Search results for: mixed integer linear programming (MILP) optimization

Authors: D. Calogine, O. Chau, S. Dotti, O. Ramiarinjanahary, P. Rasoavonjy, F. Tovondahiniriko

Abstract:

Mafate is a natural circus in the north-western part of Reunion Island, without an electrical grid and road network. A micro-grid concept is being experimented in this area, composed of a photovoltaic production combined with electrochemical batteries, in order to meet the local population for self-consumption of electricity demands. This work develops a discrete model as well as a stochastic model in order to reach an optimal equilibrium between production and consumptions for a cluster of houses. The management of the energy power leads to a large linearized programming system, where the time interval of interest is 24 hours The experimental data are solar production, storage energy, and the parameters of the different electrical devices and batteries. The unknown variables to evaluate are the consumptions of the various electrical services, the energy drawn from and stored in the batteries, and the inhabitants’ planning wishes. The objective is to fit the solar production to the electrical consumption of the inhabitants, with an optimal use of the energies in the batteries by satisfying as widely as possible the users' planning requirements. In the discrete model, the different parameters and solutions of the linear programming system are deterministic scalars. Whereas in the stochastic approach, the data parameters and the linear programming solutions become random variables, then the distributions of which could be imposed or established by estimation from samples of real observations or from samples of optimal discrete equilibrium solutions.

Keywords: photovoltaic production, power consumption, battery storage resources, random variables, stochastic modeling, estimations of probability distributions, mixed integer linear programming, smart micro-grid, self-consumption of electricity.

Procedia PDF Downloads 85

Authors: Sangchul Kim, Dosaeng Park

Abstract:

It is one of the important design issues to provide various levels of difficulty in order to suit the skillfulness of an individual. In this paper we propose an integer programming-based method for selecting a mixture of challenges for a racing game that meet a given degree of difficulty. The proposed method can also be used to dynamically adjust the difficulty of the game during the progression of playing. By experiments, it is shown that our method performs well enough to generate games with various degrees of difficulty that match the perception of players.

Keywords: level generation, level adjustment, racing game, ip

Procedia PDF Downloads 342

Authors: J. Van Engeland, C. Lavigne, S. De Jaeger

Abstract:

In the light of the transition towards a more circular economy, recovery of products, parts or materials will gain in importance. Additionally, the EU proximity principle related to waste management and emissions generated by transporting large amounts of end-of-life products, shift attention to local recovery networks. The Flemish inter-communal cooperation for municipal solid waste management Meetjesland (IVM) is currently investigating the set-up of such a network. More specifically, the network encompasses the recycling of polyvinyl chloride (PVC), which is collected in separate containers. When these containers are full, a truck should transport them to the processor which can recycle the PVC into new products. This paper proposes a model to optimize the container collection. The containers are located at different Civic Amenity sites (CA sites) in a certain region. Since people can drop off their waste at these CA sites, the containers will gradually fill up during a planning horizon. If a certain container is full, it has to be collected and replaced by an empty container. The collected waste is then transported to a single processor. To perform this collection and transportation of containers, the responsible firm has a set of vehicles stationed at a single depot and different personnel crews. A vehicle can load exactly one container. If a trailer is attached to the vehicle, it can load an additional container. Each day of the planning horizon, the different crews and vehicles leave the depot to collect containers at the different sites. After loading one or two containers, the crew has to drive to the processor for unloading the waste and to pick up empty containers. Afterwards, the crew can again visit sites or it can return to the depot to end its collection work for that day. All along the collection process, the crew has to respect the opening hours of the sites. In order to allow for some flexibility, a crew is allowed to wait a certain amount of time at the gate of a site until it opens. The problem described can be modelled as a variant to the PVRP-TW (Periodic Vehicle Routing Problem with Time Windows). However, a vehicle can at maximum load two containers, hence only two subsequent site visits are possible. For that reason, we will refer to the model as a model for building tactical waste collection schemes. The goal is to a find a schedule describing which crew should visit which CA site on which day to minimize the number of trucks and the routing costs. The model was coded in IBM CPLEX Optimization studio and applied to a number of test instances. Good results were obtained, and specific suggestions concerning route and truck costs could be made. For a large range of input parameters, collection schemes using two trucks are obtained.

