Integer Nonlinear Optimization Problem Research Articles

Deep binary constraint hashing for fast image retrieval

With the development of deep hashing learning, several end-to-end deep architectures have been proposed for fast image retrieval. However, learning to hash is essentially a mixed integer nonlinear optimisation problem with the non-deterministic polynomial-time (NP)-hard nature, which makes the standard back-propagation algorithm infeasible. A novel pairwise loss function with additional binary constraint via siamese network is proposed to improve the representation ability of hash codes. Compared to previous works, we force the output of each hidden node close to −1 or +1, which can produce more compact and discriminative hash codes. Extensive experimental results demonstrate that the method can generate more favourable results than existing state-of-the-art hash function learning methods with large margins.

Parallel Canonical Differential Evolutionary Particle Swarm Optimization for Voltage and Reactive Power Control

Abstract This paper proposes parallel canonical differential evolutionary particle swarm optimization (C-DEEPSO) for voltage and reactive power control (Volt Var Control: VVC). The problem can be formulated as a mixed integer nonlinear optimization problem (MINLP) and various evolutionary computation techniques have been applied to the problem including PSO, differential evolution (DE), and DEEPSO. Since VVC is one of the on-line controls, speed-up of computation is required. Moreover, there is still room for improvement on solution quality. This paper proposes parallel C-DEEPSO in order to speed up the calculation and improve solution quality and applies it to a VVC problem. The proposed method is applied to IEEE 118 bus system. The results indicate that the proposed method can realize fast computation and minimize active power losses more than conventional evolutionary computation techniques.

Allocation of synchronous condensers for restoration of system short-circuit power

Modern power systems, employing an increasing number of converter-based renewable energy sources (RES) and decreasing the usage of conventional power plants, are leading to lower levels of short-circuit power and rotational inertia. A solution to this is the employment of synchronous condensers in the grid, in order to provide sufficient short-circuit power. This results in the increase of the short-circuit ratio (SCR) at transmission system bus-bars serving as points of interconnection (POI) to renewable generation. Evaluation of the required capacity and grid-location of the synchronous condensers, is inherently a mixed integer nonlinear optimization problem, which could not be done on manual basis considering each type of machine and all bus-bars. This study therefore proposes a method of optimal allocation of synchronous condensers in a hypothetic future scenario of a transmission system fed by renewable generation. Total cost of synchronous condenser installations in the system is minimized and the SCRs at the POIs of central renewable power plants are strengthened. The method has potential for application on larger grids, aiding grid-integration of RES.

Cost-Aware Big Data Processing Across Geo-Distributed Datacenters

With the globalization of service, organizations continuously produce large volumes of data that need to be analysed over geo-dispersed locations. Traditionally central approach that moving all data to a single cluster is inefficient or infeasible due to the limitations such as the scarcity of wide-area bandwidth and the low latency requirement of data processing. Processing big data across geo-distributed datacenters continues to gain popularity in recent years. However, managing distributed MapReduce computations across geo-distributed datacenters poses a number of technical challenges: how to allocate data among a selection of geo-distributed datacenters to reduce the communication cost, how to determine the Virtual Machine (VM) provisioning strategy that offers high performance and low cost, and what criteria should be used to select a datacenter as the final reducer for big data analytics jobs. In this paper, these challenges is addressed by balancing bandwidth cost, storage cost, computing cost, migration cost, and latency cost, between the two MapReduce phases across datacenters. We formulate this complex cost optimization problem for data movement, resource provisioning and reducer selection into a joint stochastic integer nonlinear optimization problem by minimizing the five cost factors simultaneously. The Lyapunov framework is integrated into our study and an efficient online algorithm that is able to minimize the long-term time-averaged operation cost is further designed. Theoretical analysis shows that our online algorithm can provide a near optimum solution with a provable gap and can guarantee that the data processing can be completed within pre-defined bounded delays. Experiments on WorldCup98 web site trace validate the theoretical analysis results and demonstrate that our approach is close to the offline-optimum performance and superior to some representative approaches.

Feasibility pump for aircraft deconfliction with speed regulation

We propose Feasibility Pump heuristics for the crucial problem of aircraft conflict avoidance arising in air traffic management. This problem can be modeled as a mixed integer nonlinear optimization problem, whose solution can be very computationally demanding. Feasibility Pump is an iterative algorithm that, at each iteration, solves alternatively two easier subproblems represented by relaxations of the original problem, minimizing the distance between their solutions. We propose in this paper specific formulations for the subproblems to be handled, tailored to the problem at hand. Numerical results show that, on the considered test problems, good-quality, in some cases optimal, feasible solutions are always obtained.

