Integer Programming Method Research Articles

Consumer phase identification in low-voltage distribution network considering vacant users

Accurate consumer phase connectivity in low-voltage distribution network (LVDN) plays a key role in maintaining high reliability of electricity supply and good power quality. However, vacant consumers, a lack of connectivity between feeders and consumers, and measurement error increase the difficulty to identify consumer phase connectivity for the existing data analytics methods. To overcome these hurdles, this paper proposes a novel consumer phase identification (CPI) algorithm based on consumer classification, quadratic programming, and probability distribution. Firstly, a consumer classification method based on voltage characteristics among users is proposed to deal with the vacant user problem. Then, a quadratic programming model based on Nodal Current Law is established to identify consumer phase when the network connectivity information between feeders and consumers is lack. Moreover, in order to improve robustness of the proposed phase identification algorithm on measurement error, a Monte Carlo probability distribution model is developed. The proposed algorithm is applied on a real-world LVDN in Guangdong. The comparison analysis between the proposed method and the Mix Integer Programming (MIP) method, and the impact of the variation rate threshold of correlation coefficient on the identification accuracy are also investigated. The results indicate that the proposed method effectively increases CPI accuracy compared with the MIP method when there are vacant users and measurement error of meters in LVDN.

Ascent with quadratic assistance for the construction of exact experimental designs

In the area of statistical planning, there is a large body of theoretical knowledge and computational experience concerning so-called optimal approximate designs of experiments. However, for an approximate design to be realizable, it must be converted into an exact, i.e., integer, design, which is usually done via rounding procedures. Although rapid, rounding procedures often yield worse exact designs than heuristics that do not require approximate designs at all. In this paper, we build on an alternative principle of utilizing optimal approximate designs for the computation of optimal, or nearly-optimal, exact designs. The principle, which we call ascent with quadratic assistance (AQuA), is an integer programming method based on the quadratic approximation of the design criterion in the neighborhood of the optimal approximate information matrix. To this end, we present quadratic approximations of all Kiefer’s criteria with an integer parameter, including D- and A-optimality and, by a model transformation, I-optimality. Importantly, we prove a low-rank property of the associated quadratic forms, which enables us to use AQuA efficiently and apply it to large design spaces. We numerically demonstrate the robustness and superior performance of the proposed method for selected statistical models under various types of experimental constraints. We also show how can iterative application of AQuA be used for a stratified information-based subsampling of large datasets under a lower bound on the quality and an upper bound on the cost of the subsample.

An energy storage capacity optimization method based on partition

With the vision of large-scale deployment of grid-connected distributed energy storage system (ESS) in the distribution network, it is necessary to study the capacity optimization of ESS for striking a balance among investment, renewable energy (RE) consumption, power supply security and price arbitrage. In this paper, an ESS partition model based on the improved flame propagation model is proposed. The results of ESS partition are obtained by constructing indexes such as the flammability of nodes, the wind direction of flame propagation, and the speed of flame propagation. Then, an optimization method for ESS capacity in partition is established, which is to maximize the annual net profit and the integer programming method is used to solve the model. Finally, the effectiveness and feasibility of the method are verified by conducting case studies on the IEEE 33 bus distribution network system. The case study results show that the rational configuration of ESS capacity can improve the economy of planning, and the proposed method can improve the Photovoltaic (PV) local consumption ability and power supply reliability of distribution network.

