Water Flow-like Algorithm Research Articles

A Hybrid Water Flow-Like Algorithm and Variable Neighbourhood Search for Traveling Salesman Problem

Various metaheuristic methods have been proposed earlier and applied for solving the Travelling Salesman Problem (TSP). Water Flow Algorithm (WFA) is one of the recent population-based metaheuristic optimization techniques used for solving this problem. Past research has shown that improving WFA local search strategy has a significant impact on the algorithm performance. Therefore, this paper aims to solve TSP by enhancing WFA searching strategy based on a Variable Neighbourhood Search (VNS) known as hybrid WFA-VNS. It is a mixture of the exploration of WFA and the exploitation capability of VNS. This study is conducted in two stages: Pre-experiment and initial experiment. The objective of doing pre-experiment is to select four neighborhood structures to be used for the initial experiment. At the first stage, three instances are used, and there are five neighborhood structures involved. Those neighborhood structures are two opt, three opt, four opt, swapping, and insertion move. Because of pre-experiment, it discovers four best neighborhood structures, which are two opt, three opt, exchanging and insertion move. These neighborhood structures will be used in the initial experiment, which an improvement approach is employed. In an initial experiment, the performance of the proposed hybrid WFA-VNS is further studied and tested on 26 established benchmarked symmetric TSP datasets using four neighborhood structures selected in pre-experiment earlier. The TSP datasets involved are categorized into three types: small datasets, medium datasets, and large datasets. Selected neighborhood structures obtained in pre-experiment are applied and generated randomly to intensify the initial solution achieved at an earlier stage of hybrid WFA-VNS. The results of the comparison show that this hybrid approach represents an improvement and able to produce competitive results.

A Water-Flow Like Algorithm for Solving U-Shaped Assembly Line Balancing Problems

The problem of assigning assembly tasks to the stations arranged along a material handling device is known as assembly line balancing. This paper aims to address the U-shaped assembly line balancing problem (UALBP) which arises when a U-shaped assembly line has to be configured. It is widely known that this problem is NP-hard. Accordingly, different meta-heuristics based on a single solution (such as Simulated Annealing) or a population of solutions (such as Genetic Algorithms) have been proposed in the literature. Meanwhile, it has been argued that either of these meta-heuristics with a fixed number of solutions cannot maintain efficient search progress and thus can lead to premature convergence. Thus, this study aims at adopting a novel meta-heuristic algorithm with dynamic population sizes, namely Water Flow-like Algorithm (WFA), inspired by the behaviour of water flows in nature, to address the UALBP. The line efficiency and variation of workload are considered as the primary and the secondary objective, to be optimized, respectively. To verify the efficiency and robustness of the proposed WFA, a real case study taken from an automobile manufacturer as well as a set of standard problems are solved and the results compared with the existing approaches in the literature. The computational results demonstrate the superiority of the WFA, particularly in addressing medium to large-sized problems.

An improved water flow-like algorithm for order acceptance and scheduling with identical parallel machines

Order acceptance and scheduling (OAS) problem denotes manufactures in a make-to-order environment have to determine which orders should be accepted and how to arrange the accepted orders in a processing sequence. If the order schedule is not well-arranged, that will lead to the tardiness penalties and the impact of other orders on the allocation of resources. Therefore, this study considered the due dates, order profits, tardiness penalties, sequence-dependent setup times and proposed the integrated model for the problem of order acceptance and identical parallel machine scheduling. The modified Water Flow-like Algorithm (WFA) was developed to solve the problem. The proposed water flow-like algorithms, WFA.I and WFA.II are compared, with a well-defined classic algorithm, particle swarm optimization embedded with variable neighborhood search, to find out their solution qualities in different sizes of problems. The computational results show that, in the large-sized problems, WFA.II is performing much better than WFA.I with a range of solution gaps, 0.45% ∼38.06%. WFA.II is also competitive as the well-defined classic algorithm, PSOVNS, in the large-sized problems, with an extremely short range of solution gap, 0.17% ∼1.65%.

