Mixed-integer Nonlinear Problem Research Articles

Bookings in the European gas market: characterisation of feasibility and computational complexity results

As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special long-term capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookings-namely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.

Power Allocation and Co-Design of Multicarrier Communication and Radar Systems for Spectral Coexistence

This paper explores multicarrier waveforms to improve the spectrum efficiency of radar and communication systems that cooperatively coexist in the same bandwidth. We propose two joint design paradigms based on sharing and allocation, respectively. The allocation-based design brings in the advantage of interference avoidance and easy implementation, while the sharing-based joint design offers additional gain in spectrum efficiency. For both design paradigms, the communication throughput is maximized under a minimum signal-to-interference-plus-noise ratio (SINR) constraint for the radar along with power constraints. The sharing-based design involves non-convex optimization, which is solved via an alternating direction sequential convex programming (AD-SCP) approach. Meanwhile, the allocation-based design is a mixed integer nonlinear optimization problem, which is solved by the optimum but computationally prohibitive branch and bound algorithm, as well as a suboptimum penalized SCP method. Numerical results show that the proposed joint design paradigms significantly improve the spectrum efficiency over a conventional greedy search based allocation scheme.

Robust energy-efficient power allocation and relay selection for cooperative relay networks

One of the challenging issues in wireless relay networks is to choose the appropriate relays while keeping acceptable requirement of quality of service. In this paper, a joint optimal scheme of power allocation and relay selection is proposed for the decode-and-forward (DF) relay communication networks. The proposed scheme attempts to maximize the total energy-efficiency of the system. The cooperative relay and orthogonal-frequency-division-multiple-access (OFDMA) technologies are introduced to improve the spectral efficiency. In order to reduce the effect caused by channel uncertainty, a robust power control approach based on worst-case is applied. The formulated problem is a mixed-integer nonlinear problem, which is difficult to solve in the original form. Therefore, a novel relay selection scheme is formulated to transform it into a quasi-concave programming problem. The Dinkelbach method is used to solve the formulated optimization problem. Besides, a distributed iteration algorithm is developed to reduce the overhead of information exchange. Numerical results reveal the effectiveness of the proposed scheme and show better performance in aspect of outage reduction and energy efficiency improvement.

DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems

Nonconvex optimization problems, such as those often seen in chemical engineering applications due to integer decisions and inherent system physics, are known to scale poorly with problem size. Decomposition methods, such as Benders or Lagrangean decomposition, offer much promise for improving solution efficiency. However, automatically identifying subproblems for use with these solution methods remains an open problem. Herein, a general algorithmic framework entitled Detection of Communities for Optimization Decomposition (DeCODe) is presented. DeCODe uses community detection, a concept originating from network theory, to generate optimization subproblems which are strongly interacting within individual subproblems but weakly interacting between different ones. The importance of communities in solving problems using decomposition solution methods is showcased via a least squares regression problem. The ability of DeCODe to identify nontrivial decompositions of optimization problems is demonstrated through a large renewable energy and chemical production optimal design problem and two mixed integer nonlinear program test problems.

Device vs Edge Computing for Mobile Services: Delay-Aware Decision Making to Minimize Power Consumption

A promising technique to provide mobile applications with high computation resources is to offload the processing task to the cloud. Utilizing the abundant processing capabilities of the clouds, mobile edge computing enables mobile devices with limited batteries to run resource hungry applications and to save power. However, it is not always true that edge computing consumes less power compared to device computing. It may take more power for the mobile device to transmit a file to the cloud than running the task itself. This paper investigates the power minimization problem for the mobile devices by data offloading in multi-cell multi-user OFDMA mobile edge computing networks. We consider the maximum acceptable delay as QoS metric to be satisfied in our network. We formulate the problem as a mixed integer nonlinear problem which is converted into a convex form using D.C. approximation. To solve the converted optimization problem, we have proposed centralized and distributed algorithms for joint power allocation and channel assignment together with decision-making. Simulation results illustrate that by utilizing the proposed algorithms, considerable power savings can be achieved, e.g., about 60 percent for large bit stream size compared to local computing baseline.

