Tree-based Genetic Algorithm Research Articles

Solving non-linear fixed-charge transportation problems using nature inspired non-linear particle swarm optimization algorithm

The main objective of this study is to formulate and solve the model of non-linear fixed-charge transportation problem (NFCTP), which is one of the NP-hard problems. This type of problem is challenging to solve using conventional methods because these methods are usually inefficient, costly to compute, and may stuck at the local optimum solution. To overcome this issue, a non-linear particle swarm optimization (NPSO) algorithm with new non-linear acceleration parameters is proposed in this study. Also, to preserve the feasibility condition (non-negative integer solution) of the transportation problem, two novel negative repair and fraction repair strategies have been incorporated into the proposed NPSO. The efficiency of the NPSO algorithm is tested on both the small-scale and large-scale NFCTPs. The dataset are considered from the existing studies. The obtained results are compared with those obtained by the spanning tree-based genetic algorithm (st-GA), priority-based genetic algorithm (pb-GA), and minimum cost flow-based genetic algorithm. The comparative study reveals that for all the considered problems, the proposed NPSO provides better feasible solutions in lesser computational time. Furthermore, the effectiveness of the NPSO algorithm is shown by comparing it to other seven existing variants of PSO and is found to outperformed these variants for the small scale as well as large scale NFCTPs.

A Novel Tree‐Based Genetic Algorithm for the Multicast Protocol in Two‐Tiered WSNs

Genetic algorithms (GAs) serve as a class of powerful tools to search for an effective multicast routing scheme among multiple cluster header nodes, which strongly affects the lifetime of two-tiered Wireless sensor networks (WSNs). This paper proposes a novel Genetic algorithm (GA) with a new crossover mechanism called Leaf crossover for the multicast routing among upper tier nodes in two-tiered WSNs, which outperforms the existing popular tree-based GAs by not requiring the global network link information, encoding/decoding or repair operations. Our simulation study indicates that the proposed algorithm could prolong the lifetime of multicast service, increase the packet delivery ratio as well as converge fast by comparison with existing GAs.

A New Crossover Mechanism for Genetic Algorithms for Steiner Tree Optimization.

Genetic algorithms (GAs) have been widely applied in Steiner tree optimization problems. However, as the core operation, existing crossover operators for tree-based GAs suffer from producing illegal offspring trees. Therefore, some global link information must be adopted to ensure the connectivity of the offspring, which incurs heavy computation. To address this problem, this article proposes a new crossover mechanism, called leaf crossover (LC), which generates legal offspring by just exchanging partial parent chromosomes, requiring neither the global network link information, encoding/decoding nor repair operations. Our simulation study indicates that GAs with LC outperform GAs with existing crossover mechanisms in terms of not only producing better solutions but also converging faster in networks of varying sizes.

A new integrated data mining model to map spatial variation in the susceptibility of land to act as a source of aeolian dust

This research developed a more efficient integrated model (IM) based on combining the Nash-Sutcliffe efficiency coefficient (NSEC) and individual data mining (DM) algorithms for the spatial mapping of dust provenance in the Hamoun-e-Hirmand Basin, southeastern Iran. This region experiences severe wind erosion and includes the Sistan plain which is one of the most PM2.5-polluted regions in the world. Due to a prolonged drought over the last two decades, the frequency of dust storms in the study area is increasing remarkably. Herein, 14 factors controlling dust emissions (FCDEs) including soil characteristics, climatic variables, digital elevation map, normalized difference vegetation index, land use and geology were mapped. Correlation and collinearity among the FCDEs were examined by the Pearson test, tolerance coefficient (TC) and variance inflation factor (VIF), with the results suggesting a lack of collinearity between FCDEs. A tree-based genetic algorithm was applied to prioritize and quantify the importance weights of the FCDEs. Thirteen individual data mining models were applied for mapping dust provenance. The model performance was assessed using root mean square error, mean absolute error and NSEC. Based on clustering analysis, the 13 DM models were grouped into five clusters and then the cluster with the highest NSEC values used in an integrated modelling process. Based on the results, the IM (NSEC = 93%) outperformed the individual DM models (the NSEC values range between 51 and 92%). Using the IM, 11, 5, 7 and 77% of the total study area were classified into low, moderate, high and very high susceptibility classes for dust provenance, respectively. Overall, the results illustrate the benefits of an IM for mapping spatial variation in the susceptibility of catchment areas to act as dust sources.