Keywords: container collection, crew scheduling, mixed integer linear programming, waste management

Procedia PDF Downloads 102

Authors: Reza Hedayati, Meysam Jahanbakhshi

Abstract:

Elastic energy absorbers which consist of a ring-liked plate and springs can be a good choice for increasing the impact duration during an accident. In the current project, an energy absorber system is optimized using four optimizing methods Kuhn-Tucker, Sequential Linear Programming (SLP), Concurrent Subspace Design (CSD), and Pshenichny-Lim-Belegundu-Arora (PLBA). Time solution, convergence, Programming Length and accuracy of the results were considered to find the best solution algorithm. Results showed the superiority of PLBA over the other algorithms.

Keywords: Concurrent Subspace Design (CSD), Kuhn-Tucker, Pshenichny-Lim-Belegundu-Arora (PLBA), Sequential Linear Programming (SLP)

Procedia PDF Downloads 365

Authors: Christian Liebchen

Abstract:

Both from an environmental perspective and with respect to road traffic flow quality, planning so-called green waves along major road axes is a well-established target for traffic engineers. For one-way road axes (e.g. the Avenues in Manhattan), this is a trivial downstream task. For bidirectional arterials, the well-known necessary condition for establishing a green wave in both directions is that the driving times between two subsequent crossings must be an integer multiple of half of the cycle time of the signal programs at the nodes. In this paper, we propose an integer linear optimization model to establish fixed-time green waves in both directions that are as long and as wide as possible, even in the situation where the driving time condition is not fulfilled. In particular, we are considering an arterial along whose nodes separate left-turn signal groups are realized. In our computational results, we show that scheduling left-turn phases before or after the straight phases can reduce waiting times along the arterial. Moreover, we show that there is always a solution with green waves in both directions that are as long and as wide as possible, where absolute priority is put on just one direction. Compared to optimizing both directions together, establishing an ideal green wave into one direction can only provide suboptimal quality when considering prioritized parts of a green band (e.g., first few seconds).

Keywords: traffic light coordination, synchronization, phase sequencing, green waves, integer programming

Procedia PDF Downloads 90

Authors: Trung Hieu Tran, Jesse O'Hanley, Russell Fowler

Abstract:

When in-wheel wireless charging technology for electric vehicles becomes mature, a need for such integrated charging stations network development is essential. In this paper, we thus investigate the optimisation problem of in-wheel wireless electric vehicle charging network design. A mixed-integer linear programming model is formulated to solve into optimality the problem. In addition, a meta-heuristic algorithm is proposed for efficiently solving large-sized instances within a reasonable computation time. A parallel computing strategy is integrated into the algorithm to speed up its computation time. Experimental results carried out on the benchmark instances show that our model and algorithm can find the optimal solutions and their potential for practical applications.

Keywords: electric vehicle, wireless charging station, mathematical programming, meta-heuristic algorithm, parallel computing

Procedia PDF Downloads 49

Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: optimization, MATLAB, quadratic programming, economic dispatch

Procedia PDF Downloads 522

Authors: Yongjian Du, Jinhua Sun, Kim M. Liew, Huahua Xiao

Abstract:

Optimal allocation of emergency resources before a disaster is of great importance for emergency response. In reality, the pre-protection for a single critical node where accidents may occur is common. In this study, a model is developed to determine location and inventory decisions of multiple emergency resources among a set of candidate stations to minimize the total cost based on the constraints of budgetary and capacity. The total cost includes the economic accident loss which is accorded with probability distribution of time and the warehousing cost of resources which is increasing over time. A ratio is set to measure the degree of a storage station only serving the target node that becomes larger with the decrease of the distance between them. For the application of linear program, it is assumed that the length of travel time to the accident scene of emergency resources has a linear relationship with the economic accident loss. A computational experiment is conducted to illustrate how the proposed model works, and the results indicate its effectiveness and practicability.