Time/sequence-dependent scheduling: the design and evaluation of a general purpose tabu-based adaptive large neighbourhood search algorithm

In intelligent manufacturing, it is important to schedule orders from customers efficiently. Make-to-order companies may have to reject or postpone orders when the production capacity does not meet the demand. Many such real-world scheduling problems are characterised by processing times being dependent on the start time (time dependency) or on the preceding orders (sequence dependency), and typically have an earliest and latest possible start time. We introduce and analyze four algorithmic ideas for this class of time/sequence-dependent over-subscribed scheduling problems with time windows: a novel hybridization of adaptive large neighbourhood search (ALNS) and tabu search (TS), a new randomization strategy for neighbourhood operators, a partial sequence dominance heuristic, and a fast insertion strategy. Through factor analysis, we demonstrate the performance of these new algorithmic features on problem domains with varying properties. Evaluation of the resulting general purpose algorithm on three domains—an order acceptance and scheduling problem, a real-world multi-orbit agile Earth observation satellite scheduling problem, and a time-dependent orienteering problem with time windows—shows that our hybrid algorithm robustly outperforms general algorithms including a mixed integer programming method, a constraint programming method, recent state-of-the-art problem-dependent meta-heuristic methods, and a two-stage hybridization of ALNS and TS.

Virtual reality-based decision support model for interior design and decoration of an office building

Purpose The purpose of this paper is to develop a virtual reality (VR)-based and user-oriented decision support system for interior design and decoration. The four-phase decision-making process of the system is verified through a case study of an office building. Design/methodology/approach Different “spatial layouts” are presented by VR for users to decide their preference (Phase 1). According to the selected spatial layout, a “spatial scene” is constructed by VR and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to determine the spatial scene preference (Phase 2). Based on the binary integer programming method, the system provides the optimal preliminary solution under a limited decoration budget (Phase 3). Finally, the consistency between the overall color scheme and pattern is fine-tuned by VR in order to obtain the final solution (Phase 4). Findings The questionnaire survey results show that decision makers generally affirm the operation and application of VR, and especially recognize the advantages in the improvement of VR-based interior design feasibility, communication efficiency and design decision-making speed. The optimization of the costs and benefits enables decision makers to effectively evaluate the impact of design decisions on subsequent project implementation during the preliminary design process. Originality/value The VR-based decision support system for interior design retains the original immersive experience of VR, and offers a systematic multiple criteria decision- making and operations research optimization method, thus, providing more complete decision-making assistance. Compared with traditional design communication, it can significantly reduce cognitive differences and improve decision-making quality and speed.

Energy Market Management for Distribution Network with a Multi-Microgrid System: A Dynamic Game Approach

This paper proposes an energy market management framework to address the day-ahead optimization of a distribution network (DN) with a multi-microgrid (MMG). In this framework, an economic optimization based on a dynamic game is designed to ensure the reliability and stability of the DN operation while setting the internal transaction price to minimize the operation cost of the distribution network operator (DNO). The DNO, as a leader, sets the power flow constraints and microgrid operators (MGOs), as followers, respond to the internal transaction price and in turn affect the DNO’s price decision. The price incentive mechanism of the DNO is to encourage MGs to participate in energy market management, to promote joint operation of MGs and to reduce the operation cost of MGOs. The differential evolution algorithm and mixed integer programming method are applied to find the equilibrium solution to the dynamic game. Numerical simulations of a modified IEEE 33-bus system show the effectiveness of the proposed energy market management framework.

Technique for optimization of diagnostic parameters composition for power systems objects

A technique is proposed for optimization the composition of diagnostic parameters based on a combination of heuristic algorithms with the method of linear integer programming. The solution obtained using the heuristic algorithm with relatively small consumption of computational resources is taken as an initial one for optimization or checking the optimality of the composition of parameters using the linear integer programming method. The combination of a heuristic algorithm with the method of linear integer programming saves significant computational resources when searching for the optimal solution. The technique is aimed at minimizing costs when creating diagnostic support for monitoring performance and failure detection when considering the serviced and reconstructed electronic devices and equipment of power systems.