Probabilistic tree-based representation for solving minimum cost integer flow problems with nonlinear non-convex cost functions

The minimum cost flow problem (MCFP) is the most generic variation of the network flow problem which aims to transfer a commodity throughout the network to satisfy demands. The problem size (in terms of the number of nodes and arcs) and the shape of the cost function are the most critical factors when considering MCFPs. Existing mathematical programming techniques often assume the cost functions to be linear or convex. Unfortunately, the linearity and convexity assumptions are too restrictive for modelling many real-world scenarios. In addition, many real-world MCFPs are large-scale, with networks having a large number of nodes and arcs. In this paper, we propose a probabilistic tree-based genetic algorithm (PTbGA) for solving large-scale minimum cost integer flow problems with nonlinear non-convex cost functions. We first compare this probabilistic tree-based representation scheme with the priority-based representation scheme, which is the most commonly-used representation for solving MCFPs. We then compare the performance of PTbGA with that of the priority-based genetic algorithm (PrGA), and two state-of-the-art mathematical solvers on a set of MCFP instances. Our experimental results demonstrate the superiority and efficiency of PTbGA in dealing with large-sized MCFPs, as compared to the PrGA method and the mathematical solvers.

Balanced connected task allocations for multi-robot systems: An exact flow-based integer program and an approximate tree-based genetic algorithm

Task allocation for a multi-robot system is often imposed with various constraints to promote efficiency and avoid unwanted consequences. This study focuses on the min-max balanced connected q-partition problem (BCPq) that seeks the early completion time of a multi-robot system while satisfying mission constraints. In the problem, each environmental region is modeled as a weighted node of a graph and the graph is to be partitioned into a predefined number, q, of disjoint node sets, such that nodes in each set are connected and the largest “sum of the set” is as small as possible. The problem is NP-hard in general cases, and has a brute-force search space exponential to the number of nodes. BCPq arises in many fields besides robotics. To date, existing work has mainly been conducted on special versions of the problem, such as small q or special types of graphs. In this study, we propose two approaches for the general case: one is exact and suitable for graphs of less than 200 nodes, while the other is approximate and can handle graphs with up to 3000 nodes. Specifically, this study presents the first exact mixed integer linear program (MILP) in the literature that can partition an arbitrary graph into a given arbitrary number of components. The MILP is based on a flow model and can solve graphs with 100 more nodes than the existing MILP that can only tackle 2-partition in the q=2 case. The study also presents an approximate genetic algorithm (GA) based on tree partition and tree evolution. It is the first GA that can handle BCPq (q ≥ 2) problems. On graphs of less than 500 nodes and 2-partition, the GA achieved all the optima in 20 runs. On q ≤ 12, this GA also can achieve results close to the optima after a few individuals were evolved, i.e., a gap smaller than 3% of the ideal average value. Moreover, the GA is scalable to q as the consumed time is nearly stable, independent of q.

An uncertain furniture production planning problem with cumulative service levels

To investigate how the loss averse customer's psychological satisfaction affects the company's furniture production planning, we establish a furniture production planning model under uncertain environment, where customer demand and production costs are characterized by mutually independent uncertain variables. Based on prospect theory, customer's psychological satisfaction about stockout performance is measured by cumulative service levels in our model. In the framework of uncertainty theory, the proposed uncertain model can be transformed into an equivalent deterministic form. However, the transformed model is a nonlinear mixed integer programming problem, which cannot be solved by conventional optimization algorithms. To cope with this difficulty, a chemical reaction optimization algorithm integrated with LINGO software is designed to solve the proposed production planning problem. In order to verify the effectiveness of the designed hybrid chemical reaction optimization (CRO) algorithm, we conduct several numerical experiments via an application example and compare with a spanning tree-based genetic algorithm (hst-GA). The computational results show that our proposed CRO algorithm achieves better performance than hst-GA, and the results also provide several interesting managerial insights in production planning problems.

Binary and m-ary encoding in applications of tree-based genetic algorithms for QoS routing

Ubiquitous and Pervasive Computing (UPC) applications often have Quality of Service (QoS) requirements. These become constraints for the UPC network infrastructure. In this paper, we refer to Mobile ad Hoc Networks, one of the most important technologies supporting UPC, and investigate on Genetic Algorithms (GAs) for QoS routing. GAs are part of the soft computing paradigm and can solve the NP search of QoS routes with multiple constraints. We elaborate on tree-based GAs, which represent the set of paths from source to destination as a tree and encode them through the crossed junctions. While their most well-known applications use m-ary encoding representing single paths in the chromosomes, in this paper we discuss a binary encoding with the objective of improving the convergence speed. The binary encoding represents classes of paths in the chromosomes and allows local search on classes of paths. These classes are both collectively exhaustive and mutually exclusive. Simulation results compare convergence speed and scalability of GA applications with binary and m-ary encoding in networks with an increasing number of nodes and links per node. As the per-class processing is reason of additional computational cost, an hybrid GA application that uses both binary and m-ary encoding is introduced.