An Evaluation of Inventory System via Evidence Theory for Deteriorating Items under Uncertain Condition and Advanced Payment

The inventory model for deteriorating items, which is developed by The Evidential Reasoning Algorithm (ERA) and the imprecise inventory costs, is one of the most important factors in complex systems which plays a vital role in Payment. The ERA is able to strengthen the precision of the model and give the perfect interval-valued utility. In this model, during lead-time and reorder level two different cases can be happened which the mathematical model turns into an imposed nonlinear mixed integer problem with interval objective for each case. Placement of an order, which is overlooked by many researchers till now, is normally connected with the advance payment (AP) in business. Specifying the optimal profit and the optimal number of cycles in the finite time horizon and lot-sizing in each cycle, are our goals so. In order to solve this model, we apply the real-coded genetic algorithm (RCGA) with ranking selection. By the model, we represent some numerical examples and also a sensitivity analysis with the variation of different inventory parameters.

A swarm intelligence-based approach for reliability–redundancy allocation problems

This paper presents a new algorithm belonging to the class of swarm intelligence methods, called the adaptive simplified PSO (ASPSO)-based algorithm, for solving reliability–redundancy allocation problems. In this constrained nonlinear mixed-integer problem, both the number of redundant components and their reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The proposed ASPSO operates with a new updating model to adjust the position of particles, without dealing with velocity. In addition, a randomization technique, based on the dispersion of particle bests through the search space, is used to speed up the convergence of the proposed approach and prevent it from being trapped within the local optimum. Moreover, to control the balance between exploration and exploitation, during the search process, two adaptive functions are utilized. The simulation results of four different benchmarks for the reliability–redundancy allocation problem are reported and compared. Accordingly, the solutions given by the new presented approach are all superior to those best known solutions provided by several methods in the literature.

Cost minimization of large-scale infrastructure for electricity generation and transmission

Electricity infrastructure confronts societies with immense costs as it must ensure the generation of power and its transmission to locations with consumption requirements. We minimize these costs by formulating an electricity generation and transmission problem that facilitates the design of electricity infrastructure on a macro level. Our problem specifies the capacity, type, and location of power plants and, at the same time, determines the appropriate arrangement of high-voltage transmission lines in order to fulfill the demand of individual cities. We specifically incorporate the non-linear nature of cost functions for power generation that are common in practice. This results in a mixed integer non-linear problem, for which the branch-and-reduce solver from GAMS exceeds runtime constraints, even for small instances with 25 locations. As a remedy, we develop heuristics based on the reduced variable neighborhood search and the greedy randomized adaptive search procedure (GRASP). Their performance enables us to address large-scale problems that arise in real-world applications. We demonstrate this with an actual, nationwide example that spans all 4537 municipalities in Germany.

Cost Minimization of Large-Scale Infrastructure for Electricity Generation and Transmission

Electricity infrastructure confronts societies with immense costs as it must ensure the generation of power and its transmission to locations with consumption requirements. We minimize these costs by formulating an electricity generation and transmission problem that facilitates the design of electricity infrastructure on a macro level. Our problem specifies the capacity, type, and location of power plants and, at the same time, determines the appropriate arrangement of high-voltage transmission lines in order to fulfill the demand of individual cities. We specifically incorporate the non-linear nature of cost functions for power generation that are common in practice. This results in a mixed integer non-linear problem, for which the branch-and-reduce solver from GAMS exceeds runtime constraints, even for small instances with 25 locations. As a remedy, we develop heuristics based on the reduced variable neighborhood search and the greedy randomized adaptive search procedure (GRASP). Their performance enables us to address large-scale problems that arise in real-world applications. We demonstrate this with an actual, nationwide example that spans all 4,537 municipalities in Germany.

