Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.

An Exact Virtual Network Embedding Algorithm Based on Integer Linear Programming for Virtual Network Request with Location Constraint

Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.

Short-Term Scheduling of Combined Cycle Units Using Mixed Integer Linear Programming Solution

Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes based on the number of combustion and steam turbines. In this paper a model CCs based on a mixed integer linear programming approach to be included into an optimal short term resource optimization problem is presented. The proposed method allows modeling of CCs in different modes of operation taking into account the non convex operating costs for the different combined cycle mode of operation.

A new heuristic algorithm for general integer linear programming problems

A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of assistant sets, an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane. A simple numerical example shows that the algorithm is efficient for some problems, and therefore, of practical interest.

Revision of stratified OWL ontologiesbased on integer linear programming

To revise stratified web ontology language(OWL)ontologies,the kernel revision operator is extended by defining novel conflict stratification and the incision function based on integer linear programming(ILP).The ILP-based model considers an optimization problem of minimizing a linear objective function which is suitable for selecting the minimal number of axioms to remove when revising ontologies.Based on the incision function,a revision algorithm is proposed to apply ILP to all minimal incoherence-preserving subsets(MIPS).Although this algorithm can often find a minimal number of axioms to remove,it is very time-consuming to compute MIPS.Thus,an adapted revision algorithm to deal with unsatisfiable concepts individually is also given.Experimental results reveal that the proposed ILP-based revision algorithm is much more efficient than the commonly used algorithm based on the hitting set tree.In addition,the adapted algorithm can achieve higher efficiency,while it may delete more axioms.

Application of Optimization Principle in Landmark University Project Selection under Multi-Period Capital Rationing Using Linear and Integer Programming

The current structure of Landmark University (LU) was induced by raising a generation of solution providers through a qualitative and life-applicable training system that focuses on values and creative knowledge by making it more responsive and relevant to the modern-day demands of demonstration, industrialization and development. The challenge facing Landmark University is the question of which of its numerous projects they should invest to give maximum output with minimum input. In this paper, we maximize the Net Present Value (NPV) and maintain the net discount cash overflow of each project per period as contained and extracted as the secondary data of cash inflows of the Landmark University (LU) monthly financial statement and annual reports from 2012 to 2017 of which the documents have been regrouped as small and large scale projects as many enterprises make more use of the trial-and-error method and as such firms have been finding it difficult in allocating scarce resources in a manner that will ensure profit maximization and/or cost minimization with a simple and accurate decision making by the company through an optimization principle in selecting LU project under multi-period capital rationing using linear programming (LP) and integer programming (IP). The annual net cash flow which is the difference between the cash inflows and cash outflows during each period for the project was estimated and recorded. The discount factors were estimated at cost of capital of 10% for each cash flow per period with the corresponding NPV at 10% which revealed that the optimal decision achieves maximum returns of $110 × 102 and this assisted the project manager to select a large number of the variable projects that can maximize the profit which is far better than relying on an ad-hoc judgmental approach to project investment that could have cost 160 × 102 for the same project. Sensitivity analysis on the project parameters are also carried out to test the extent to which project selection is sensitive to changes in the parameters of the system revealed that a little reduction and or addition of reduced cost by certain amount or percentages to its corresponding coefficient in the objective function effect no changes in the shadow prices with solution values for variables (x1), (x4), (x5) and the optimal objective function.

Multi-Document Summarization Model Based on Integer Linear Programming

This paper proposes an extractive generic text summarization model that generates summaries by selecting sentences according to their scores. Sentence scores are calculated using their extensive coverage of the main content of the text, and summaries are created by extracting the highest scored sentences from the original document. The model formalized as a multiobjective integer programming problem. An advantage of this model is that it can cover the main content of source (s) and provide less redundancy in the generated sum- maries. To extract sentences which form a summary with an extensive coverage of the main content of the text and less redundancy, have been used the similarity of sentences to the original document and the similarity between sentences. Performance evaluation is conducted by comparing summarization outputs with manual summaries of DUC2004 dataset. Experiments showed that the proposed approach outperforms the related methods.

A mixed integer linear programming approach for municipal solid waste management

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Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Solving Integer Programming by Evolutionary Soft Agent

Many practical problems in commerce and industry involve finding the best way to allocate scarce resources a-mong competing activities. This paper focuses on the problem of integer programming, and describes an evolutionary soft a-gent model to solve it. In proposed model, agent is composed of three components: goal, environment and behavior. Experimental shows the model has the characters of parallel computing and goal driving.