Glowworm swarm optimisation algorithm for nonlinear fixed charge transportation problem in a single stage supply chain network

In this paper, Glowworm swarm optimisation (GSO) is proposed to solve nonlinear fixed charge transportation problem (NLFCTP) in a single stage supply chain network. In a fixed charge transportation problem, fixed cost is incurred for every route, along with the variable cost that is proportional to the amount shipped. In some cases, the variable cost is associated with quadratic variables in which the cost function will be nonlinear. This problem is more difficult to solve due to presence of the fixed costs that result in discontinuities in the objective function. The objective of this paper is to determine the least cost transportation plan that minimises the total variable and fixed costs while satisfying the supply and demand requirements of each plant and customer. The performance of GSO is compared in terms of total distribution cost with a spanning tree-based genetic algorithm. The comparison reveals that GSO provides better solutions.

Particle swarm optimisation for multi stage supply chain network associated with fixed charges

This paper develops a particle swarm optimisation (PSO) algorithm for the multi stage supply chain network problem associated with the fixed charges. In many distribution problems, the transportation cost consists of fixed costs, that are independent of the quantities transported and variable costs, which are proportional to the quantities transported. The objective of this paper is to select the optimum set of suppliers, plants, distribution centres (DCs) to be opened and determine the quantities to be supplied to satisfy the customer demand with minimum total distribution cost. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard while considering the fixed costs. The performance of PSO is compared in terms of total distribution cost with spanning tree-based genetic algorithm (st-GA), improved Prufer number encoding-based genetic algorithm (IPEGA) and with LINGO. Computational results showed that the proposed PSO is capable of producing good quality solutions.

A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems

In this paper, we propose a genetic algorithm using priority-based encoding (pb-GA) for linear and nonlinear fixed charge transportation problems (fcTP) in which new operators for more exploration are proposed. We modify a priority-based decoding procedure proposed by Gen et al. [1] to adapt with the fcTP structure. After comparing well-known representation methods for a transportation problem, we explain our proposed pb-GA. We compare the performance of the pb-GA with the recently used spanning tree-based genetic algorithm (st-GA) using numerous examples of linear and nonlinear fcTPs. Finally, computational results show that the proposed pb-GA gives better results than the st-GA both in terms of the solution quality and computation time, especially for medium- and large-sized problems. Numerical experiments show that the proposed pb-GA better absorbs the characteristics of the nonlinear fcTPs.

A simple heuristics for optimisation of unbalanced multistage supply chain logistics associated with fixed charges

This paper presents a mathematical model and a simple heuristics-based solution procedure for the multistage supply chain logistics associated with the fixed charges. The objective of this paper is to select the optimum set of suppliers, plants, distribution centres (DC) to be opened and determine the quantities to be supplied to satisfy the customer demand with minimum distribution cost. Fixed charge problems arise in a large number of distribution systems. In many distribution problems, the transportation cost consists of fixed charges, which are independent of the amount transported and variable costs, which are proportional to the amount shipped. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard while considering the fixed charges. We present a simple heuristics for optimisation of unbalanced multistage logistics system and compared it in terms of distribution cost with spanning tree-based genetic algorithm (st-GA) and improved Prufer number encoding-based genetic algorithm (IPE-GA). The comparison reveals that the proposed heuristics is capable of providing better solutions.

A new approach for integrating process planning with scheduling

Integrated process planning with scheduling is a core activity in the manufacturing chain. Modern manufacturing processes require higher flexibility and capability of supporting distributed activities. In this paper, a novel STEP-NC Compliant Process Planning and Scheduling Algorithm (STEP-NCPPSA) is proposed to meet such requirements. The STEP-NCPPSA utilises STEP-NC compliant data models to represent the related manufacturing information. STEP-NCPPSA aims to achieve an Integrated, Intelligent, Informative and Interoperable (I4) manufacturing in a distributed manufacturing environment. Three phases, STEP-NC initial process planning, initial bidding, and Tree-based Genetic Algorithm optimisation are naturally integrated by the supporting STEP-NC concepts. STEP-NCPPSA is also capable of handling shop-floor information and re-process planning and scheduling to adapt to shop floor changes.

A note on “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007)

In 2007, a spanning tree-based genetic algorithm approach for solving nonlinear fixed charge transportation problem proposed by Jo et al. [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022] was published in Computers & Industrial Engineering journal. In 2008, comments like calculation of total cost, indication of problem size were given by Kannan et al. [Kannan, G., Kumar, P. S., Vinay V. P. (2008). Comments on ‘‘Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007). Computers & Industrial Engineering. doi:10.1016/j.cie.2007.12.019] for the published model of [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022]. In this note, as a response to the comments of Kannan et al., the formula for calculating the total cost of nonlinear fixed charge transportation problem is illustrated with examples, to which the near-optimal solutions are given.

Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm

In this paper, we consider the fixed-charge transportation problem (FCTP) in which a fixed cost, sometimes called a setup cost, is incurred if another related variable assumes a nonzero value. To tackle such an NP-hard problem, there are several genetic algorithms based on spanning tree and Prüfer number representation. Contrary to the findings in previous works, considering the genetic algorithm (GA) based on spanning tree, we present a pioneer method to design a chromosome that does not need a repairing procedure for feasibility, i.e. all the produced chromosomes are feasible. Also, we correct the procedure provided in previous works, which designs transportation tree with feasible chromosomes. We show the previous procedure does not produce any transportation tree in some situations. Besides, some new crossover and mutation operators are developed and used in this work. Due to the significant role of crossover and mutation operators on the algorithm’s quality, the operators and parameters need to be accurately calibrated to ensure the best performance. For this purpose, various problem sizes are generated at random and then a robust calibration is applied to the parameters using the Taguchi method. In addition, two problems with different sizes are solved to evaluate the performance of the presented algorithm and to compare that performance with LINGO and also with the solution presented in previous work.

The Memetic Tree-based Genetic Algorithm and its application to Portfolio Optimization

We introduce a Memetic system to solve the application problem of Financial Portfolio Optimization. This problem consists of selecting a number of assets from a market and their relative weights to form an investment strategy. These weights must be optimized against a utility function that considers the expected return of each asset, and their co-variance; which means that as the number of available assets increases, the search space increases exponentially. Our method introduces two new concepts that set it apart from previous evolutionary based approaches. The first is the Tree-based Genetic Algorithm (GA), a recursive representation for individuals which allows the genome to learn information regarding relationships between the assets, and the evaluation of intermediate nodes. The second is the hybridization with local search, which allows the system to fine-tune the weights of assets after the tree structure has been decided. These two innovations make our system superior than other representations used for multi-weight assignment of portfolios.

A new spanning tree-based genetic algorithm for the design of multi-stage supply chain networks with nonlinear transportation costs

The design of configuration and the transportation planning are crucial issues to the effectiveness of multi-stage supply chain networks. The decision makers are interested in the determination the optimal locations of the hubs and the optimal transportation routes to minimize the total costs incurred in the whole system. One may formulate this problem as a 0-1 mixed integer non-linear program though commercial packages are not able to efficiently solve this problem due to its complexity. This study proposes a new spanning tree-based Genetic Algorithm (GA) using determinant encoding for solving this problem. Also, we employ an efficient heuristic that fixes illegal spanning trees existing in the chromosomes obtained from the evolutionary process of the proposed GA. Our numerical experiments demonstrate that the proposed GA outperforms the other previously published GA in the solution quality and convergence rate.

Comments on “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007)

A spanning tree-based genetic algorithm approach for solving nonlinear fixed charge transportation problem proposed by Jo et al. [Jo, J. B., Li, Y., & Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022] was recently published in Computers & Industrial Engineering journal. In this work, comments like calculation of total cost, indication of problem size are given for the published model of [Jo, J.B., Li, Y., & Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022.].

A class of multi-objective supply chain networks optimal model under random fuzzy environment and its application to the industry of Chinese liquor

An important issue, when shipping cost and customers demand are random fuzzy variables in supply chain network (SCN) design problem, is to find the network strategy that can simultaneously achieve the objectives of minimization total cost comprised of fixed costs of plants and distribution centers (DCs), inbound and outbound distribution costs, and maximization customer services that can be rendered to customers in terms of acceptable delivery time. In this paper, we propose a random fuzzy multi-objective mixed-integer non-linear programming model for the SCN design problem of Luzhou Co., Ltd. which is representative in the industry of Chinese liquor. By the expected value operator and chance constraint operator, the model has been transformed into a deterministic multi-objective mixed-integer non-linear programming model. Then, we use spanning tree-based genetic algorithms (st-GA) by the Prüfer number representation to find the SCN to satisfy the demand imposed by customers with minimum total cost and maximum customer services for multi-objective SCN design problem of this company under condition of random fuzzy customers demand and transportation cost between facilities. Furthermore, the efficacy and the efficiency of this method are demonstrated by the comparison between its numerical experiment results and those of tradition matrix-based genetic algorithm.

Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm

Abstract Networks provide a useful way for modeling real world problems and are extensively used in many different types of systems: communications, hydraulic, mechanical, electronic, and logistics. The transportation problem (TP) is known as one of the important network problems. When the TP problem is associated with additional fixed cost for establishing the facilities or fulfilling the demand of customers, then it is called fixed charge transportation problem (fcTP). This problem is one of the NP-hard (IE/OR) problems that are difficult to solve using traditional methods. This paper aims to show the application of spanning tree-based Genetic Algorithm (GA) approach for solving nonlinear fixed charge transportation problem. Our new idea lies on the GA representation that includes the feasibility criteria and repairing procedure for the chromosome. Several numerical experimental results are presented to show the effectiveness of the proposed method.