Keywords: emergency response, integer linear program, multiple emergency resources, pre-allocation decisions, single potential accident node

Procedia PDF Downloads 126

Authors: Zeinab Haji Abolhasani, Romeo Marian, Lee Luong

Abstract:

This paper and its companions (Part II, Part III) will concentrate on optimizing a class of supply chain problems known as Multi- Commodities Consumer Supply Chain (MCCSC) problem. MCCSC problem belongs to production-distribution (P-D) planning category. It aims to determine facilities location, consumers’ allocation, and facilities configuration to minimize total cost (CT) of the entire network. These facilities can be manufacturer units (MUs), distribution centres (DCs), and retailers/end-users (REs) but not limited to them. To address this problem, three major tasks should be undertaken. At the first place, a mixed integer non-linear programming (MINP) mathematical model is developed. Then, system’s behaviors under different conditions will be observed using a simulation modeling tool. Finally, the most optimum solution (minimum CT) of the system will be obtained using a multi-objective optimization technique. Due to the large size of the problem, and the uncertainties in finding the most optimum solution, integration of modeling and simulation methodologies is proposed followed by developing new approach known as GASG. It is a genetic algorithm on the basis of granular simulation which is the subject of the methodology of this research. In part II, MCCSC is simulated using discrete-event simulation (DES) device within an integrated environment of SimEvents and Simulink of MATLAB® software package followed by a comprehensive case study to examine the given strategy. Also, the effect of genetic operators on the obtained optimal/near optimal solution by the simulation model will be discussed in part III.

Keywords: supply chain, genetic algorithm, optimization, simulation, discrete event system

Procedia PDF Downloads 277

Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

Abstract:

Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

Procedia PDF Downloads 105

Authors: Wennan Long, Yuhao Nie, Yunan Li, Adam Brandt

Abstract:

To fight against climate change, California government issued the Senate Bill No. 100 (SB-100) in 2018 September, which aims at achieving a target of 100% renewable electricity by the end of 2045. A capacity expansion problem is solved in this case study using a binary quadratic programming model. The optimal locations and capacities of the potential renewable power plants (i.e., solar, wind, biomass, geothermal and hydropower), the phase-out schedule of existing fossil-based (nature gas) power plants and the transmission of electricity across the entire network are determined with the minimal total annualized cost measured by net present value (NPV). The results show that the renewable electricity contribution could increase to 85.9% by 2030 and reach 100% by 2035. Fossil-based power plants will be totally phased out around 2035 and solar and wind will finally become the most dominant renewable energy resource in California electricity mix.

Keywords: 100% renewable electricity, California, capacity expansion, mixed integer non-linear programming

Procedia PDF Downloads 145

Authors: Yan-Shen Yang, Bai-Chen Xie

Abstract:

Background and significance of the study: Both green power trading schemes and interregional power transmission are effective ways to increase green power absorption and achieve renewable power development goals. China accelerates the construction of interregional power transmission lines and the green power market. A critical issue focusing on the close interaction between these two approaches arises, which can heavily affect the green power quota allocation and renewable power development. Existing studies have not discussed this issue adequately, so it is urgent to figure out their relationship to achieve a suitable power market design and a more reasonable power grid construction.Basic methodologies: We develop an equilibrium model of the power market in China to analyze the coupling effect of these two approaches as well as their influence on power generation and interregional transmission in China. Our model considers both the Tradable green certificate (TGC) and green power market, which consists of producers, consumers in the market, and an independent system operator (ISO) minimizing the total system cost. Our equilibrium model includes the decision optimization process of each participant. To reformulate the models presented as a single-level one, we replace the producer, consumer, ISO, and market equilibrium problems with their Karush-Kuhn-Tucker (KKT) conditions, which is further reformulated as a mixed-integer linear programming (MILP) and solved in Gurobi solver. Major findings: The result shows that: (1) the green power market can significantly promote renewable power absorption while the TGC market provides a more flexible way for green power trading. (2) The phenomena of inefficient occupation and no available transmission lines appear simultaneously. The existing interregional transmission lines cannot fully meet the demand for wind and solar PV power trading in some areas while the situation is vice versa in other areas. (3) Synchronous implementation of green power and TGC trading mechanism can benefit the development of green power as well as interregional power transmission. (4) The green power transaction exacerbates the unfair distribution of carbon emissions. The Carbon Gini Coefficient is up to 0.323 under the green power market which shows a high Carbon inequality. The eastern coastal region will benefit the most due to its huge demand for external power.