An integer programming method for the design of multi-criteria multi-action conservation plans

The design of conservation management plans is a crucial task for ensuring the preservation of ecosystems. A conservation plan is typically embodied by two types of decisions: in which areas of a given territory it will be implemented, and how actions against threats will be deployed across these areas. These decisions are usually guided by the resulting ecological benefit, their spatial effectiveness, and their implementation cost.In this paper, we propose a multi-criteria optimization framework, for modeling and solving a mixed integer programming characterization of a multi-action and multi-species conservation management design problem. The optimization tool seeks for a management plan that maximizes ecological benefit and minimizes spatial fragmentation, simultaneously, while ensuring an implementation cost no greater than a given budget.For showing the effectiveness of the methodology, we consider a case study corresponding to a portion of the Mitchell river catchment, located in northern Australia, where 31 freshwater fish species are affected by four threats.The attained results show how the methodology exploits the trade-offs among the ecological, spatial and cost criteria, enabling decision-makers to explore and analyze a broad range of conservation plans. Selecting conservation plans in a more informed way allows to obtain the best outcomes from a strategic and operational point of view.

Optimizing inspection routes in pipeline networks

Maintaining an aging network is a challenge for many water utilities due to limited budgets and uncertainty surrounding the physical condition of buried pipeline assets. The deployment of robotic inspections provides high quality data, but these platforms have limited use due to cost and operational constraints. To facilitate cost-efficient inspections, operators need to identify high-risk assets while accounting for the effectiveness of the tools at hand. This paper addresses inspection planning with the goal of finding an optimal route while considering tool limitations. An exact integer programming formulation is presented where only three factors are used to characterize tool constraints. Two classes of solution methods are explored: 1) tree based searches, and 2) integer programming. This paper demonstrates how each method can be used to identify optimal paths within a real water distribution system. Empirical trials suggest that tree-based search methods are the most efficient when the path limit is short, but do not scale well when the path length increases. In contrast, integer-programming methods are more effective for longer path lengths but have scalability issues for large network sizes. Data preprocessing, where the input network size is reduced, can provide large computation time reductions while returning near-optimal solutions.

Determining [formula omitted]- and [formula omitted]-robustness of digraphs using mixed integer linear programming

There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of r- and (r,s)-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers r and s are sufficiently large. However, determining an arbitrary graph’s robustness is a highly nontrivial problem. This paper introduces a novel method for determining the r- and (r,s)-robustness of digraphs using mixed integer linear programming; to the best of the authors’ knowledge it is the first time that mixed integer programming methods have been applied to the robustness determination problem. The approach only requires knowledge of the graph Laplacian matrix, and can be formulated with binary integer variables. Mixed integer programming algorithms such as branch-and-bound are used to iteratively tighten the lower and upper bounds on r and s. Simulations are presented which compare the performance of this approach to prior robustness determination algorithms.

Control model of technological operations of mounting automatic printed circuit boards based on a multiparameter fuzzy classifier

In the context of creating digital production, ensuring the concept of continuous support for the product life cycle and the use of big data management systems contributes to the creation of a permanent relationship between all computer-aided design systems implemented at the enterprise. The purpose of the article is to develop a procedure for ensuring the quality of electronic products based on the introduction of intelligent equipment for automatic installation of printed circuit boards based on a multiparameter self-learning fuzzy classifier. To solve the problems of interfacing big data management systems and modern computer-aided design systems, it is proposed to apply the methods of discrete linear or mixed integer programming. Application of logical operations will allow one to simulate the production process in more detail and predict possible disturbances with maximum accuracy.

User Association and Path Planning for UAV-Aided Mobile Edge Computing With Energy Restriction

Mobile edge computing (MEC) provides computational services at the edge of networks by offloading tasks from user equipments (UEs). This letter employs an unmanned aerial vehicle (UAV) as the edge computing server to execute offloaded tasks from the ground UEs. We jointly optimize user association, UAV trajectory, and uploading power of each UE to maximize sum bits offloaded from all UEs to the UAV, subject to energy constraint of the UAV and quality of service (QoS) of each UE. To address the non-convex optimization problem, we first decompose it into three subproblems that are solved with integer programming and successive convex optimization methods respectively. Then, we tackle the overall problem by the multi-variable iterative optimization algorithm. Simulations show that the proposed algorithm can achieve a better performance than other baseline schemes.