Day-Ahead Active Power Scheduling in Active Distribution Network Considering Renewable Energy Generation Forecast Errors

With large-scale integration of distributed energy resources (DERs), distribution networks have turned into active distribution networks (ADNs). However, management risks and obstacles are caused by this in due to renewable energy generation (REG) forecasting errors. In this paper, a day-ahead active power scheduling method considering REG forecast errors is proposed to eliminate the risks, minimize the costs of distribution companies and achieve optimal power flow. A hierarchical coordination optimization model based on chance constrained programming is established to realize day-ahead optimal scheduling of active power in ADNs coordinated with network reconfiguration, achieving an optimal solution of network topologies and DER outputs. The hierarchical method includes three levels: the first level provides initial values, and multiple iterations between the second and third level are used to solve the multi-period mixed integer nonlinear optimization problem. The randomness due to REG forecast errors is tackled with chance constrained programming in the scheduling procedure. The hybrid particle swarm optimization algorithm is employed to solve the proposed model. Simulation results verify the validity of the proposed method with an improved 33 nodes distribution network.

Design of component reliability test plan for a series system having time dependent testing cost with the presence of covariates

Consider a series system with n different components. Assume that the lifetime of \(i\text {-}th\) component follows exponential distribution with parameter \( \lambda _{i}(\mathbf {x}), \ \mathbf {x} \in \mathbb {R}^{k} \) is a covariate vector, \( 1\le i \le n \). For example, \( \mathbf {x} \) may be (temperature, pressure, humidity), so that \( \mathbf {x} \in \mathbb {R}^{3} \) represents a three dimensional covariate vector. Assume that each \( \lambda _{i}(\mathbf {x}),1\le i \le n \), is distinct and depends upon \( \mathbf {x} \) through linear relationship. Prior information available in the form of upper bounds on \( \lambda _{i}(\mathbf {x}) \) are also incorporated in the design. We propose to obtain optimal reliability test plan based on maximum likelihood estimator of system reliability. A non-linear integer optimization problem is formulated for minimizing the maximum of total expected cost involved in testing satisfying usual probability requirements (Type-I and Type-II error constraints). In addition, it is also established through simulation that the derived sampling plan meets the specified producer’s and consumer’s risks as well. A sensitivity analysis is carried out to study the effect of various input parameters on maximum total expected testing cost. Finally, a qualitative analysis is presented at the end to discuss the nature of sampling plan derived. Several numerical examples are discussed to illustrate our test plan, and it is observed that the proposed plan has significant potential to reduce the total number of components to be tested for failure. It is noted that the number of components to be tested for failure is reduced by about 96% as compared to the existing test plans in the literature.

Reliability test plan for a series system with variable failure rates

PurposeThis paper considers a series system consisting of n different components having unknown and variable failure rates, where the lifetime of components follow exponential distribution having non-constant failure rates. Moreover, the failure rates are bounded by above and are dependent on environmental factors such as temperature, pressure, through linear relationship. The purpose of this paper is to design a component reliability test plan for such a series system with an unknown variable failure rate.Design/methodology/approachThe reliability of the system is estimated with the help of the unbiased estimator of failure rate. The testing procedure is stopped when a fixed number of failures occur for each component.FindingsAn optimal reliability test plan is designed and the resultant non-linear integer optimization problem is formulated satisfying the constraints of producer’s and consumer’s risks. The obtained results are compared with the results available in the literature. Some examples are considered to illustrate the approach.Originality/valueIt is observed that use of prior information in the form of an upper bound and incorporation of environmental factors have the advantage of savings in the total testing cost.

Design of energy-Efficient timetables in two-way railway rapid transit lines

A methodology to design energy-efficient timetables in Rapid Railway Transit Networks is presented. Using an empirical description of the train energy consumption as a function of running times, the timetable design problem is modelled as a Mixed Integer Non-Linear optimization problem (MINLP) for a complete two-way line. In doing so, all the services in both directions along a certain planning horizon are considered while attending a known passengers’ demand. The MINLP formulation, which depends on train loads, is fully linearised supposing train loads are fixed. A sequential Mixed Integer Linear solving procedure is then used to solve the timetabling optimization problem with unknown train loads. The proposed methodology emphasizes the need of considering all the services running during the planning horizon when designing energy-efficient timetables, as consequence of the relationship among train speeds, frequency and fleet size of each line. Moreover, the convenience of considering the energy consumption as part of a broad objective function that includes other relevant costs is pointed out. Otherwise, passengers and operators could face up to an increase in the whole cost and a decrease in the quality of service. A real data scenario, based on the C-2 Line of the Madrid Metropolitan Railways, is used to illustrate the proposed methodology and to discuss the differences between the energy-efficient solutions and those obtained when considering operation and acquisition costs.

