Solving for nonlinear integer programming problem using genetic algorithm and its application

Genetic algorithm for non-linear mixed integer programming problems and its applications

A computational comparison of cargo prioritization and terminal allocation problem models

Preventive maintenance (PM) is a maintenance program with activities created at a determined interval or according to certain principles, designed to reduce the likelihood of failure or deterioration of item performance. This aims to improve overall reliability and system availability. In this research, a preventive maintenance schedule (PMS) was designed for electricity and desalination of water in power plants, subject to meeting relevant constraints. The proposed methodology is used to generate a PMS for the boilers, turbines, and distillers. A nonlinear integer programming (NLIP) model was employed to address this problem. The results of the proposed method were compared with the PMS for a power station in Kuwait. The results were better in terms of the volume of production and in terms of the gap between the available production and demand in order to continue providing consumers with electricity and water without a shortage in the event of a breakdown in equipment. It produces an improvement of 12.12% and 16.58% respectively, for water and electricity. Furthermore, the sensitivity and robustness of the proposed method were analysed by increasing the maintenance duration for some equipment, increasing the demand, and adding various additional conditions. In addition, a comparison of additional conditions with a binary problem method in terms of computer time for the search for an optimal solution was carried out, where the model provided an optimal solution in a reasonable time. Among the most important benefits that the user can obtain for this technique are extending the life of the equipment, increasing efficiency, and reducing expenses.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Network function virtualization (NFV) brings the potential to provide the flexible implementation of network functions and reduce overall hardware cost by running service function chains (SFCs) on commercial off-the-shelf servers with many-core processors. Towards this direction, both academia and industry have spent vast amounts of effort to address the optimal placement challenges of NFV middleboxes. Most of the servers usually are equipped with Intel X86 processors, which adopt Non-Uniform Memory Access (NUMA) architecture. However, existing solutions for placing SFCs in one server either ignore the impact of hardware architecture or overlook the dependency between middleboxes. Our empirical analysis shows that the placement of virtual network functions (VNFs) with interdependency in a server needs more particular consideration. In this paper, we first manage the optimal placement of VNFs by jointly considering the discrepancy of cores in different NUMA nodes and interdependency between network functions (NFs), and formulate the optimization problem as a Non-Linear Integer Programming (NLIP) model. Then we find a reasonable metric to describe the dependency relation formally. Finally, we propose a heuristic-based backtracking placement algorithm (BPA) to find the near-optimal placement solution. The evaluation shows that, compared with two state-of-art placement strategies, our algorithm can improve the aggregate performance by an average of 20% or 45% within an acceptable time range.

Network Function Virtualization (NFV) offers service delivery flexibility and reduces overall costs by running service function chains (SFCs) on commodity servers with many cores. Existing solutions for placing SFCs in one server treat all CPU cores as equal and allocate isolated CPU cores to network functions (NFs). However, advanced servers often adopt Non-Uniform Memory Access (NUMA) architecture to improve the scalability of many-core systems. CPU cores are grouped into nodes, incurring performance degradation due to cross-node memory access and intra-node resource contention. Our evaluation shows that randomly selecting cores to place NFs in an SFC could suffer from 39.2 percent lower throughput comparing to an optimal placement solution. In this article, we propose Octans, an NFV orchestrator to achieve maximum aggregate throughput of all SFCs in many-core systems. Octans first formulates the optimization problem as a Non-Linear Integer Programming (NLIP) Model. Then we identify the key factor for problem solving as evaluating the throughput drop of an NF caused by other NFs in the same SFC or different SFCs, i.e., performance drop index, and propose a formal and accurate prediction model based on system level performance metrics. Finally, we propose two online algorithms to quickly find near-optimal placement solutions for one-time and incremental deployment. Extensive evaluation on a prototype implementation shows that Octans significantly improves the aggregate throughput comparing to two state-of-the-art placement solutions by 27.1 ~ 45.2 percent for one-time deployment and by 20.9 ~ 38.1 percent for incremental deployment, with very low prediction errors. Moreover, Octans could quickly find a near-optimal placement solution with tiny optimality gap.

Hard-to-access health infrastructure is likely to lead to increased morbidity and mortality. The optimal layout of health facilities is significant for disease control and prevention. This study aims to propose a method to provide equitable access to capacitated preventive health facilities, which captures the key features of the effect of congestion in a competitive choice environment. The problem is formulated as a bilevel nonlinear integer programming model. The upper level is a biobjective programming model subject to investment budget (B) constraint, and the lower level is a user equilibrium analogous model resulting from the users’ choice of facility location. An efficient and operable heuristic algorithm was designed according to the bilevel decision structure where a genetic algorithm (GA) with elite strategy is developed to solve the upper-level problem and the method of successive averages (MSA) is adopted to solve the lower-level problem. A case study is employed to validate the performance of the proposed method. The results show that the method is robust and could reach an equal service quality in a reasonable computation time. However, the sensitivity analysis indicated that the marginal benefit of the investment decreased. There is an optimal B beyond which further increments in investment would not offset the benefits. In addition, the proposed method could be beneficial for other congested public service facilities that users are free to choose from.

