Development of a new approach for deterministic supply chain network design

This paper proposes a mixed integer linear programming model and solution algorithm for solving supply chain network design problems in deterministic, multi-commodity, single-period contexts. The strategic level of supply chain planning and tactical level planning of supply chain are aggregated to propose an integrated model. The model integrates location and capacity choices for suppliers, plants and warehouses selection, product range assignment and production flows. The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables. Consequently, this problem is a binary mixed integer linear programming problem. In this paper, a modified version of Benders’ decomposition is proposed to solve the model. The most difficulty associated with the Benders’ decomposition is the solution of master problem, as in many reallife problems the model will be NP-hard and very time consuming. In the proposed procedure, the master problem will be developed using the surrogate constraints. We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint. The generated problem with the strongest surrogate constraint is a valid relaxation of the main problem. Furthermore, a near-optimal initial solution is generated for a reduction in the number of iterations

An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

Continuous network design problem (CNDP) is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE) to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC) by describing UE as a non-linear complementarity problem (NCP). To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB) function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP) by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.</p

An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

Continuous network design problem (CNDP) is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE) to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC) by describing UE as a non-linear complementarity problem (NCP). To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB) function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP) by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.</p

Scheduled service network design with synchronization and transshipment constraints for intermodal container transportation networks

In this paper we address the problem of scheduled service network design for container freight distribution along rivers, canals, and coastlines. We propose a new concise continuous- time mixed-integer linear programming model that accurately evaluates the time of occurrence of transportation events and the number of containers transshipped between vehicles. Given the transportation network, the eet of available vehicles, the demand and the supply of containers, the sailing time of vehicles, and the structure of costs, the objective of the model is to build a minimum cost service network design and container distribution plan that denes services, their departure and arrival times, as well as vehicle and container routing. The model is solved with a commercial solver and is tested on data instances inspired from real-world problems encountered by EU carrier companies. The results of the computational study show that in scheduled service networks direct routes happen more often when either the eet capacity is tight or the handling costs and the lead time interval increase. The increase of the same parameters leads to the decrease of the number of containers transshipped between vehicles

Superstructure Optimization of Petroleum Refinery Design: Processing Alternatives for Naphtha Produced from the Atmospheric Distillation Unit

This research project concerns superstructure optimization for the design of petroleum refineries focusing on the subsystem that considers the alternatives for naphtha produced from the atmospheric distillation unit (ADU). The intricate complexities associated with this process synthesis problem in general and the refinery design problem in specific necessitates the development and implementation of a systematic and automated approach that efficiently and rigorously integrate the elaborate interactions involving the design decision variables. The primary objective of this research is to establish a systematic procedure to determine the optimal topology of the refinery subsystem of naphtha produced from the ADUusing the optimization or mathematical programming approach. Through the identification of equipment, raw materials, products, and process alternatives in terms of the different feasible choices of states (material streams) and tasks (process units) for the mentioned subsystem, the first step is to represent the problem as the interconnections between these elements in a network representation of a superstructure. Subsequently, an optimization model is formulated with binary and continuous variables in order to arrive at the optimum flowsheet design. The scope of this work is focused on the formulation of a mixed-integer linear programming (MILP) and a generalized disjunctive programming (GDP) optimization models. The independent design decision variables are flows of materials and the continuous variables of stream flowrates with the discrete variables denoting the existence of streams. Logical constraints are extensively incorporated in the models to represent qualitative design knowledge through design specifications and structural specifications on the interconnectivity relationships involving the states and the tasks. Computational studies to demonstrate the implementation of the proposed modeling approaches are carried out on the GAMS modeling language platform using the established GAMS/CPLEX solver and the new code of GAMS/LOGMIP solver for the MILP and GDP, respectively. Two design scenarios are considered as distinguished by the API gravity (specific gravity) of the crude charge to the ADU. The optimal refinery topology generated from the MILP and GDP model agree with the typical existing refinery topology. The way forward for this project is to account for varying sulphur content in the crude charge as well as to introduce nonlinearity in the composition modeling to obtain a more practical representation of a real-world refinery design problem