Water Flow-Like Algorithm with Simulated Annealing for Travelling Salesman Problems

Water Flow-like Algorithm (WFA) has been proved its ability obtaining a fast and quality solution for solving Travelling Salesman Problem (TSP). The WFA uses the insertion move with 2-neighbourhood search to get better flow splitting and moving decision. However, the algorithms can be improved by making a good balance between its solution search exploitation and exploration. Such improvement can be achieved by hybridizing good search algorithm with WFA. This paper presents a hybrid of WFA with various three neighbourhood search in Simulated Annealing (SA) for TSP problem. The performance of the proposed method is evaluated using 18 large TSP benchmark datasets. The experimental result shows that the hybrid method has improved the solution quality compare with the basic WFA and state of art algorithm for TSP.

Reverse logistics network design: a water flow-like algorithm approach

This study investigates the reverse logistics network design problem, including collection/inspection, recovery and disposal centers that a mixed integer linear programming model is considered. In this network, returned products from customer zones are collected in collection/inspection centers and after quality inspection, and also after separation, recoverable products are shipped to recovery centers and scrapped ones are transported to disposal centers. NP-hardness of this problem is proved in many papers, so a novel meta-heuristic solution method aiming minimization of total costs comprised fixed opening cost of collection/inspection, recovery and disposal centers and transportation cost of products between opened centers using priority based encoding presentation is proposed. Comparison of outputs from this proposed algorithm and a modified genetic algorithm shows the excellence of this new solution method. Finally, some directions for future research are proposed.

Network-based Type-2 Fuzzy System with Water Flow Like Algorithm for System Identification and Signal Processing

This paper introduces a network-based interval type-2 fuzzy inference system (NT2FIS) with a dynamic solution agent algorithm water flow like algorithm (WFA), for nonlinear system identification and blind source separation (BSS) problem. The NT2FIS consists of interval type-2 asymmetric fuzzy membership functions and TSK-type consequent parts to enhance the performance. The proposed scheme is optimized by a new heuristic learning algorithm, WFA, with dynamic solution agents. The proposed WFA is inspired by the natural behavior of water flow. Splitting, moving, merging, evaporation, and precipitation have all been introduced for optimization. Some modifications, including new moving strategies, such as the application of tabu searching and gradient-descent techniques, are proposed to enhance the performance of the WFA in training the NT2FIS systems. Simulation and comparison results for nonlinear system identification and blind signal separation are presented to illustrate the performance and effectiveness of the proposed approach.

Network-based Type-2 Fuzzy System with Water Flow Like Algorithm for System Identification and Signal Processing

This paper introduces a network-based interval type-2 fuzzy inference system (NT2FIS) with a dynamic solution agent algorithm water flow like algorithm (WFA), for nonlinear system identification and blind source separation (BSS) problem. The NT2FIS consists of interval type-2 asymmetric fuzzy membership functions and TSK-type consequent parts to enhance the performance. The proposed scheme is optimized by a new heuristic learning algorithm, WFA, with dynamic solution agents. The proposed WFA is inspired by the natural behavior of water flow. Splitting, moving, merging, evaporation, and precipitation have all been introduced for optimization. Some modifications, including new moving strategies, such as the application of tabu searching and gradient-descent techniques, are proposed to enhance the performance of the WFA in training the NT2FIS systems. Simulation and comparison results for nonlinear system identification and blind signal separation are presented to illustrate the performance and effectiveness of the proposed approach.

A Water Flow-Like Algorithm for the Travelling Salesman Problem

The water flow-like algorithm (WFA) is a relatively new metaheuristic that performs well on the object grouping problem encountered in combinatorial optimization. This paper presents a WFA for solving the travelling salesman problem (TSP) as a graph-based problem. The performance of the WFA on the TSP is evaluated using 23 TSP benchmark datasets and by comparing it with previous algorithms. The experimental results show that the proposed WFA found better solutions in terms of the average solution and the percentage deviation of the average solution from the best-known solution.

