Nonlinear Programming Formulation Research Articles

Thermo-economic and environmental optimization of a solar-driven zero-liquid discharge system for shale gas wastewater desalination

Wastewater management is one of the main hurdles encountered by the shale gas industry for boosting overall process cost-effectiveness while reducing environmental impacts. In this light, this paper introduces a new multi-objective model for the thermo-economic and environmental optimization of solar-based zero-liquid discharge (ZLD) desalination systems. The solar-driven ZLD system is especially developed for desalinating high-salinity wastewaters from shale gas process. A decentralized system is proposed, encompassing a solar thermal system, a Rankine power cycle, and a multiple-effect evaporator combined with mechanical vapor recompression. The environment-friendly ZLD operation is ensured by specifying the salt concentration of brine discharges close to saturation conditions. The mathematical modelling approach is centered on a multi-objective non-linear programming (MoNLP) formulation, which is aimed at simultaneously minimizing thermo-economic and environmental objective functions. The latter objective function is quantified by the ReCiPe methodology based on life cycle assessment. The MoNLP model is implemented in GAMS software, and solved through the epsilon-constraint method. A set of trade-off Pareto-optimal solutions is presented to support decision-makers towards implementing more sustainable and cost-efficient solar-driven ZLD desalination systems. The comprehensive energy, economic and environmental analysis reveals that the innovative system significantly decreases costs and environmental impacts in shale gas wastewater operations.

Extracting maximal objects from three-dimensional solid materials

In the problem of extracting maximal items/objects from three-dimensional materials, we are given a piece of solid material and an object with predefined ratios. The goal is to extract the largest possible convex or non-convex object from the solid material. There are two variants of the problem: the general case where the solid material is non-convex and its special case consisting of a convex solid material. We propose a matheuristic approach for solving both problems. For the special case, the problem is also modeled as a non-linear programming formulation. Meanwhile, for the general case a mixed integer linear programming formulation is provided based on the decomposition of the non-convex material into a finite number of convex regions. Computational experiments evaluate the performance of both models for small-scale instances considering objects with at most 1400 and 370 vertices for the special and general case, respectively. We observe that the required computational effort increases with the number of vertices of the objects, therefore, it is also evaluated the efficiency of the proposed matheuristic approach for more complicated instances, considering objects with a higher number of vertices. In order to establish benchmark instances for future research, all instances used are publicly available.

Relax-tighten-round algorithm for optimal placement and control of valves and chlorine boosters in water networks

In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of average zone pressure, while penalizing deviations from a target chlorine concentration. We propose a relax-tighten-round algorithm based on tightened polyhedral relaxations and a rounding scheme to compute feasible solutions, with bounds on their optimality gaps. This is because off-the-shelf global optimization solvers failed to compute feasible solutions for the considered non-convex mixed integer nonlinear program. The implemented algorithm is evaluated using three benchmarking water networks, and they are shown to outperform off-the-shelf solvers, for these case studies. The proposed heuristic has enabled the computation of good quality feasible solutions in most instances, with bounds on the optimality gaps that are comparable to the order of uncertainty observed in operational water network models.

A Lagrangean relaxation approach to lifetime maximization of directional sensor networks

AbstractWe consider the directional sensor network lifetime maximization problem (DSLMP). Given a set of directional sensor and target locations, the problem consists in assigning, at each time unit of a given time horizon, the action radius, the aperture angle, and the orientation direction to all sensors. The objective is to maximize the number of time units when all targets are covered, under certain constraints on sensor available energy. We present a mixed integer nonlinear programming formulation and tackle it by Lagrangean decomposition and subgradient optimization. The algorithm is equipped with a repairing heuristics aimed at finding good‐quality feasible solutions to DSLMP. The results of the application of the proposed approach to a number of problem instances are also reported.

Network Slicing with MEC and Deep Reinforcement Learning for the Internet of Vehicles

The interconnection of vehicles in the future fifth generation (5G) wireless ecosystem forms the so-called Internet of Vehicles (IoV). IoV offers new kinds of applications requiring delay-sensitive, compute-intensive, and bandwidth-hungry services. Mobile edge computing (MEC) and network slicing are two of the key enabler technologies in 5G networks that can be used to optimize the allocation of the network resources and guarantee the diverse requirements of IoV applications. As traditional model-based optimization techniques generally end up with NP-hard and strongly non-convex and nonlinear mathematical programming formulations, in this article, we introduce a model-free approach based on deep reinforcement learning (DRL) to solve the resource allocation problem in MEC-enabled IoV networks based on network slicing. Furthermore, the solution uses non-orthogonal multiple access (NOMA) to enable better exploitation of the scarce channel resources. The considered problem addresses jointly the channel and power allocation, the slice selection, and the vehicle selection (vehicle grouping). We model the problem as a single-agent Markov decision process. Then we solve it using DRL with the well-known deep Q learning (DQL) algorithm. We show that our approach is robust and effective under different network conditions compared to benchmark solutions.