Road network pricing and design for ordinary and hazmat vehicles: Integrated model and specialized local search

In the context of vehicle transportation in congested roads, we propose an optimization framework to integrate the operator decisions on network pricing, regulation, and expansion, while accounting for the shipments of hazardous materials. Current research trends only provide partial modeling integrations of the well-known toll optimization, hazmat transportation, and network design problems. However, the growing complexity of traffic management requires a stronger coordination in the operator decisions. In this paper, a mixed-integer non-linear bi-level problem is introduced to model this integration. The model considers a road network operator (acting as a leader), who maximizes its profit –the toll income minus the costs from roads construction and risk exposure to hazmat transportation–, and vehicles (acting as a follower), who minimize their travel costs –due to traffic congestion and toll charges. We introduce a reformulation approach that approximates this complex integrated problem with arbitrary precision and apply a specialized local search to exploit the structure of such reformulation. This combined resolution strategy relies upon a binary-search-based procedure, which sequentially updates the road prices intervals in such a way that the operator profit is monotonically improved. The effectiveness of the proposed approach is shown on a variety of structural configurations and economic settings, involving 1620 instances tested on the well-known Sioux Falls road network.

Estimation of Distribution Algorithm for Joint Resource Management in D2D Communication

Device to device (D2D) communication technique is one of the established means to enhance data rate in next generation wireless systems. Use of same resource of cellular users by D2D pairs creates interference problem among users. Simultaneous resource management and mode selection in emerging cellular networks having D2D capabilities can surely improve overall system throughput. This work addresses the problem of overall throughput maximization of emerging cellular networks while ensuring the power and interference constraints. The joint resource management problem is NP-Hard and is classified as mixed integer non-linear constraint optimization problem. Due to the fact that, the computational complexity of the system increases exponentially with the increase in users, it is almost impossible to find sub-optimal solution in polynomial time using greedy approach. Therefore, this paper applies evolutionary technique, like estimation of distribution algorithm which has the potential to address the complex problems having combinatorial nature such as joint resource management strategy in D2D. Near optimal solution convergence is achieved by the algorithm with minimal number of iterations. Simulation results show the effectiveness of the proposed approach as compared to other algorithms.

Optimal Configuration of Isolated Hybrid AC/DC Microgrids

This paper proposes a model for planning isolated microgrids. The goal of the proposed model is to minimize the investment, operational, and total costs of an isolated microgrid through the full identification of the system configuration. The model designates the optimal type of microgrid, i.e., ac, dc, or hybrid ac/dc, and the optimal sizing of both the distributed energy resources (DERs) and the electronic power converters, if needed. To render this planning approach generic, the model accommodates a wide variety of DERs, including ac and dc generators, capacitors, and energy storage systems. The detailed operational criteria of each power apparatus are taken into account in order to provide reliable operational scenarios. As a means of guaranteeing active and reactive power adequacy in isolated microgrids, the stochastic nature of generation and demand are also considered. The proposed model was developed analytically as a mixed integer nonlinear problem so that obtaining solution optima is thus possible with the use of a deterministic branch-and-bound nonlinear solver. The validity and effectiveness of the new formulation have been demonstrated through several case studies involving varied load topologies.

Optimal shared mobility planning for electric vehicles in the distribution network

Shared electric vehicle (EV) is an emerging component across interdependent power and transportation networks that affect economic, environmental and societal benefits. Studies on how to collaboratively enable the optimal planning of these interacted networks is less explored. In this work, a joint distribution network expansion planning framework integrated with a shared EV charging station is proposed. One of the objectives is to minimise overall investment cost considering operational waiting cost of shared EV charging service and power loss, while the other aims to maximise the utilisation of charging infrastructures. To overcome the difficulties in solving the multi-objective mixed-integer non-linear problem, Tchebycheff decomposition based evolutionary algorithm is modified to find the Pareto front showing the trade-offs between goals above. Besides, stochastic traffic assignment model is used to obtain traffic distribution and travel demand. The final optimal solution is decided by the fuzzy satisficing method. The performance of the proposed approach is evaluated on a 54-node test system. Sensitivity analysis is performed to assess the impact of key parameters from the perspectives of transportation and distribution network sectors. The numerical results demonstrate the capability and feasibility of the proposed method.