A Water Flow-like Algorithm for Cell Formation, Cell Layout, and Intracellular Machine Layout Problems

A Water Flow-like Algorithm for Cell Formation, Cell Layout, and Intracellular Machine Layout Problems

Bi-criteria SDST hybrid flow shop scheduling with learning effect of setup times: water flow-like algorithm approach

In studies on automatic scheduling problems, processing times do not differ according to repetition of job or process sequences so it may also be necessary to consider processing times independent from setup times. While considering setup times, the human factor has an important effect on setup, so by the processing of similar tasks frequently worker skills improve and they are able to perform setup at a greater pace. This fact is known as the ‘learning effect’ in the literature. This paper deals with sequence-dependent setup times (SDSTs) hybrid flow shop scheduling with learning effect of setup times for minimising weighted sum of makespan and total tardiness. A mathematical programming model that incorporates these aspects of the problem is developed which belongs to the NP-hard class. Thus, because of the intensive computation, we propose a novel meta-heuristic approach called water flow-like algorithm (WFA) which has the feature of multiple and dynamic numbers of solution agents. Various parameters of the problem and the WFA are reviewed by means of Taguchi experimental design. For the evaluation of the proposed WFA, problem data was generated to compare it against a random key genetic algorithm (RKGA). The results demonstrate the high performance of the WFA with respect to the RKGA.

A water flow-like algorithm for manufacturing cell formation problems

Available research on the manufacturing cell formation problem shows that most solution approaches are either single- or multiple-solution-agent-based, with a fixed size of solution agents. Frequent problems encountered during the process of solving the cell formation problem include solutions being easily trapped in local optima and bad solution efficiency. Yang and Wang [Yang, F.-C., Wang, Y.-P., 2007. Water flow-like algorithm for object grouping problems. Journal of the Chinese Institute of Industrial Engineers, 24 (6), 475–488] proposed the water flow-like algorithm (WFA) to overcome the shortcomings of single- and multiple-solution -agent-based algorithms. WFA has the features of multiple and dynamic numbers of solution agents, and its mimicking of the natural behavior of water flowing from higher to lower levels coincides exactly with the process of searching for optimal solutions. This paper therefore adopts the WFA logic and designs a heuristic algorithm for solving the cell formation problem. Computational results obtained from running a set of 37 test instances from the literature and newly created have shown that the proposed algorithm has performed better than other benchmarking approaches both in solution effectiveness and efficiency, especially in large-sized problems. The superiority of the proposed WFACF over other approaches from the literature should be attributed to the collaboration of the WFA logic, the proposed prior estimation of the cell size, and the insertion-move. The WFA is a novel heuristic approach that deserves more attention. More attempts on adopting the WFA logic to solve many other combinatorial optimization problems are highly recommended.

WATER FLOW-LIKE ALGORITHM FOR OBJECT GROUPING PROBLEMS

ABSTRACT This paper presents a novice heuristic algorithm, Water Flow-like Algorithm (WFA), for solving discrete optimization problems, particularly the bin packing problems. WFA simulates solution agents as water flows traversing the terrain mapped from the objective function. Governed by the gravitation force, water flows from higher attitudes to lower ones. Driven by the fluid momentum, water flows adjust their compositions and directions against the landforms by splitting into and merging from other flows. Water flows are allowed to move upward to higher attitudes once they possess enough momentum to overcome the potential barrier. Mostly, at least one flow can travel to the lowest region of the terrain under the consideration. In the atmosphere, some water of a flow will evaporate and return to the ground by precipitation. Inspired by the water flowing of the nature, WFA is designed as an optimization algorithm performing the water flow splitting, merging, and dropping (precipitation) operations to traverse the solution space. The number of solution agents deployed is dynamically changing. WFA is an evolutionary algorithm involving four water flow operations: splitting and moving, merging, evaporation, and precipitation. The computational flow and the four operations are extensively discussed. In addition to general operations of WFA, specific operations for bin packing problems are presented. A designed problem and a benchmark problem from OR-Lib are used to test WFA and to compare results with other methods, such as GA, POS, and EM. Numerical results show that WFA outperforms others in solving these BPPs.