Keywords: green power market, tradable green certificate, interregional power transmission, power market equilibrium model

Procedia PDF Downloads 93

Authors: Ghada Moussa, Mamoud Owais

Abstract:

Transit Route Network Design Problem (TrNDP) is the most important component in Transit planning, in which the overall cost of the public transportation system highly depends on it. The main purpose of this study is to develop a novel solution methodology for the TrNDP, which goes beyond pervious traditional sophisticated approaches. The novelty of the solution methodology, adopted in this paper, stands on the deterministic operators which are tackled to construct bus routes. The deterministic manner of the TrNDP solution relies on using linear and integer mathematical formulations that can be solved exactly with their standard solvers. The solution methodology has been tested through Mandl’s benchmark network problem. The test results showed that the methodology developed in this research is able to improve the given network solution in terms of number of constructed routes, direct transit service coverage, transfer directness and solution reliability. Although the set of routes resulted from the methodology would stand alone as a final efficient solution for TrNDP, it could be used as an initial solution for meta-heuristic procedures to approach global optimal. Based on the presented methodology, a more robust network optimization tool would be produced for public transportation planning purposes.

Keywords: integer programming, transit route design, transportation, urban planning

Procedia PDF Downloads 236

Authors: Ons Sassi, Wahiba Ramdane Cherif-Khettaf, Ammar Oulamara

Abstract:

In this paper, we consider a new real-life Heterogenous Electric Vehicle Routing Problem with Time Dependant Charging Costs and a Mixed Fleet (HEVRP-TDMF), in which a set of geographically scattered customers have to be served by a mixed fleet of vehicles composed of a heterogenous fleet of Electric Vehicles (EVs), having different battery capacities and operating costs, and Conventional Vehicles (CVs). We include the possibility of charging EVs in the available charging stations during the routes in order to serve all customers. Each charging station offers charging service with a known technology of chargers and time-dependent charging costs. Charging stations are also subject to operating time windows constraints. EVs are not necessarily compatible with all available charging technologies and a partial charging is allowed. Intermittent charging at the depot is also allowed provided that constraints related to the electricity grid are satisfied. The objective is to minimize the number of employed vehicles and then minimize the total travel and charging costs. In this study, we present a Mixed Integer Programming Model and develop a Charging Routing Heuristic and a Local Search Heuristic based on the Inject-Eject routine with three different insertion strategies. All heuristics are tested on real data instances.

Keywords: charging problem, electric vehicle, heuristics, local search, optimization, routing problem

Procedia PDF Downloads 436

Authors: Nima Khosravi

Abstract:

This paper describes an integrated optimization technique with concurrent use of sequential quadratic programming, genetic algorithm, and simulated annealing particle swarm optimization for the design and optimization of a beam column. In this research, the comparison between 4 different types of optimization methods. The comparison is done and it is found out that all the methods meet the required constraints and the lowest value of the objective function is achieved by SQP, which was also the fastest optimizer to produce the results. SQP is a gradient based optimizer hence its results are usually the same after every run. The only thing which affects the results is the initial conditions given. The initial conditions given in the various test run were very large as compared. Hence, the value converged at a different point. Rest of the methods is a heuristic method which provides different values for different runs even if every parameter is kept constant.

