Binary Mixed Integer Linear Programming Research Articles

Optimal correlation of non-renewable and renewable generating systems for producing hydrogen and methane by power to gas process

This paper presents an efficient framework for converting renewable energy to gas and reducing Carbon dioxide (CO2) footprint at the same time. The problem is presented in two levels. The first level is a minimization programming that minimizes operational cost and CO2 of generators. The CO2 is forwarded to the second level. In the second level, Carbon Capture and Storage (CCS) is designed to capture CO2. The CO2 is combined with Hydrogen and makes Methane (CH4). The required Hydrogen is obtained from water electrolyzer that is supplied by the solar system. The capacity and size of water electrolyzer, solar system, and CCS is designed by the planning in the second level while this programming maximizes profit from selling Methane. As a result, the first level presents minimization programming (i.e., minimizing cost and CO2) and the second level presents maximization programming (i.e., maximizing profit). The programming is developed taking into account solar uncertainty. The stochastic programming is implemented to cope with uncertainties. The problem is formulated as binary mixed integer linear programming and solved by GAMS software. The proposed power to gas (P2G) procedure efficiently designs proper solar system and deals with intermittency of solar energy, reduces CO2 footprint, maximizes profit, and minimizes operational cost of generators at the same time.

The symmetric intersection design and traffic control optimization

It is well recognized that the left-turning movement reduces the intersection capacity significantly, because exclusive left turn phases are needed to discharge left turn vehicles only. This paper proposes the concept of Left-Hand Traffic (LHT) arterial, on where vehicles follow left-hand traffic rules as in England and India. The unconventional intersection where a LHT arterial intersects with a Right-Hand Traffic (RHT) arterial is named as symmetric intersection. It is only need three basic signal phases to separate all conflicts at symmetric intersection, while it at least need four signal phases at a conventional intersection. So, compared with the conventional intersection, the symmetric intersection can provide longer green time for the left-turning and the through movement, which can increase the capacity significantly. Through-movement waiting areas (TWAs) can be set at the symmetric intersection effectively, which can increase the capacity and short the cycle length furthermore. And the symmetric intersection is Channelized to improve the safety of TWAs. The Binary-Mixed-Integer-Linear-Programming (BMILP) model is employed to formulate the capacity maximization problem and signal cycle length minimization problem of the symmetric intersection. The BMILP model can be solved by standard branch-and-bound algorithms efficiently and outputs the lane allocation, signal timing decisions, and other decisions. Experiments analysis shows that the symmetric intersection with TWAs can increase the capacity and short the signal cycle length.

Optimization of crane setup location and servicing schedule for urgent material requests with non-homogeneous and non-fixed material supply

Abstract Reducing hook movement distances could decrease crane operation times to deliver heavyweight materials in construction sites. Conventional scheduling methods include first-in-first-serve (FIFS), shortest-job-first (SJF), nearest-neighbor-first (NNF), and Traveling salesman problem (TSP). A new optimization model to optimize crane setup location, hook movement sequences and servicing schedules serving all supply and demand locations is proposed. Proposed model is able to model homogeneous and non-homogeneous material supply. Initial hook location can be given as input for optimization. Fixed material supply and demand location pairs are relaxed as model variables. Maximum crane lifting capacity is considered and multiple hook movement trips between material supply and demand locations are modeled if requested material weights exceed this maximum crane lifting capacity. Users may place “urgent” material demand requests and the proposed optimization model can optimize a servicing sequence to prioritize all urgent requests. The problem is formulated as a Binary-Mixed-Integer-Linear-Program (BMILP) which is solved by standard branch-and-bound techniques. Significant reduction in total operation time is achieved while comparing to other conventional scheduling strategies.

Signal Timing Optimization of an Isolated Intersection Considering the Allocation of Exit Lanes

Unconventional intersection designs have been used to increase the capacity of intersections that are over-saturated under conventional ones. However, existing unconventional designs typically require extra land space and their effectiveness often depends on drivers' familiarity with the uncommon operating rules. To overcome these challenges, we propose a new unconventional design, where movements that are mutually incompatible under the conventional design can be made compatible of each other by allocating exit lanes to them appropriately, thereby creating opportunities for capacity improvement. We develop a lane-based capacity optimization model that incorporates the allocation of exit lanes as decision variables. The model is formulated as a Binary Mixed Integer Linear Programming problem, which can be efficiently solved by standard branch-and-bound algorithms. Numerical experiments show that significant capacity improvement can be obtained under our design. Besides proposing a new unconventional design, we also contribute to the literature of lane-based signal optimization methods by providing a novel linear formulation for the latest, yet nonlinear, model described in Wong and Heydecker (2011). This improvement is methodologically beneficial as linear models are computationally much more convenient than nonlinear models.