Driven by ever growing concern to environments, legislative regulation and economic profitability, more and more firms pay attentions to physical design of reverse logistics networks. This paper considers the problem of determining the numbers and locations of centralized return centers (i.e., reverse consolidation points) where returned products from retailers or end-customers were collected, sorted and consolidated into a large shipment destined for manufacturers' or distributors' repair facilities. A stochastic nonlinear mixed integer programming model for the reverse logistics problem involving product returns is established. Genetic algorithm and Monte Carlo Method are used to solve the proposed model. The usefulness of the proposed model and algorithm was validated by its application to an illustrative example dealing with products returned from online sales.

Cell formation problem mainly addresses how machines should be grouped and parts be processed in cells. In dynamic environments, product mix and demand are changed in each period of the planning horizon. Incorporating such assumption in the model increases flexibility of the system to meet customers' requirements. In this model, to ensure the reliability of the system in presence of unreliable machines, alternative routing process as well as buffer storage are considered to reduce detrimental effects of machine failure. This problem is presented by a nonlinear mixed integer programming model attempting to minimize the overall cost of the system. To solve the model in large scale for practical purposes, a genetic algorithm approach is adopted as the model belongs to NP-hard class of problems. Sensitivity analysis is used to show the validity of the proposed model. Besides, numerical examples are used both, for small-sized and large- sized instances to show the efficiency of the method in finding near optimal solution.

Providing effective Through Train Services (TTSs) faces challenges due to complex infrastructure conditions, train performances and passenger demands. To enhance TTSs between two different classes of urban rail transit lines with variations in train speed and capacity, we propose a multi-objective Integer Non-Linear Programming (INLP) model. This model maximizes passenger travel time savings and average train load utilization, and develops an integrated approach to simultaneously optimize the frequencies of through express trains and local trains, as well as the operation zones, stopping patterns and type selection of through trains. Additionally, a Non-Dominated Sorting Genetic Algorithm II is designed to solve the INLP model based on a simple test network and a real-world case from the Nanjing Subway. The unique benefits of our proposed method are demonstrated by a comprehensive compared with the Single Line Operation Mode and the all-stop plans under Through Operation Mode.

This study focuses on a real-world case that is defined as an extension of the container loading problem (CLP) with weakly heterogeneous types of boxes. A company producing plastic cups wants to increase its efficiency in container loading operations. To solve the problem, a hybrid approach including a static rule to rank orders and integer nonlinear programming (INLP) models is developed. INLP models form box sizes according to the properties of the cups, and determine the position of the boxes in layers while simultaneously minimizing the layer-depth. The presented approach is tested on real-world cases and benchmark data sets. The results show that simultaneously forming boxes and solving the CLP increases the effectiveness of container loading operations.

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.

In this paper we study the problem of minimizing total weighted tardiness, a proxy for maximizing on-time delivery performance, on parallel nonidentical batch processing machines. We first formulate the (primal) problem as a nonlinear integer programming model. We then show that the primal problem can be solved exactly by solving a corresponding dual problem with a nonlinear relaxation. Since both the primal and the dual problems are NP-hard, we use genetic algorithms, based on random keys and multiple choice encodings, to heuristically solve them. We find that the genetic algorithms consistently outperform a standard mathematical programming package in terms of solution quality and computation time. We also compare the smaller problem instances to a breadth-first tree search algorithm that gives evidence of the quality of the solutions.

In this study, an optimization of supply chain network for New Energy Vehicle Power Batteries (NEVPB) from the perspective of resource circulation is proposed. The model consists of seven stages in terms of collection center (CC), repairing center (RC), distribution center (DC), recycling center (RY), part supplier (PS), material supplier (MS), and disposal center (DP). The model is formulated as a nonlinear integer programming model and a comparison of LINGO and genetic algorithm (GA접근법) are conducted respectively. In numerical experiment, it has found a way to repair and recycle NEVPB. Retrieving as many NEVPBs in use demonstrates sustainable power generation benefits by maximizing the use of recovery through resource recycling and searching for recovery classification of batteries as well as shortening lifespan that occur during the process of producing initial parts and modules from raw materials.

The scarce radio resources available to any cellular radio network have to be shared between its revenue-generating voice- and data-carrying services, and non-revenue-generating management services. One of these management services is location management, crucial for the network to keep track of the location of its subscribers and to connect their incoming calls. Location management consists of the two activities, paging and location updating, both of which are structured around a subdivision of the network service area called the location area (LA). The ways in which the service area is partitioned therefore has a direct impact on the amount of radio bandwidth that has to be spent on location management. However, paging and location updating share an antagonistic relationship, and finding the optimal LA partitioning that strikes a balance between the two is a challenging design problem. In this paper, the problem of finding the optimal LA partitioning of a cellular radio network service area in order to minimise the total location management signalling cost is addressed. The choice of the decision variables used in the mathematical programming model results in an objective function that is conceptually easy to understand and a solution method that is simple and straightforward.