Finance-based scheduling using integer programming method for building construction project in Jakarta

Construction project management consists of planning, scheduling, and controlling. Planning is important because it’s set down the target of project to achieve successfulness. Successfulness of a project consists of several aspects, including: cost, quality, time, and HSE (Health, Safety, and Environment). In many cases, scheduling is optimized with minimum costs for achieving a project’s goal. This doesn’t necessarily guarantee that contactors can provide the budget according to the scheduling. This paper will focus on optimizing scheduling by considering financial capabilities. The method used to optimize scheduling by considering financial capabilities is called Finance-based Scheduling Method. The stages to do finance-based scheduling method, are: arranging initial scheme, arranging extension scheme, and formulating an integer programming model. This study have purpose to obtain optimal scheduling by considering contractor’s financial capabilities. Analysis of this study uses integer programming to find the most optimal solution. However, integer programming requires different modeling for each case and result from it must be simplifying become a bar chart so it’s make easier to understand.

Optimal and fast sensor geometry design method for TDOA localisation systemswith placement constraints

The sensor geometry design problem of time difference of arrival (TDOA) localisation systems based on Cramer-Rao bound is studied. Sensor placement constraints are considered, which means the available placement area is limited. This makes sensor geometry design a sensor selection problem. In two-dimensional (2D) TDOA localisation or 3D TDOA localisation on the earth surface, sensor selection can be implemented through solving a fractional integer programming problem. However, traditional fractional integer programming methods are either suboptimal or too time consuming. For this reason, a new method named path-varying sphere decoding is proposed in two steps. In step one, the programming problem is relaxed into two sphere decoding (SD) subproblems. Solving these subproblems leads to the optimal solution, and the required computational complexity is much less than those of traditional optimal methods. In step two, the structure of the cost function is explored. This makes it possible to calculate the path-varying upper-bound of a quadratic function. Thus the quadratic function constraint used in one SD subproblem becomes tighter and the calculation speed is enhanced. Theory analyses and simulation results show that the proposed method is not only optimal but also much faster than traditional optimal methods when solving large-scale programming problems.

An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets

A new exact algorithm for bi-objective linear integer problems is presented, based on the classic ϵ-constraint method and algebraic test sets for single-objective linear integer problems. Our method provides the complete Pareto frontier N of non-dominated points and, for this purpose, it considers exactly |N| single-objective problems by using reduction with test sets instead of solving with an optimizer. Although we use Gröbner bases for the computation of test sets, which may provoke a bottleneck in principle, the computational results are shown to be promising, especially for unbounded knapsack problems, for which any usual branch-and-cut strategy could be much more expensive. Nevertheless, this algorithm can be considered as a potentially faster alternative to IP-based methods when test sets are available.

A Variable Reduction Method for Large-Scale Unit Commitment

Efficient solution methods for large-scale unit commitment (UC) problems have long been an important research topic and a challenge, especially in market clearing computation. For large-scale UC, the Lagrangian relaxation methods (LR) and the mixed integer programming methods (MIP) are most widely adopted. However, LR usually suffers from slow convergence; and the computational burden of MIP is heavy when the binary variable number is large. In this paper, a variable reduction method is proposed. First, the time-coupled constraints in the original UC problem are relaxed, and many single-period UC problems (s-UC) are obtained. Second, LR is used to solve the s-UCs. Different from traditional LR with iterative subgradient method, the optimal multipliers and the approximate UC solutions of the s-UCs are obtained by solving linear programs. Third, a criterion for choosing and fixing the UC variables in the UC problem is established; hence, the number of binary variables is reduced. Finally, the UC with reduced binary variables is solved to obtain the final UC solution. The proposed method is tested on the IEEE 118-bus system and a 6484-bus system. The results show the method is very efficient and effective.

Modeling and Solution Techniques Used for Hydro Generation Scheduling

The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.