Integer Programming Formulations for Maximum Lifetime Broadcasting Problems in Wireless Sensor Networks

Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.

The Linear Formulation of Thermal Unit Commitment Problem with Uncertainties through a Computational Mixed Integer

The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.

An Integer Programming Approach for Scheduling a Professional Sports League

This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.

Improved Balas and Mazzola Linearization for Quadratic 0-1 Programs with Application in a New CuttingPlane Algorithm

Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.

A Hybrid Dynamic Programming Method for Concave Resource Allocation Problems

Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.

耦合调峰与通航需求的梯级水电站群短期多目标优化调度的MILP方法

电网调峰任务与河道通航需求间的矛盾是水电航运梯级调度时所面临的突出问题,区间回水的顶托作用增大了该问题的复杂性。建立考虑回水影响的梯级水电站群短期多目标优化调度的混合整数线性规划模型,模型以剩余负荷平均距与下游尾水位平均距最小为目标,在将非线性约束通过函数聚合后,利用六面体栅格化技术与第二类特殊有序集约束方法实现该约束的线性化。利用法线边界交叉方法对模型进行求解。算例结果表明,所提方法可以充分计及回水顶托的影响,兼顾调峰与通航需求,高效求解多目标调度问题并获得较理想的结果。

基于FT-MILP算法的大规模水电中长期优化调度研究

随着国内水利事业的快速发展,水电系统规模不断扩大,已有的模型设计通用性不强,优化调度维数灾问题日益凸显。为此,采用森林结构(FT)描述水电站群拓扑结构,利用混合整数线性规划算法(MILP)对模型中非线性函数进行分段线性插值处理,构建了基于FT-MILP算法的大规模水电系统中长期优化调度模型。以我国四川地区大型水电基地277座水电站为例,将所提FT-MILP算法与传统POA算法进行优化调度计算,并将优化调度结果与实际运行结果相比。结果表明,在丰、平、枯水年,大规模水电场景下,FT-MILP算法的水库群总发电量分别为传统POA算法的99.27%、99.14%、99.55%,计算效率约为传统POA算法的20倍,丰枯电量比分别由实际运行的2.26∶1、2.13∶1、1.98∶1减少为1.79∶1、1.70∶1、1.62∶1。因此FT-MILP算法在牺牲少量理论发电效益的同时,大幅缩短了计算耗时,且优化了丰枯出力结构,对于研究我国巨大规模的水电优化调度问题有一定的借鉴意义。

Detection of gross errors using mixed integer optimization approach in process industry

A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper. Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information cri- terion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP) approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.

分组密码复杂线性层可分性传播的MILP刻画方法

混合整数线性规划(MILP)作为一种自动化搜索工具,被广泛地应用于搜索分组密码的差分、线性、积分等密码性质.提出一种基于动态选取策略构建MILP模型的新技术,该技术在不同的条件下采用不同的约束不等式刻画密码性质的传播.具体地,从可分性出发根据输入可分性汉明重量的不同,分别采用不同的方法构建线性层可分性传播的MILP模型.最后,将该技术应用于搜索uBlock和Saturnin算法的积分区分器.实验结果表明:对于uBlock128算法,该技术可以搜索到比之前最优区分器多32个平衡比特的8轮积分区分器.除此之外,搜索到uBlock128和uBlock256算法比之前最优区分器更长一轮的9和10轮积分区分器.对于Saturnin256算法,同样搜索到比之前最优区分器更长一轮的9轮积分区分器.

基于MILP的轻量级密码算法ACE与SPIX的线性分析

研究了轻量级密码算法ACE与SPIX的线性性质.给出了环型与门组合结构精确的混合整数线性规划下的线性性质刻画,并将算法ACE与SPIX的非线性操作转化为环型与门组合.基于此构建了ACE置换与SLISCP置换的混合整数线性规划下的线性模型,求解模型得到了2至4步ACE置换与2至5步SLISCP置换最优的线性迹.证明了7步、12步ACE置换分别达到了128比特与320比特的安全目标,7步、13步SLISCP置换分别达到了128比特与256比特的安全目标.对于任意步数的ACE置换与SLISCP置换,认证加密算法ACE-AE-128与SPIX均能够抵抗明文处理阶段的线性区分攻击.