Lane-Based Optimization for Macroscopic Network Configuration Designs

Lane markings (arrows) at individual intersections serve as interfaces to connect upstream and downstream intersections in signal-controlled networks. Demand flows from origins to destinations may need to pass through a series of intersections. If lane markings are not well established to ban turns at intersections, then paths connecting origin and destination (OD) pairs could be inefficient. Due to indirect connections, road users need to take longer paths to reach their destinations. Conventionally, network configurations are fixed inputs for network analysis. In the present study, concepts of the lane-based designs for individual signalized intersections are extended for signal-controlled network designs. Taking OD demand flows as inputs, the proposed algorithm will optimize all lane markings and assigned lane flows on approach lanes. Paths (flows) will then be optimized by linking up the optimized lane markings across upstream and downstream intersections. Traffic signal settings at individual intersections will be optimized simultaneously by maximizing the reserve capacity for the entire OD demand flow matrix. The problem is formulated as a Binary-Mixed-Integer-Linear-Program (BMILP) and a standard branch-and-bound routine is applied to solve for global optimum solutions. A numerical example using a 4-intersection network will be given to demonstrate the effectiveness of the proposed design methodology.

Increasing the capacity of signalized intersections by allocating exit lanes to turning movements

AbstractUnconventional intersection designs have been used to increase the capacity of intersections that are over‐saturated under conventional ones. However, existing unconventional designs typically require extra land space and their effectiveness often depends on drivers' familiarity with the uncommon operating rules. To overcome these challenges, we propose a new unconventional design, where movements that are mutually incompatible under the conventional design can be made compatible of each other by allocating exit lanes to them appropriately, thereby creating opportunities for capacity improvement. We develop a lane‐based capacity optimization model that incorporates the allocation of exit lanes as decision variables. The model is formulated as a Binary Mixed Integer Linear Programming problem, which can be efficiently solved by standard branch‐and‐bound algorithms. Numerical experiments show that significant capacity improvement can be obtained under our design. Besides proposing a new unconventional design, we also contribute to the literature of lane‐based signal optimization methods by providing a novel linear formulation for the latest, yet nonlinear, model described in Wong and Heydecker [Transportation Research Part B 45(4):667–681]. This improvement is methodologically beneficial as linear models are computationally more convenient than nonlinear ones. Copyright © 2017 John Wiley & Sons, Ltd.

Discretized Cell Modeling for Optimal Facility Layout Plans of Unequal and Irregular Facilities

AbstractFacility layout design is an essential planning task to resolve potential spatial conflicts and overlapping during practical operations. A discretized cell optimization model is developed to optimize site space usages. Site areas and facilities are represented by small unit cells to effectively model irregularities, and the availability of unit cells for use in a facility setup is modeled by binary-type variables. With size and shape requirements through linear constraints, the site layout design can be formulated as a binary mixed integer-linear programming (BMILP) problem to allocate different facilities onto different site available areas in optimal shapes and locations. Total material transportation costs across facilities are optimized subject to various design constraints ensuring safety, homogenous facility setups, physical size, and orientation requirements. The proposed cell model is verified by comparing optimization results with results obtained by conventional point notation methods. A...

Transit signal priority accommodating conflicting requests under Connected Vehicles technology

In this research, a person-delay-based optimization method is proposed for an intelligent Transit Signal Priority (TSP) logic that resolves multiple conflicting TSP requests at an isolated intersection. This TSP with Connected Vehicles accommodating Conflicting Requests (TSPCV-CR) overcomes the challenge bore by the conventional “first come first serve” strategy and presents significant improvement on bus service performance. The feature of TSPCV-CR includes green time re-allocation, simultaneous multiple buses accommodation, and signal-transit coordination. These features help maximize the transit TSP service rate and minimize adverse effect on competing travel directions. The TSPCV-CR is also designed to be conditional. That is, TSP is granted only when the bus is behind schedule and the grant of TSP causes no extra total person delay. The optimization is formulated as a Binary Mixed Integer Linear Program (BMILP) which is solved by standard branch-and-bound routine. Minimizing per person delay is the objective of the optimization model.The logic developed in this research is evaluated using both analytical and microscopic traffic simulation approaches. Both analytical tests and simulation evaluations compared three scenarios: without TSP (NTSP), conventional TSP (CTSP), and TSP with Connected Vehicles that resolves Conflicting Requests (TSPCV-CR). The measures of effectiveness used include bus delay and total travel time of all travelers. The performance of TSPCV-CR is compared against conventional TSP (CTSP) under four congestion levels and three different conflicting scenarios. The results show that the TSPCV-CR greatly reduces bus delay at signalized intersection for all congestion levels and conflicting scenarios considered. Simulation based evaluation results show that the TSPCV-CR logic reduces average bus delay between 5% and 48% compared to the conventional TSP. The range of improvement corresponding to the four different v/c ratios tested, which are 0.5, 0.7, 0.9 and 1.0, respectively. No statistically significant negative effects are observed.