3-D Dynamic UAV Base Station Location Problem

We address a dynamic covering location problem of an unmanned aerial vehicle base station (UAV-BS), in which the location sequence of a single UAV-BS in a wireless communication network is determined to satisfy data demand arising from ground users. This problem is especially relevant in the context of smart grid and disaster relief. The vertical movement ability of the UAV-BS and nonconvex covering functions in wireless communication restrict utilizing classical planar covering location approaches. Therefore, we develop new formulations to this emerging problem for a finite time horizon to maximize the total coverage. In particular, we develop a mixed-integer nonlinear programming formulation that is nonconvex in nature and propose a Lagrangean decomposition algorithm (LDA) to solve this formulation. Because of the high complexity of the problem, the LDA is still unable to find good local solutions to large-scale problems. Therefore, we develop a continuum approximation (CA) model and show that CA would be a promising approach in terms of both computational time and solution accuracy. Our numerical study also shows that the CA model can be a remedy to build efficient initial solutions for exact solution algorithms. Summary of Contribution: This paper addresses a facet of mixed integer nonlinear programming formulations. Dynamic facility location problems (DFLPs) arise in a wide range of applications. However, classical DFLPs typically focus on the two-dimensional spaces. Emerging technologies in wireless communication and some other promising application areas, such as smart grids, have brought new location problems that cannot be solved with classical approaches. For practical reasons, many research attempts to solve this new problem, especially by researchers whose primary research area is not OR, have seemed far from analyzing the characteristics of the formulations. Rather, solution-oriented greedy heuristics have been proposed. This paper has two main objectives: (i) to close the gap between practical and theoretical sides of this new problem with the help of current knowledge that OR possesses to solve facility location problems and (ii) to support the findings with an exhaustive computational study to show how these findings can be applied to practice.

Stochastic programming model for production planning with stochastic aggregate demand and spreadsheet-based solution heuristics

The production planning problem with stochastic aggregate demand is considered in the article. By discretising the stochastic demand, a deterministic nonlinear programming formulation is developed. Then, a hybrid simulation-optimisation heuristic that capitalises on the nature of the problem is designed. The outcome is an evaluation problem that is efficiently solved using a spreadsheet model. The main contribution of the paper is providing production managers with a tractable formulation of the production planning problem in a stochastic environment and an efficient solution scheme. A key benefit of this approach is that it provides quick near-optimal solutions without requiring in-depth knowledge or significant investments in optimisation techniques and software.

БИЗНЕС-СТРАТЕГИЧЕСКОЕ ПРИНЯТИЕ РЕШЕНИЙ С УЧЕТОМ МОДЕЛЕЙ МАРКЕТИНГА И ЦЕПОЧКИ ПОСТАВОК

A supply chain model that includes the components of business strategic decisions is an es-sential tool for gaining a competitive advantage in today's global marketplace. Enterprise models of this type need to cover not only the supply chain but also the demand chain, since understanding the market is critical to formulating good business policy. To work effectively, marketing activities must be coordinated with other functional areas of the company. Specifically, managers must evaluate the trade-off between marketing and supply chain decisions to improve the performance of an overall metric: shareholder value. The article formu-lates a mathematical model that takes into account the main business functions. A mixed integer nonlinear programming formulation is presented for the integrated optimization of strategic supply chain decisions and marketing decisions. This allows you to more accurately form a financial model and estimate the value of the enterprise. Keywords

A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.