Parameterized Modeling and Planning of Distributed Energy Storage in Active Distribution Networks

In recent years, distributed energy storage (DES) has experienced rapid growth and has been widely applied in active distribution networks (ADNs). Owing to the close correlation between the characteristics and the application scenarios, DES modeling needs to be parameterized separately for various application demands. In this paper, a parameterized model for optimal DES planning in ADNs is proposed. The typical scenarios for DES planning are generated by the clustering technique, containing the patterns of load demand, wind turbine output and photovoltaic output. Secondly, an optimal planning model of DES considering parameterized characteristics is established, which is essentially a mixed integer non-linear optimization problem. Then, the model is converted to a mixed-integer second-order cone programming model, which can be solved efficiently by available commercial software. Finally, case studies on the modified IEEE 33-node system and IEEE 123-node system verify the efficiency of the proposed method, and the effects of DES planning are validated by two evaluation indexes.

Scenario-Based Design for Multiple Microgrids with High DG Penetration Considering Uncertainty on Demand and Generation Side

In this paper a new scenario-based approach is proposed to design optimized multiple-microgrids considering the uncertainty of load consumption and renewable DGs generation. The proposed method is used to determine the optimal capacity, type, number and location of renewable and controllable distributed generation resources along with the switch optimal location to cluster the traditional distribution network into a set of interconnected microgrids with economic and reliable structured. This study aims to decrease the total design costs including investment and operation costs, system loss cost, air pollution cost as well as the microgrids energy not supplied cost. Different considered objective functions have been modeled using weighted coefficients method as a single-objective nonlinear mixed integer problem. In addition, the uncertainty of the problem input parameters is modeled using scenario generation method, and in order to decrease the computational burden and increase the program execution speed, the backward scenario reduction technique is used. The Cuckoo optimization algorithm is used to optimize the objective function, and also the effect of optimization coefficients on the design problem and the robustness of the proposed algorithm are investigated using sensitivity analysis. Finally, the efficiency and performance of the proposed method are evaluated on the standard 33-bus network and the results show that the proposed method is an effective tool to design interconnected microgrids with consideration of uncertainty.

An Efficient Grey Wolf Optimizer with Opposition-Based Learning and Chaotic Local Search for Integer and Mixed-Integer Optimization Problems

Determining the global optima of integer and mixed-integer nonlinear problems is a useful contribution in various engineering applications. Swarm intelligence is a well-known branch of nature-inspired algorithms which tries to determine the solution with the help of intelligent and collective behaviour of social creatures. Grey wolf optimizer (GWO) is one of the recently developed efficient algorithms which are quite popular nowadays. In the present study, first, the GWO is proposed for solving integer and mixed-integer optimization problems, and secondly, an improved version of GWO named IMI-GWO is proposed. The IMI-GWO attempts to alleviate from the major issues of premature convergence and slow convergence of classical GWO. In IMI-GWO, the opposition-based learning maintains the diversity and the chaotic search locally exploits the regions around the best solutions. To evaluate the performance of IMI-GWO, a set of 16 integer and mixed-integer problems and two engineering application problems, namely gear train and pressure vessel design problems, have been considered. The performance of the IMI-GWO is compared with other algorithms which are applied to solve these problems in the literature and with some recent algorithms. The comparison illustrates the better performance of the proposed algorithm.