Reliability and Makespan Optimization of Hardware Task Graphs in Partially Reconfigurable Platforms

This paper addresses the problem of reliability and makespan optimization of hardware task graphs in reconfigurable platforms by applying fault tolerance (FT) techniques to the running tasks based on the exploration of the Pareto set of solutions. In the presented solution, in contrast to the existing approaches in the literature, task graph scheduling, tasks parallelism, reconfiguration delay, and FT requirements are taken into account altogether. This paper first presents a model for hardware task graphs, task prefetch and scheduling, reconfigurable computer, and a fault model for reliability. Then, a mathematical model of an integer nonlinear multi-objective optimization problem is presented for improving the FT of hardware task graphs, scheduled in partially reconfigurable platforms. Experimental results show the positive impacts of choosing the FT techniques selected by the proposed solution, which is named Pareto-based . Thus, in comparison to nonfault-tolerant designs or other state-of-the-art FT approaches, without increasing makespan, about 850% mean time to failure (MTTF) improvement is achieved and, without degrading reliability, makespan is improved by 25%. In addition, experiments in fault-varying environments have demonstrated that the presented approach outperforms the existing state-of-the-art adaptive FT techniques in terms of both MTTF and makespan.

SURE: A Novel Approach for Self Healing Battery Starved Users Using Energy Harvesting

Radio Frequency (RF) energy harvesting holds a promising future for energizing low power mobile devices in next generation wireless networks. Harvesting from a dedicated RF energy source acquires much more energy than simply harvesting from ambient RF sources. In this paper, novel Self-healing of Users equipment by RF Energy transfer scheme is introduced between the network operator and battery starved users to heal and extend their battery life time by sending dedicated energy from different sources in order to be aggregated and harvested by starved users. This approach depends on the concept of Energy as a Service where the network operator delivers energy to battery starved users in the next generation networks. A mixed integer non-linear optimization problem is formulated and solved efficiently using three heuristic algorithms. Simulation results prove that sufficient amounts of energy can be delivered to starved users while minimizing their uplink power requirements and guaranteeing a minimum uplink data rate.

Fractional 0–1 programming: applications and algorithms

We consider a class of nonlinear integer optimization problems commonly known as fractional 0---1 programming problems (also, often referred to as hyperbolic 0---1 programming problems), where the objective is to optimize the sum of ratios of affine functions subject to a set of linear constraints. Such problems arise in diverse applications across different fields, and have been the subject of study in a number of papers during the past few decades. In this survey we overview the literature on fractional 0---1 programs including their applications, related computational complexity issues and solution methods including exact, approximation and heuristic algorithms.

Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints

Optimal reactive power dispatch (ORPD) is well known as a complex mixed integer nonlinear optimization problem where many constraints are required to handle. In the last decades, many artificial intelligence-based optimization methods have been used to solve ORPD problem. But, these optimization methods lack an effective means to handle constraints on state variables. Thus, in this paper, the novel and feasible conditional selection strategies (CSS) are devised to handle constraints efficiently in the proposed improved gravitational search algorithm (GSA-CSS). In addition, considering the weakness of GSA itself, the improved GSA-CSS (IGSA-CSS) is presented which employs the memory property of particle swarm optimization (PSO) to enhance global searching ability and utilizes the concept of opposition-based learning (OBL) for optimizing initial population. The presented GSA-CSS and IGSA-CSS methods are applied to ORPD problem on IEEE14-bus, IEEE30-bus and IEEE57-bus test systems for minimization of power transmission losses (Ploss) and voltage deviation (Vd), respectively. The comparisons of simulation results reveal that IGSA-CSS provides better results and the improvements of algorithm in this work are feasible and effective.

Optimal dynamic formation control of multi-agent systems in constrained environments

We address the optimal dynamic formation problem in mobile leader–follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem. For the class of optimal formation problems where the objective is to maximize coverage, we show that the optimal formation is a tree which can be efficiently constructed without solving a MINLP. In a mission space constrained by obstacles, we separate the formation process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process.

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.

Integrated short‐term scheduling and production planning in an ethylene plant based on Lagrangian decomposition

AbstractA cracking furnace, which is the major unit involved in ethylene production, produces various petrochemical products ranging from ethylene to pitch and determines the production yield of an ethylene plant. It is essential to consider the operational performances of the cracking furnaces and to incorporate them into the whole plant's planning problem. Facing this challenge, this paper developed an optimization model, which integrates the scheduling problem of upstream cracking furnaces and the operational planning of the downstream units under a synchronized global time scale. Moreover, a modified Lagrangian decomposition algorithm is proposed for solving the large‐scale mixed integer nonlinear optimization problem. An industrial case study demonstrates the feasibility of the integrated model and the effectiveness of the solution algorithm.