Planning rolling stock maintenance: Optimization of train arrival dates at a maintenance center

<p style='text-indent:20px;'>A railway network is an indispensable part of the public transportation system in many major cities around the world. In order to provide a safe and reliable service, a fleet of passenger trains must undergo regular maintenance. These maintenance operations are lengthy procedures, which are planned for one year or a longer period. The planning specifies the dates of trains' arrival at the maintenance center and should take into account the uncertain duration of maintenance operations, the periods of validity of the previous maintenance, the desired number of trains in service, and the capacity of the maintenance center. The paper presents a nonlinear programming formulation of the considered problem and several optimization procedures which were compared by computational experiments using real world data. The results of these experiments indicate that the presented approach is capable to be used in real world planning process.</p>

Approach for improving the life-cycle profit exploding remanufacturing conditions

This work presents a mixed-integer nonlinear programming (MINLP) formulation for the multi-period planning of a Closed-Loop Supply Chain (CLSC) with the emphasis placed on remanufacturing conditions. The approach considers the life-cycle of products related to processes industry. It is taken into account that two types of products flow through the CLSC, products with traditional and modular design (TD and MD). While products with traditional design (PTD) uses only new raw materials, products with modular design (PMD) utilizes partially or totally materials that are recovered from discarded products. The manufacturing process connected with the PMD is characterized by improving the manufacturing and material separation. As part of the problem, it must be determined the selling prices, the amount of manufactured products, the return rates of discarded products and the level of materials recovery. Demand functions and customer utility measures for products with traditional and modular design are considered. The objective function is to maximize the total life-cycle profit taking into account the sum of the profits from selling products with traditional and modular designs. The MINLP approach is applied to the planning problem of a firm dedicated to manufactures carpets that wants to produce according to a new modular design where recovered materials must be used. The performance of the model is evaluated solving several case scenarios. The results obtained with the model for the carpet design allow to achieve important practical conclusions, such as the consideration of both designs, traditional and modular, has a positive impact on the total profit and allows the company to have a greater presence in the market.

Optimal design and operation of an islanded water-energy network including a combined electrodialysis-reverse osmosis desalination unit

This paper proposes an optimization framework to simultaneously optimize the saline and freshwater water sources as well as decentralized renewable and conventional energy sources, which consequently results in an economic and efficient water-energy system operation. The inextricable links between water and energy systems are taken into considerations, and a mixed integer nonlinear programming formulation is used to solve the proposed optimization model. A hybrid electrodialysis-reverse osmosis is integrated in the water distribution system and its electricity consumption is minimized. Also, the day-ahead economic dispatch problem of the energy system incorporates the random behavior of solar and wind generation units, along with charging and discharging modes of battery storage systems. The outcomes of the proposed models highlight: 1) integrating the hybrid desalination module in the water-energy system will reduce peak demands by more than 30% if the water and energy systems are solely supplied by saline water and renewable energy sources, respectively; 2) presence of an extra water storage tank also decreases peak demands by 13%. The impact of key elements of the combined system such as pumps’ speeds, water tank constraints, and presence of renewable sources on the output cost, generated energy, and hydraulic parameters is investigated through case studies.

Short-term oil production global optimization with operational constraints: A comparative study of nonlinear and piecewise linear formulations

The short-term oil production optimization of offshore platforms which use continuous gas lift and consider several operational constraints is a challenging task, specially when decision variables include both continuous and integer ones. The intrinsic non-linearity of the Gas Lift Performance Curves (GLPC) naturally yields to Mixer-Integer Nonlinear Program formulation. Picewise linear approximations of the GLPC are usually applied in order to reduce the complexity of the optimization problem and to ensure an approximate solution, leading to Mixer-Integer Linear Program formulation. However, a comprehensive and comparative study of these two formulations for the oil production optimization problem is scarce in the literature. This paper provides a deep performance evaluation of these two approaches, showing the limitations of both strategies, and proposes a hybrid two-stage optimization strategy to achieve the global optimal operating condition which maximizes the oil production subject to safety, environmental and processing capacity constraints.

Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method

Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term.

A new robust dynamic Bayesian network approach for disruption risk assessment under the supply chain ripple effect

Dynamic Bayesian network (DBN) theory provides a valid tool to estimate the risk of disruptions, propagating along the supply chain (SC), i.e. the ripple effect. However, in cases of data scarcity, obtaining perfect information on probability distributions required by the DBN is impractical. To overcome this difficulty, a new robust DBN approach is, for the first time, proposed in this study to analyse the worst-case oriented disruption propagation in the SC. This work considers an SC with multiple suppliers and one manufacturer over several time periods, in which only probability intervals of the suppliers' states and those of the related disruption propagations are known. The objective is to acquire the robust performance of risk estimation, measured by the worst-case probability in the disrupted state for the manufacturer. We first establish a nonlinear programming formulation to mathematically materialise the proposed robust DBN, which can be used to solve small-size problems. To overcome the computational difficulty in solving large-size problems, an efficient simulated annealing algorithm is further designed. Numerical experiments are conducted to validate its efficiency.

