and protective devices in distribution networks allow for better operation and improved system reliability indices. Control devices (used to reconfigure the feeders) are allocated in distribution networks to obtain an optimal operation strategy in order to facilitate power supply restoration in case of a contingency. Protective devices (used to isolate faults) are allocated in distribution systems to improve the reliability and continuity of power supply. Protective devices significantly reduce the impacts of faults in terms of customer outages and the time needed for fault location and system restoration. This work presents a mixed-integer non-linear programming model for the sectionalizing switches and protective devices allocation and/or reallocation problem. The constraints considered for the problem reflect technical and economical limitations, such as in-series protective devices coordination, number of available equipment, importance of the analyzed feeder, circuit topology, quality of power supply, and physical limitations of the system. A dedicated reactive tabu search algorithm is proposed for solving this problem. Results and optimized strategies for allocating or reallocating protection devices and switches considering a real-life network restoration are presented.

A reactive tabu search algorithm for the multi-depot container truck transportation problem

A container truck transportation problem that involves multiple depots with time windows at both origins and destinations, including the reposition of empty containers, is formulated as a multi-traveling salesman problem with time windows (m-TSPTW) with multiple depots. Since the problem is NP-hard, a cluster method and a reactive tabu search (RTS) algorithm are developed to solve the problem. The two methods are compared with the mixed integer program which can be used to find optimum solutions for small size problems. The computational results show that the developed methods, particularly the RTS algorithm, can be efficiently used to solve the problem.

A novel two-phase heuristic method for vehicle routing problem with backhauls

This paper raises a novel two-phase heuristic method to solve vehicle routing problems with backhauls. Differing from other vehicle routing problems, we consider the travel speed of vehicle to be time dependent, which will be used for the model of rush hour in an urban city. In the first phase, the original solution is generated by extending traditional heuristic methods and in the second phase, the reactive tabu search algorithm is used to optimize the original solution. We verified that this algorithm is efficient in a number of standard test cases. After comparison with the closest neighboring search algorithm, we found that the results of two-phase heuristic methods are more reasonable.

A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries

The vehicle routing problem with pickups and deliveries (VRPPD) extends the vehicle routing problem (VRP) by allowing customers to both send and receive goods. The main difficulty of the problem is that the load of vehicles is fluctuating rather than decreasing as in the VRP. We design a reactive tabu search metaheuristic that can check feasibility of proposed moves quickly and reacts to repetitions to guide the search. Several new best solutions are found for benchmark problems.

Optimised placement of control and protective devices in electric distribution systems through reactive tabu search algorithm

Optimised placement of control and protective devices in distribution networks allows for a better operation and improvement of the reliability indices of the system. Control devices (used to reconfigure the feeders) are placed in distribution networks to obtain an optimal operation strategy to facilitate power supply restoration in the case of a contingency. Protective devices (used to isolate faults) are placed in distribution systems to improve the reliability and continuity of the power supply, significantly reducing the impacts that a fault can have in terms of customer outages, and the time needed for fault location and system restoration. This paper presents a novel technique to optimally place both control and protective devices in the same optimisation process on radial distribution feeders. The problem is modelled through mixed integer non-linear programming (MINLP) with real and binary variables. The reactive tabu search algorithm (RTS) is proposed to solve this problem. Results and optimised strategies for placing control and protective devices considering a practical feeder are presented.

A Reactive Tabu Search algorithm with variable clustering for the Unicost Set Covering Problem

We develop a Reactive Tabu Search (RTS) algorithm for solving the Unicost Set Covering Problem (SCP) – USCP-TS. We solve a Linear Programming (LP) relaxation of the problem and use the LP optimum to construct a quality solution profile. We cluster the problem variables based on this profile and partition the solution space into orbits. We tested our algorithm on 65 benchmark problems and compared the results against the previous best-known solutions and those obtained by CPLEX 9.0 under varied settings. USCP-TS outperforms CPLEX in solution quality for 32 of the problems and achieves the same solution as CPLEX faster on 21 of the remaining problems.