Keywords: beam column, genetic algorithm, particle swarm optimization, sequential quadratic programming, simulated annealing

Procedia PDF Downloads 356

Authors: Wlodzimierz Ogryczak, Michal Przyluski, Tomasz Sliwinski

Abstract:

In problems of portfolio selection, the reward-risk ratio criterion is optimized to search for a risky portfolio with the maximum increase of the mean return in proportion to the risk measure increase when compared to the risk-free investments. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several Linear Programming (LP) computable risk measures have been introduced and applied in portfolio optimization. In particular, the Mean Absolute Deviation (MAD) measure has been widely recognized. The reward-risk ratio optimization with the MAD measure can be transformed into the LP formulation with the number of constraints proportional to the number of scenarios and the number of variables proportional to the total of the number of scenarios and the number of instruments. This may lead to the LP models with huge number of variables and constraints in the case of real-life financial decisions based on several thousands scenarios, thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by an alternative model based on the inverse risk-reward ratio minimization and by taking advantages of the LP duality. In the introduced LP model the number of structural constraints is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability. Moreover, we show that under natural restriction on the target value the MAD risk-reward ratio optimization is consistent with the second order stochastic dominance rules.

Keywords: portfolio optimization, reward-risk ratio, mean absolute deviation, linear programming

Procedia PDF Downloads 379

Authors: H. R. Kamali, A. Sadegheih, M. A. Vahdat-Zad, H. Khademi-Zare

Abstract:

In this paper, a single product, multi-echelon, multi-period closed loop supply chain is surveyed, including a variety of costs, time conditions, and capacities, to plan and determine the values and time of the components procurement, production, distribution, recycling and disposal specially for high-tech products that undergo a decreasing production cost and sale price over time. For this purpose, the mathematic model of the problem that is a kind of mixed integer linear programming is presented, and it is finally proved that the problem belongs to the category of NP-hard problems.

Keywords: closed loop supply chain, continuous price decrease, NP-hard, planning

Procedia PDF Downloads 336

Authors: Siti Indati Mustapa, Hussain Ali Bekhet

Abstract:

Transportation sector represents more than 40% of total energy consumption in Malaysia. This sector is a major user of fossils based fuels, and it is increasingly being highlighted as the sector which contributes least to CO2 emission reduction targets. Considering this fact, this paper attempts to investigate the problem of reducing CO2 emission using linear programming approach. An optimization model which is used to investigate the optimal level of CO2 emission reduction in the road transport sector is presented. In this paper, scenarios have been used to demonstrate the emission reduction model: (1) utilising alternative fuel scenario, (2) improving fuel efficiency scenario, (3) removing fuel subsidy scenario, (4) reducing demand travel, (5) optimal scenario. This study finds that fuel balancing can contribute to the reduction of the amount of CO2 emission by up to 3%. Beyond 3% emission reductions, more stringent measures that include fuel switching, fuel efficiency improvement, demand travel reduction and combination of mitigation measures have to be employed. The model revealed that the CO2 emission reduction in the road transportation can be reduced by 38.3% in the optimal scenario.

Keywords: CO2 emission, fuel consumption, optimization, linear programming, transportation sector, Malaysia

Procedia PDF Downloads 388

Authors: Mao Zhaofang, Xu Yida, Fang Kan, Fu Enyuan, Zhao Zhao

Abstract:

Nowadays, last-mile distribution plays an increasingly important role in the whole industrial chain delivery link and accounts for a large proportion of the whole distribution process cost. Promoting the upgrading of logistics networks and improving the layout of final distribution points has become one of the trends in the development of modern logistics. Due to the discrete and heterogeneous needs and spatial distribution of customer demand, which will lead to a higher delivery failure rate and lower vehicle utilization, last-mile delivery has become a time-consuming and uncertain process. As a result, courier companies have introduced a range of innovative parcel storage facilities, including pick-up points and lockers. The introduction of pick-up points and lockers has not only improved the users’ experience but has also helped logistics and courier companies achieve large-scale economy. Against the backdrop of the COVID-19 of the previous period, contactless delivery has become a new hotspot, which has also created new opportunities for the development of collection services. Therefore, a key issue for logistics companies is how to design/redesign their last-mile distribution network systems to create integrated logistics and distribution networks that consider pick-up points and lockers. This paper focuses on the introduction of self-pickup facilities in new logistics and distribution scenarios and the heterogeneous demands of customers. In this paper, we consider two types of demand, including ordinary products and refrigerated products, as well as corresponding transportation vehicles. We consider the constraints associated with self-pickup points and lockers and then address the location-routing problem with self-pickup facilities and heterogeneous demands (LRP-PFHD). To solve this challenging problem, we propose a mixed integer linear programming (MILP) model that aims to minimize the total cost, which includes the facility opening cost, the variable transport cost, and the fixed transport cost. Due to the NP-hardness of the problem, we propose a hybrid adaptive large-neighbourhood search algorithm to solve LRP-PFHD. We evaluate the effectiveness and efficiency of the proposed algorithm by using instances generated based on benchmark instances. The results demonstrate that the hybrid adaptive large neighbourhood search algorithm is more efficient than MILP solvers such as Gurobi for LRP-PFHD, especially for large-scale instances. In addition, we made a comprehensive analysis of some important parameters (e.g., facility opening cost and transportation cost) to explore their impacts on the results and suggested helpful managerial insights for courier companies.

Keywords: city logistics, last-mile delivery, location-routing, adaptive large neighborhood search

Procedia PDF Downloads 31

Authors: Seyedehsomayeh Hosseini

Abstract:

Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

Procedia PDF Downloads 336

Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

Abstract:

In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

Procedia PDF Downloads 353

Authors: Yixun Shi

Abstract:

Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

Procedia PDF Downloads 374

Authors: Jun Yuan

Abstract:

Shipping is a major transportation mode all over the world, and it has a significant contribution to global carbon emissions. Electrification of ships is one of the main strategies to reduce shipping carbon emissions. The number of electric ships has continued to grow in recent years. However, charging infrastructure is still scarce, which severely restricts the development of electric ships. Therefore, it is very important to design ship charging stations reasonably by comprehensively considering charging demand and investment costs. This study aims to minimize the full life cycle cost of charging stations, considering the uncertainty of charging demand. A mixed integer programming model is developed for this optimization problem. Based on the characteristics of the mathematical model, a simulation based optimization method is proposed to find the optimal number and rated power of chargers. In addition, the impact of renewable energy and storage systems is analyzed. The results can provide decision support and a reference basis for the design of ship charging stations.

Keywords: shipping emission, electricity ship, charging station, optimal design

Procedia PDF Downloads 36

Authors: Pablo Oteiza, Ricardo Alvarez, Mehrdad Pirnia, Fuat Can

Abstract:

To effectively combat climate change, many countries around the world have committed to a decarbonisation of their electricity, along with promoting a large-scale integration of renewable energy sources (RES). While this trend represents a unique opportunity to effectively combat climate change, achieving a sound and cost-efficient energy transition towards low-carbon power systems poses significant challenges for the multi-year Transmission Network Expansion Planning (TNEP) problem. The objective of the multi-year TNEP is to determine the necessary network infrastructure to supply the projected demand in a cost-efficient way, considering the evolution of the new generation mix, including the integration of RES. The rapid integration of large-scale RES increases the variability and uncertainty in the power system operation, which in turn increases short-term flexibility requirements. To meet these requirements, flexible generating technologies such as energy storage systems must be considered within the TNEP as well, along with proper models for capturing the operational challenges of future power systems. As a consequence, TNEP formulations are becoming more complex and difficult to solve, especially for its application in realistic-sized power system models. To meet these challenges, there is an increasing need for developing efficient algorithms capable of solving the TNEP problem with reasonable computational time and resources. In this regard, a promising research area is the use of artificial intelligence (AI) techniques for solving large-scale mixed-integer optimization problems, such as the TNEP. In particular, the use of AI along with mathematical optimization strategies based on decomposition has shown great potential. In this context, this paper presents an efficient algorithm for solving the multi-year TNEP problem. The algorithm combines AI techniques with Column Generation, a traditional decomposition-based mathematical optimization method. One of the challenges of using Column Generation for solving the TNEP problem is that the subproblems are of mixed-integer nature, and therefore solving them requires significant amounts of time and resources. Hence, in this proposal we solve a linearly relaxed version of the subproblems, and trained a binary classifier that determines the value of the binary variables, based on the results obtained from the linearized version. A key feature of the proposal is that we integrate the binary classifier into the optimization algorithm in such a way that the optimality of the solution can be guaranteed. The results of a study case based on the HRP 38-bus test system shows that the binary classifier has an accuracy above 97% for estimating the value of the binary variables. Since the linearly relaxed version of the subproblems can be solved with significantly less time than the integer programming counterpart, the integration of the binary classifier into the Column Generation algorithm allowed us to reduce the computational time required for solving the problem by 50%. The final version of this paper will contain a detailed description of the proposed algorithm, the AI-based binary classifier technique and its integration into the CG algorithm. To demonstrate the capabilities of the proposal, we evaluate the algorithm in case studies with different scenarios, as well as in other power system models.

Keywords: integer optimization, machine learning, mathematical decomposition, transmission planning

Procedia PDF Downloads 43

Authors: Nader A. Al Theeb, Zaid Abu Manneh, Ibrahim Al-Qadi

Abstract:

Traveling salesman problem (TSP) is a combinatorial integer optimization problem that asks "What is the optimal route for a vehicle to traverse in order to deliver requests to a given set of customers?”. It is widely used by the package carrier companies’ distribution centers. The main goal of applying the TSP in courier organizations is to minimize the time that it takes for the courier in each trip to deliver or pick up the shipments during a day. In this article, an optimization model is constructed to create a new TSP variant to optimize the routing in a courier organization with a consideration of congestion in Amman, the capital of Jordan. Real data were collected by different methods and analyzed. Then, concert technology - CPLEX was used to solve the proposed model for some random generated data instances and for the real collected data. At the end, results have shown a great improvement in time compared with the current trip times, and an economic study was conducted afterwards to figure out the impact of using such models.

Keywords: travel salesman problem, congestions, pick-up, integer programming, package carriers, service engineering

Procedia PDF Downloads 394

Authors: Sema Kayapinar, Ismail Karaoglan, Turan Paksoy, Hadi Gokcen

Abstract:

Green Supply Chain Management is gaining growing interest among researchers and supply chain management. The concept of Green Supply Chain Management is to integrate environmental thinking into the Supply Chain Management. It is the systematic concept emphasis on environmental problems such as reduction of greenhouse gas emissions, energy efficiency, recycling end of life products, generation of solid and hazardous waste. This study is to present a green supply chain network model integrated Internet of Things applications. Internet of Things provides to get precise and accurate information of end-of-life product with sensors and systems devices. The forward direction consists of suppliers, plants, distributions centres and sales and collect centres while, the reverse flow includes the sales and collects centres, disassembled centre, recycling and disposal centre. The sales and collection centre sells the new products are transhipped from factory via distribution centre and also receive the end-of life product according their value level. We describe green logistics activities by presenting specific examples including “recycling of the returned products and “reduction of CO2 gas emissions”. The different transportation choices are illustrated between echelons according to their CO2 gas emissions. This problem is formulated as a mixed integer linear programming model to solve the green supply chain problems which are emerged from the environmental awareness and responsibilities. This model is solved by using Gams package program. Numerical examples are suggested to illustrate the efficiency of the proposed model.