Power control and clustering in heterogeneous cellular networks

Recently, it is widely believed that significant coverage and performance improvement can be achieved through the deployment of small cells in conjunction with the well-established macro cells. However, it is expected that the high density of base stations in such heterogeneous cellular networks will give rise to multiple design problems related to both co-tier (small-to-small) and cross-tier (between small and macro cells) interference. Fortunately, cooperation between base stations will play a major role to cope with these problems and hence to enhance the users’ data rates. In this paper, we consider a two-tier cellular network comprised of a macro cell underlaid with multiple small cells where both co-tier and cross-tier interference are taken into account. We study the scenario where the small cell base stations seek to maximize a common objective by forming multiple clusters through cooperation. These base stations have also to allocate power to their associated users and, at the same time, control the total aggregate interference caused to the macro cell user which has to be kept below a threshold prefixed by the macro cell base station. We consider two utility functions: the overall sum rate of the small cell network and the minimum data rate of the small cell users. We formulate the studied problems as mixed integer nonlinear optimization problems and we discuss their NP hardness. Therefore, due to the complexity of finding the optimal solution, we design heuristic algorithms which resolves efficiently the tradeoff between computational complexity and performance. We show through simulations that the designed heuristics approach the optimal solution (obtained using the complex exhaustive search algorithm) with highly reduced computational complexity.

Error bounds for mixed integer nonlinear optimization problems

We introduce a-posteriori and a-priori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the NLP relaxation of a mixed-integer nonlinear optimization problem. Our analysis mainly bases on the construction of a tractable approximation of the so-called grid relaxation retract. Under appropriate Lipschitz assumptions on the defining functions, we thereby generalize and slightly improve results for the mixed-integer linear case from Stein (Mathematical Programming, 2015, doi: 10.1007/s10107-015-0872-7 ). In particular, we identify cases in which the optimality and feasibility errors tend to zero at an at least linear rate for increasingly refined meshes.

A Heuristic Algorithm Based on Line-up Competition and Generalized Pattern Search for Solving Integer and Mixed Integer Non-linear Optimization Problems

THE GLOBAL OPTIMIZATION OF INTEGER AND MIXED INTEGER NON-LINEAR PROBLEMS HAS A LOT OF APPLICATIONS IN ENGINEERING. IN THIS PAPER A HEURISTIC ALGORITHM IS DEVELOPED USING LINE-UP COMPETITION AND GENERALIZED PATTERN SEARCH TO SOLVE INTEGER AND MIXED INTEGER NONLINEAR OPTIMIZATION PROBLEMS SUBJECTED TO VARIOUS LINEAR OR NONLINEAR CONSTRAINTS. DUE TO ITS ABILITY TO FIND MORE THAN ONE LOCAL OR GLOBAL OPTIMAL POINTS, THE PROPOSED ALGORITHM IS MORE BENEFICIAL FOR MULTI-MODAL PROBLEMS. THE PERFORMANCE OF THIS ALGORITHM IS DEMONSTRATED THROUGH SEVERAL NON-CONVEX INTEGER AND MIXED INTEGER OPTIMIZATION PROBLEMS EXHIBITING GOOD AGREEMENT WITH THOSE REPORTED IN THE LITERATURE. IN ADDITION, THE CONVERGENCE TIME IS COMPARED WITH LCAS€™ ONE DEMONSTRATING THE EFFICIENCY AND SPEED OF THE ALGORITHM. MEANWHILE, THE CONSTRAINTS ARE SATISFIED AFTER PASSING ONLY A FEW ITERATIONS.

Distributed generations planning using flower pollination algorithm for enhancing distribution system voltage stability

Abstract Distributed generations (DGs) have been utilized in some electric power networks. Power loss reductions, voltage improvement, increasing reliability, postponement of system upgrading and environmental friendliness are some advantages of DG-unit applications. This paper presents a new optimization approach that employs a flower pollination algorithm (FPA) to determine the optimal DG-unit’s size and location in order to minimize the total system real power loss and improve the system buses voltage. The FPA is a new metaheuristic optimization technique and it is inspired by the reproduction strategy of the flow pollination process of flowering plants. To reveal the validity of the FPA algorithm, IEEE 33-bus, 69-bus and 136-bus radial distribution test systems are examined with different test cases of the objective function using the MATLAB. Furthermore, the results obtained by the proposed FPA algorithm are compared with other metaheuristic optimization techniques such as backtracking search optimization algorithm, artificial bee colony, and selection algorithm. The outcomes verify that the FPA algorithm is efficient, robust, and capable of handling mixed integer nonlinear optimization problems.