AReN: Assured ReLU NN architecture for model predictive control of LTI systems

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture that is sufficient to implement the optimal Model Predictive Control (MPC) strategy for an LTI system with quadratic cost. Specifically, we propose AReN, an algorithm to generate Assured ReLU Architectures. AReN takes as input an LTI system with quadratic cost specification, and outputs a ReLU NN architecture with the assurance that there exist network weights that exactly implement the associated MPC controller. AReN thus offers new insight into the design of ReLU NN architectures for the control of LTI systems: instead of training a heuristically chosen NN architecture on data - or iterating over many architectures until a suitable one is found - AReN can suggest an adequate NN architecture before training begins. While several previous works were inspired by the fact that ReLU NN controllers and optimal MPC controllers are both Continuous, Piecewise-Linear (CPWL) functions, exploiting this similarity to design NN architectures with correctness guarantees has remained elusive. AReN achieves this using two novel features. First, we reinterpret a recent result about the implementation of CPWL functions via ReLU NNs to show that a CPWL function may be implemented by a ReLU architecture that is determined by the number of distinct affine regions in the function. Second, we show that we can efficiently over-approximate the number of affine regions in the optimal MPC controller without solving the MPC problem exactly. Together, these results connect the MPC problem to a ReLU NN implementation without explicitly solving the MPC: the result is a NN architecture that has the assurance that it can implement the MPC controller. We show through numerical results the effectiveness of AReN in designing an NN architecture

Fast Design Space Exploration of Nonlinear Systems: Part II

Nonlinear system design is often a multi-objective optimization problem involving search for a design that satisfies a number of predefined constraints. The design space is typically very large since it includes all possible system architectures with different combinations of components composing each architecture. In this article, we address nonlinear system design space exploration through a two-step approach encapsulated in a framework called Fast Design Space Exploration of Nonlinear Systems (ASSENT). In the first step, we use a genetic algorithm to search for system architectures that allow discrete choices for component values or else only component values for a fixed architecture. This step yields a coarse design since the system may or may not meet the target specifications. In the second step, we use an inverse design to search over a continuous space and fine-tune the component values with the goal of improving the value of the objective function. We use a neural network to model the system response. The neural network is converted into a mixed-integer linear program for active learning to sample component values efficiently. We illustrate the efficacy of ASSENT on problems ranging from nonlinear system design to design of electrical circuits. Experimental results show that ASSENT achieves the same or better value of the objective function compared to various other optimization techniques for nonlinear system design by up to 54%. We improve sample efficiency by 6-10x compared to reinforcement learning based synthesis of electrical circuits.Comment: 14 pages, 24 figures. arXiv admin note: substantial text overlap with arXiv:2009.1021

Nonlinear and sampled data control with application to power systems

Sampled data systems have come into practical importance for a variety of reasons. The earliest of these had primarily to do with economy of design. A more recent surge of interest was due to increase utilization of digital computers as controllers in feedback systems. This thesis contributes some control design for a class of nonlinear system exhibition linear output. The solution of several nonlinear control problems required the cancellation of some intrinsic dynamics (so-called zero dynamics) of the plant under feedback. It results that the so-dened control will ensure stability in closed-loop if and only if the dynamics to cancel are stable. What if those dynamics are unstable? Classical control strategies through inversion might solve the problem while making the closed loop system unstable. This thesis aims to introduce a solution for such a problem. The main idea behind our work is to stabilize the nonminimum phase system in continuous- time and undersampling using zero dynamics concept. The overall work in this thesis is divided into two parts. In Part I, we introduce a feedback control designs for the input-output stabilization and the Disturbance Decoupling problems of Single Input Single Output nonlinear systems. A case study is presented, to illustrate an engineering application of results. Part II illustrates the results obtained based on the Articial Intelligent Systems in power system machines. We note that even though the use of some of the AI techniques such as Fuzzy Logic and Neural Network does not require the computation of the model of the application, but it will still suer from some drawbacks especially regarding the implementation in practical applications. An alternative used approach is to use control techniques such as PID in the approximated linear model. This design is very well known to be used, but it does not take into account the non-linearity of the model. In fact, it seems that control design that is based on nonlinear control provide better performances

Application of Finite-Time Stability Concepts to the Control of ATM Networks

When dealing with the stability of a system, a distinction should be made between classical Lyapunov Stability and Finite-Time Stability (FTS) (or Short-Time Stability). The concept of Lyapunov Asymptotic Stability is largely known to the control community; on the other hand a system is said to be finite-time stable if, once we fix a time-interval, its state does not exceeds some bounds during this time-interval. Often asymptotic stability is enough for practical applications, but there are some cases where large values of the state are not acceptable, for instance in the presence of saturations. In these cases, we need to check that these unacceptable values are not attained by the state; for these purposes FTS could be used. Some early results on FTS can be found in [9], [12] and [8]; more recently the concept of FTS has been revisited in the light of recent results coming from Linear Matrix Inequalities (LMIs) theory, which has allowed to find less conservative conditions guaranteeing FTS and finite time stabilization of uncertain, linear continuous-time systems (see [3]). In this note we consider the problem of applying some sufficient conditions for finite time stabilization to design the control algorithm of an ATM network described via a discrete-time system. The extended abstract is organized as follows: in Section 2 we provide a sufficient condition for finite time stabilization of a discrete time system; in Section 3 we detail the model of an ATM network; finally in Section 4 some concluding remarks and plans for the final version of the paper are given