Keywords: green supply chain optimization, internet of things, greenhouse gas emission, recycling

Procedia PDF Downloads 295

Authors: Rui Li, Min Wen, Kim Bang Salling

Abstract:

For the modern railways, maintenance is critical for ensuring safety, train punctuality and overall capacity utilization. The cost of railway maintenance in Europe is high, on average between 30,000 – 100,000 Euros per kilometer per year. In order to reduce such maintenance expenditures, this paper presents a mixed 0-1 linear mathematical model designed to optimize the predictive railway tamping activities for ballast track in the planning horizon of three to four years. The objective function is to minimize the tamping machine actual costs. The approach of the research is using the simple dynamic model for modelling condition-based tamping process and the solution method for finding optimal condition-based tamping schedule. Seven technical and practical aspects are taken into account to schedule tamping: (1) track degradation of the standard deviation of the longitudinal level over time; (2) track geometrical alignment; (3) track quality thresholds based on the train speed limits; (4) the dependency of the track quality recovery on the track quality after tamping operation; (5) Tamping machine operation practices (6) tamping budgets and (7) differentiating the open track from the station sections. A Danish railway track between Odense and Fredericia with 42.6 km of length is applied for a time period of three and four years in the proposed maintenance model. The generated tamping schedule is reasonable and robust. Based on the result from the Danish railway corridor, the total costs can be reduced significantly (50%) than the previous model which is based on optimizing the number of tamping. The different maintenance strategies have been discussed in the paper. The analysis from the results obtained from the model also shows a longer period of predictive tamping planning has more optimal scheduling of maintenance actions than continuous short term preventive maintenance, namely yearly condition-based planning.

Keywords: integer programming, railway tamping, predictive maintenance model, preventive condition-based maintenance

Procedia PDF Downloads 412

Authors: Ming-Jong Yao, Chin-Sum Shui, Chih-Han Wang

Abstract:

This paper is developed based on a real-world decision scenario that an industrial gas company that applies the Vendor Managed Inventory model and supplies liquid oxygen with a self-operated heterogeneous vehicle fleet to hospitals in nearby cities. We name it as a Joint Replenishment and Heterogeneous Vehicle Routing Problem with Cyclical Schedule and formulate it as a non-linear mixed-integer linear programming problem which simultaneously determines the length of the planning cycle (PC), the length of the replenishment cycle and the dates of replenishment for each customer and the vehicle routes of each day within PC, such that the average daily operation cost within PC, including inventory holding cost, setup cost, transportation cost, and overtime labor cost, is minimized. A solution method based on genetic algorithm, embedded with an encoding and decoding mechanism and local search operators, is then proposed, and the hash function is adopted to avoid repetitive fitness evaluation for identical solutions. Numerical experiments demonstrate that the proposed solution method can effectively solve the problem under different lengths of PC and number of customers. The method is also shown to be effective in determining whether the company should expand the storage capacity of a customer whose demand increases. Sensitivity analysis of the vehicle fleet composition shows that deploying a mixed fleet can reduce the daily operating cost.

Keywords: cyclic inventory routing problem, joint replenishment, heterogeneous vehicle, genetic algorithm

Procedia PDF Downloads 51

Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

Abstract:

To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II

Procedia PDF Downloads 187

Authors: Sagar Hedaoo, Fazle Baki, Ahmed Azab

Abstract:

In supply chain management, network design for scalable manufacturing facilities is an emerging field of research. Facility location allocation assigns facilities to customers to optimize the overall cost of the supply chain. To further optimize the costs, capacities of these facilities can be changed in accordance with customer demands. A mathematical model is formulated to fully express the problem at hand and to solve small-to-mid range instances. A dedicated constraint has been developed to restrict emissions in line with the Kyoto protocol. This problem is NP-Hard; hence, a simulated annealing metaheuristic has been developed to solve larger instances. A case study on the USA-Canada cross border crossing is used.

Keywords: emission, mixed integer linear programming, metaheuristic, simulated annealing

Procedia PDF Downloads 281