Deployment Strategies of Multiple Aerial BSs for User Coverage and Power Efficiency Maximization

Unmanned aerial vehicle-based aerial base stations (BSs) can provide rapid communication services to ground users and are thus promising for future communication systems. In this paper, we consider a scenario where no functional terrestrial BSs are available and the aim is deploying multiple aerial BSs to cover a maximum number of users within a certain target area. To this end, we first propose a naive successive deployment method, which converts the non-convex constraints in the involved optimization into a combination of linear constraints through geometrical relaxation. Then, we investigate a deployment method based on $K$ -means clustering. The method divides the target area into $K$ convex subareas, where within each subarea, a mixed integer non-linear problem is solved. An iterative power efficient technique is further proposed to improve coverage probability with reduced power. Finally, we propose a robust technique for compensating the loss of coverage probability in the existence of inaccurate user location information. Our simulation results show that the proposed techniques achieve an up to 30% higher coverage probability when users are not distributed uniformly. In addition, the proposed simultaneous deployment techniques, especially the one using iterative algorithm, improve power-efficiency by up to 15% compared with the benchmark circle packing theory.

A modelling approach for the comparison between intensified extraction in small channels and conventional solvent extraction technologies

In this paper, the application of small channels to the extraction separations in spent nuclear fuel reprocessing has been investigated via a modelling approach. The results are compared with conventional liquid-liquid extraction technologies such as mixer-settlers and pulsed columns, using models from the literature.In the model mass transfer, redox reactions, pressure drop and nuclear criticality are taken into account, as well as manifold and two-phase separator designs for the small-scale technology. The resulting model, posed as an optimisation problem, is a mixed integer nonlinear problem, implemented in the General Algebraic Modeling System (GAMS).An alternative flowsheet for the codecontamination section of the PUREX process, as a case study, has been investigated. The results show that the small-scale technology could be beneficial, in particular in terms of volumetric mass transfer coefficients, nuclear criticality safety and short residence time, which improves neptunium separation and reduces solvent degradation.

Systems engineering based advanced optimization for sustainable water management in refineries

Refineries are increasingly compelled to play an imperative role in achieving sustainable management of water as mandated by sustainable development goals (SDGs). Existing optimization models lack the ability to addresses this challenge of obtaining optimal refinery water network configuration for problems of industrial scale due to difficulty in application of complex solution algorithms of mixed integer non-linear problem (MINLP) formulations to large dimensions. Therefore, the optimization formulation in this work exploits process engineering derived constraints to build an integrated superstructure, which results in a simplified non-linear problem (NLP), and thus reduces computational complexity. Further, to substantially minimize fresh water consumption, the proposed model incorporates novel features of a modern refinery complex viz. distributed effluent treatment plant based on total dissolved solids (TDS) levels in waste water, segregation of sour water treatment based on phenolics content in condensate stream, and minimizing cooling tower blowdown rates by optimizing the cycles of concentration in cooling tower operation. The formulation is demonstrated for optimal water routing and economic benefits of the proposed approach through a representative case study of a real refinery complex. Towards the goal of zero liquid discharge, an efficient new scheme of recycling treated water to the boiler feed water system and cooling tower make up water requirements in optimal ratios, has been suggested from the results of the proposed model. Sensitivity of water reallocation in optimal refinery water network with respect to crude quality and desalter performance is also presented through application of proposed optimization framework in the case studies.

A bi-level capacitated P-median facility location problem with the most likely allocation solution

In this paper, a bi-level model is introduced to evaluate the capacitated p-median facility location problem with the most likely allocation solution. The classical capacitated p-median problem is considered in the upper-level to minimize the cost of locating facilities and serving demands while a log-based model resulting from the minimum information approach is used in the lower-level to determine the most likely allocation solution based on the available information. Using Lagrangian dual theory, the proposed bi-level problem is reduced to a new one-level nonlinear mixed-integer problem whose solution is obtained by comparing two mixed-integer linear problems. Some numerical examples are provided to illustrate the added value of the proposed model.