A combinatorial approach to determine earthquake magnitude distributions on a variable slip-rate fault

SUMMARYCombinatorial methods are used to determine the spatial distribution of earthquake magnitudes on a fault whose slip rate varies along strike. Input to the problem is a finite sample of earthquake magnitudes that span 5 kyr drawn from a truncated Pareto distribution. The primary constraints to the problem are maximum and minimum values around the target slip-rate function indicating where feasible solutions can occur. Two methods are used to determine the spatial distribution of earthquakes: integer programming and the greedy-sequential algorithm. For the integer-programming method, the binary decision vector includes all possible locations along the fault where each earthquake can occur. Once a set of solutions that satisfy the constraints is found, the cumulative slip misfit on the fault is globally minimized relative to the target slip-rate function. The greedy algorithm sequentially places earthquakes to locally optimize slip accumulation. As a case study, we calculate how earthquakes are distributed along the megathrust of the Nankai subduction zone, in which the slip rate varies significantly along strike. For both methods, the spatial distribution of magnitudes depends on slip rate, except for the largest magnitude earthquakes that span multiple sections of the fault. The greedy-sequential algorithm, previously applied to this fault (Parsons et al., 2012), tends to produce smoother spatial distributions and fewer lower magnitude earthquakes in the low slip-rate section of the fault compared to the integer-programming method. Differences in results from the two methods relate to how much emphasis is placed on minimizing the misfit to the target slip rate (integer programming) compared to finding a solution within the slip-rate constraints (greedy sequential). Specifics of the spatial distribution of magnitudes also depend on the shape of the target slip-rate function: that is, stepped at the section boundaries versus a smooth function. This study isolates the effects of slip-rate variation along a single fault in determining the spatial distribution of earthquake magnitudes, helping to better interpret results from more complex, interconnected fault systems.

Study on optimization algorithm of tuned mass damper parameters to reduce vehicle-bridge coupled vibration

A vehicle-bridge tuned mass damper (TMD) coupled dynamic analysis and vibration-control model was established to optimize TMD damping effects on a steel-box girder bridge bearing vehicle loads. It was also used to investigate optimization efficiency of different algorithms in TMD design parameters. This model simulated bridges and vehicles with the use of a 7 degrees of freedom curved-beam element model and a 7 degrees of freedom vehicle model, respectively. The TMD system was simulated with the use of multiple rigid-body systems linked with springs and dampers. Road surface condition, as a vibration source, was simulated with the use of a frequency equivalent method based on a power spectrum. A variably-accelerated pattern search algorithm was proposed in line with the initial TMD parameters calculated by Den Hartog formula. Visual software was compiled by Fortran and used for an optimization study of vibration reduction. A three-span, curved, continuous steel-box girder bridge was used as the numerical example. Optimized effects and computational efficiency of vibration reduction under different methods were compared. The comparison included a single variable optimization based on Den Hartog formula, an ergodic search method, an integer programming method, a traditional genetic algorithm, a traditional pattern search algorithm, and a variably-accelerated pattern search algorithm. The results indicate that variably-accelerated pattern search algorithm is more efficient at improving TMD optimal parameter design. Final TMD parameter optimization values obtained by different methods are quite close to each other and tends verify the reliability of the optimization results.

Control Algorithm Using a Revised MIP Method to Deal with Livelocks in S4R of Petri Nets

Livelocks, like deadlocks, can result in serious results in running process of flexible manufacturing systems (FMSs). Current deadlock control policies (DCPs) based on mixed integer programming (MIP) cannot detect siphons that cause and cope with livelocks in Petri nets. This study proposes a revised mixed integer programming (RMIP) method to directly solve the new smart siphons (NSSs) associated with livelocks in a system of sequential systems with shared resources (S4R), a typical subclass of generalized Petri net models. Accordingly, the solved NSSs are max’-controlled by adding the corresponding control places (CPs). As a result, an original S4R system with livelocks can be converted into the live controlled Petri net system. The related theoretical analysis and an example are given to demonstrate the proposed RMIP and the corresponding control algorithm (CA).