Coordinated transit signal priority supporting transit progression under Connected Vehicle Technology

In this paper, a person-delay-based optimization method is proposed for an intelligent TSP logic that enables bus/signal cooperation and coordination among consecutive signals under the Connected Vehicle environment. This TSP logic, called TSPCV-C, provides a method to secure the mobility benefit generated by the intelligent TSP logic along a corridor so that the bus delay saved at an upstream intersection is not wasted at downstream intersections. The problem is formulated as a Binary Mixed Integer Linear Program (BMILP) which is solved by standard branch-and-bound method. Minimizing per person delay has been adopted as the criterion for the model. The TSPCV-C is also designed to be conditional. That is, TSP is granted only when the bus is behind schedule and the grant of TSP causes no extra total person delay.The logic developed in this research is evaluated using both analytical and microscopic traffic simulation approaches. Both analytical tests and simulation evaluations compared four scenarios: without TSP (NTSP), conventional TSP (CTSP), TSP with Connected Vehicle (TSPCV), and Coordinated TSP with Connected Vehicle (TSPCV-C). The measures of effectiveness used include bus delay and total travel time of all travelers. The performance of TSPCV-C is compared against conventional TSP (CTSP) under four congestion levels and five intersection spacing cases. The results show that the TSPCV-C greatly reduces bus delay at signalized intersection for all congestion levels and spacing cases considered. Although the TSPCV is not as efficient as TSPCV-C, it still demonstrates sizable improvement over CTSP. An analysis on the intersection spacing cases reveals that, as long as the intersections are not too closely spaced, TSPCV can produce a delay reduction up to 59%. Nevertheless, the mechanism of TSPCV-C is recommended for intersections that are spaced less than 0.5 mile away. Simulation based evaluation results show that the TSPCV-C logic reduces the bus delay between 55% and 75% compared to the conventional TSP. The range of improvement corresponding to the four different v/c ratios tested, which are 0.5, 0.7, 0.9 and 1.0, respectively. No statistically significant negative effects are observed except when the v/c ratio equals 1.0.

Operation of signalized diamond interchanges with frontage roads using dynamic reversible lane control

Signalized diamond interchanges (SDI), connecting major highways and surface streets in urban and suburban areas, are probably the most widely used interchange patterns. The limited storage space between the two closely joined intersections coupled with heavy traffic volumes may easily oversaturate the facility and cause spillback problems, especially with the presence of frontage roads. This paper presents an innovative design and operational model for SDI by dynamically reversing certain lanes in the internal link on a regular basis with the deployment of overhead reversible lane control signs. A Binary-Mixed-Integer-Linear-Program (BMILP) is formulated to simultaneously optimize lane markings, dynamic usage of the reversible lane, and signal timings for the new SDI system. Results from extensive numerical analyses reveal the promising property of the proposed design and operational model in expanding capacity and reducing congestion at the SDI with frontage roads.

Integrated optimization of transit priority operation at isolated intersections: A person-capacity-based approach

In this paper, a person-capacity-based optimization method for the integrated design of lane markings, exclusive bus lanes, and passive bus priority signal settings for isolated intersections is developed. Two traffic modes, passenger cars and buses, have been considered in a unified framework. Person capacity maximization has been used as an objective for the integrated optimization method. This problem has been formulated as a Binary Mixed Integer Linear Program (BMILP) that can be solved by a standard branch-and-bound routine. Variables including, allocation of lanes for different passenger car movements (e.g., left turn lanes or right turn lanes), exclusive bus lanes, and passive bus priority signal timings can be optimized simultaneously by the proposed model. A set of constraints have been set up to ensure feasibility and safety of the resulting optimal lane markings and signal settings. Numerical examples and simulation results have been provided to demonstrate the effectiveness of the proposed person-capacity-based optimization method. The results of extensive sensitivity analyses of the bus ratio, bus occupancy, and maximum degree of saturation of exclusive bus lanes have been presented to show the performance and applicable domain of the proposed model under different composition of inputs.

Capacity optimization of an isolated intersection under the phase swap sorting strategy

It is well recognized that the left turn reduces the intersection capacity significantly, because some of the traffic lanes cannot be used to discharge vehicles during its green phases. In this paper, we operationalize the phase swap sorting strategy (Xuan, 2011) to use most, if not all, traffic lanes to discharge vehicles at the intersection cross-section to increase its capacity. We explicitly take into consideration all through, left- and right-turning movements on all arms and formulate the capacity maximization problem as a Binary-Mixed-Integer-Linear-Programming (BMILP) model. The model is efficiently solved by standard branch-and-bound algorithms and outputs optimal signal timings, lane allocations, and other decisions. Numerical experiments show that substantially higher reserve capacity can be obtained under our approach.

A Sorting Area Strategy to Increase the Capacity of Isolated Intersections

It is well recognized that the left turn reduces the intersection capacity significantly, because some of the traffic lanes cannot be used to discharge vehicles during its green phases. In this paper, we operationalize the phase swap sorting strategy (Xuan, 2011) to use most, if not all, traffic lanes to discharge vehicles at the intersection cross section to increase its capacity. We explicitly take into consideration all through, left- and right-turning movements on all arms and formulate the capacity maximization problem as a Binary-Mixed-Integer-Linear-Programming (BMILP) model. The model is efficiently solved by standard branch-and-bound algorithms and outputs optimal signal timings, lane allocations, and other decisions. Numerical experiments show that substantially higher reserve capacity can be obtained under our approach.

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 real-life 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.