Stealthy Cyberattacks on Loads and Distributed Generation Aimed at Multi-Transmission Line Congestions in Smart Grids

Developing attack models is the first step to understand cyberattacks in smart grids and develop countermeasures. In this article, a three-level nonlinear programming formulation is proposed for false data injection (FDI) cyberattacks that could result in multiple transmission line congestions without being detected by conventional bad data detection (BDD) algorithms. The model is then converted to a mixed integer linear programming (MILP) formulation to guarantee a global optimum exists. A detection framework based on recursive least-square estimation (RLSE) is developed that can successfully detect the stealthy FDIs. The developed model with the detection framework is validated through various case studies in IEEE 118-bus benchmark.

Three-dimensional guillotine cutting problems with constrained patterns: MILP formulations and a bottom-up algorithm

In this paper, we address the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP), which consists of cutting a larger cuboid block (object) to produce a limited number of smaller cuboid pieces (items) using orthogonal guillotine cuts only. This way, all cuts must be parallel to the object’s walls and generate two cuboid sub-blocks, and there is a maximum number of copies that can be manufactured for each item type. The C3GCP arises in industrial manufacturing settings, such as the cutting of steel and foam for mattresses. To model this problem, we propose a new compact mixed-integer non-linear programming (MINLP) formulation by extending its two-dimensional version, and develop a mixed-integer linear programming (MILP) version. We also propose a new model for a particular case of the problem which considers 3-staged patterns. As a solution method, we extend the algorithm of Wang (1983) to the three-dimensional case. We emphasise that the C3GCP is different from 3D packing problems, namely from the Container Loading Problem, because of the guillotine cut constraints. All proposed approaches are evaluated through computational experiments using benchmark instances. The results show that the approaches are effective on different types of instances, mainly when the maximum number of copies per item type is small, a situation typically encountered in practical settings with low demand for each item type. These approaches can be easily embedded into existing expert systems for supporting the decision-making process.

A game‐theoretic approach for the location of terror response facilities with both disruption risk and hidden information

AbstractRecently, locating emergency response facilities has been drawing increasing attention with the highly strategic nature of terrorist attacks. To this end, we present a game‐theoretic approach for the location of terror response facilities when both disruption risk and hidden information are taken into account. The game is described as a two‐stage game, in which the first stage allows the State, that is, defender, to locate the terror response facilities, including disclosed and undisclosed facilities, and assign them to the attacked city, while the second stage allows the terrorist, that is, attacker, to select one city to attack with partial information about facility location and assignment. We propose a mixed integer bi‐level nonlinear programming formulation, and in response, a heuristic algorithm is developed to find the equilibrium solution. Extensive computational tests on both synthetic data and a real‐world dataset of provincial capital cities in China demonstrate the effectiveness of the developed algorithm.

Optimal 3D time-energy trajectory planning for AUVs using ocean general circulation models

This paper develops a new approach for solving optimal time and energy trajectory planning problems for Autonomous Underwater Vehicles (AUVs) in transient, 3D, ocean currents. Realistic forecasts using an Ocean General Circulation Model (OGCM) are used for this purpose. The approach is based on decomposing the problem into a minimal time problem, followed by minimal energy subproblems. In both cases, a non-linear programming (NLP) formulation is adopted. The scheme is demonstrated for time-energy trajectory planning problems in the Gulf of Aden. In particular, the numerical experiments illustrate the capability of generating Pareto optimal solutions in a broad range of mission durations. In addition, the analysis also highlights how the methodology effectively exploits both the vertical structure of the current field, as well as its unsteadiness, namely to minimize travel time and energy consumption.

Location-routing problem with time-dependent demands

This study, by considering the time-dependent demand (TDD) characteristic, investigates the location-routing problem with time-dependent demands (LRPTDD) as an extension of the location-routing problem (LRP). The demand in each customer site is represented by a constant demand rate over a known production period. In the LRPTDD, the locations are selected, and the routes are constructed to pick up all the demands and minimize the total distance. The picked load depends on the vehicle arrival time at the site; thus, the “time-dependency” characteristic of the LRPTDD is based on the vehicle arrival time. A mixed-integer nonlinear programming (MINLP) formulation is presented. A simulated annealing (SA) algorithm for the LRPTDD is developed. The computational study demonstrates the competitiveness of the proposed SA heuristic against other well-known algorithms for LRPs, and most importantly, its effectiveness for the LRPTDD.