Two-phase Optimization Approach Research Articles

Optimization Automates Emergency Department Nurse Scheduling at Hartford Hospital

A collaboration between Hartford Hospital, MIT, and Dynamic Ideas LLC optimizes nurse staffing in emergency department using a two-phase optimization approach. We developed and implemented robust optimization models and automated scheduling software, reducing staffing costs by 5%–8%, enhancing patient care coverage by 8%–25%. This streamlined process is projected to save approximately $720,000 annually, replacing a labor-intensive scheduling method previously in place.

Logistics in the Sky: A Two-Phase Optimization Approach for the Drone Package Pickup and Delivery System

The application of drones in last-mile distribution has been a contentious research topic in recent years. Existing urban distribution modes mostly depend on trucks. This paper proposes a novel package pickup and delivery mode and system wherein multiple drones collaborate with automatic devices. The proposed mode uses free areas on top of residential buildings to set automatic devices as delivery and pickup points of packages, and employs drones to transport packages between buildings and depots. The integrated scheduling problem of package drop-pickup considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -drones, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -depots, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -customers is crucial for the system. Therefore, we propose a simulated-annealing-based two-phase optimization (SATO) approach to solve this problem. In the first phase, tasks are allocated to depots for serving, such that the initial problem is decomposed into multiple single-depot scheduling problems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -drone. In the second phase, considering the drone capability and task demand constraints, we generated a route-planning scheme for drones in each depot. Concurrently, an improved variable neighborhood descent (IVND) algorithm was designed in the first phase to reallocate tasks, and a local search (LS) algorithm was proposed to search for high-quality solutions in the second phase. Finally, extensive experiments and comparative studies were conducted to verify the effectiveness of the proposed approach.

Designing an efficient vaccine supply chain network using a two-phase optimization approach: a case study of COVID-19 vaccine

The upsurge of the COVID-19 pandemic and its consequences on the world’s population has led to the accelerated production of vaccines across the world. The next challenge in the fight against COVID-19 is to distribute those vaccines to the right person in an optimized way by establishing an efficient vaccine supply network. Consequently, this paper studies an integrated two-phase planning framework for the vaccine distribution network. In the first phase, the population target is classified into several groups to determine their priority for vaccination using a multiple attribute decision making (MADM) technique. The second phase uses a mathematical model to decide on the location of distribution centers, inventory policies, and routing decisions to minimize the total procurement, inventory, and distribution costs. Since the proposed model falls into the category of NP-hard problems, a metaheuristic algorithm entitled population-based simulated annealing (PBSA) is developed to solve the presented model. Besides, the improved grey wolf optimizer (I-GWO) is customized and used as another solution method. A few generated datasets are utilized to evaluate and validate the performance of these solution methods. In addition, this methodology is implemented in a case study of the COVID-19 vaccine supply chain in Iran to demonstrate its practicability.

Two-phase optimization approach for maintenance workforce planning in power distribution utilities

This work addresses the maintenance workforce planning in electric power distribution utilities. A two-phase optimization procedure is proposed to consider the strategic (long-term) and tactical/operational (medium/short-term) planning. In the first phase (strategic planning), a bi-objective optimization problem is solved to locate depots and to size the number of repair teams at each depot. One of the objectives includes operating and capital expenses, while the other one is based on continuity indicators related to the interruption in the electrical energy supply. In order to solve this problem, we use a memetic algorithm which combines a metaheuristic with a mixed-integer linear programming (MILP) model. On the other hand, the second phase (tactical/operational planning) consists of solving other MILP model to determine, for each depot, the required number of electricians (now based on more detailed forecasts) and define their work schedules, minimizing the wage costs and hiring/firing expenses. The results show that a larger number of solutions can be found through the memetic algorithm compared to the purely metaheuristic approach. The proposed optimization algorithm is part of an innovative web-based system developed during a research and development project and it is now available for eleven Brazilian power distribution utilities.

Three-Dimensional Subject-Specific Knee Shape Reconstruction with Asynchronous Fluoroscopy Images Using Statistical Shape Modeling.

Background and objectives: Statistical shape modeling (SSM) based on computerized tomography (CT) datasets has enabled reasonably accurate reconstructions of subject-specific 3D bone morphology from one or two synchronous radiographs for clinical applications. Increasing the number of radiographic images may increase the reconstruction accuracy, but errors related to the temporal and spatial asynchronization of clinical alternating bi-plane fluoroscopy may also increase. The current study aimed to develop a new approach for subject-specific 3D knee shape reconstruction from multiple asynchronous fluoroscopy images from 2, 4, and 6 X-ray detector views using a CT-based SSM model; and to determine the optimum number of planar images for best accuracy via computer simulations and in vivo experiments. Methods: A CT-based SSM model of the knee was established from 60 training models in a healthy young Chinese male population. A new two-phase optimization approach for 3D subject-specific model reconstruction from multiple asynchronous clinical fluoroscopy images using the SSM was developed, and its performance was evaluated via computer simulation and in vivo experiments using one, two and three image pairs from an alternating bi-plane fluoroscope. Results: The computer simulation showed that subject-specific 3D shape reconstruction using three image pairs had the best accuracy with RMSE of 0.52 ± 0.09 and 0.63 ± 0.085 mm for the femur and tibia, respectively. The corresponding values for the in vivo study were 0.64 ± 0.084 and 0.69 ± 0.069 mm, respectively, which was significantly better than those using one image pair (0.81 ± 0.126 and 0.83 ± 0.108 mm). No significant differences existed between using two and three image pairs. Conclusion: A new two-phase optimization approach was developed for SSM-based 3D subject-specific knee model reconstructions using more than one asynchronous fluoroscopy image pair from widely available alternating bi-plane fluoroscopy systems in clinical settings. A CT-based SSM model of the knee was also developed for a healthy young Chinese male population. The new approach was found to have high mode reconstruction accuracy, and those for both two and three image pairs were much better than for a single image pair. Thus, two image pairs may be used when considering computational costs and radiation dosage. The new approach will be useful for generating patient-specific knee models for clinical applications using multiple asynchronous images from alternating bi-plane fluoroscopy widely available in clinical settings. The current SSM model will serve as a basis for further inclusion of training models with a wider range of sizes and morphological features for broader applications.

Customer-Oriented Vehicle Routing Problem with Environment Consideration: Two-Phase Optimization Approach and Heuristic Solution

With the fastest consumer demand growth, the increasing customer’s demands trend to multivarieties and small-batch and the customer requires an efficient distribution planning. How to plan the vehicle route to meet customer satisfaction of mass distribution as well as reduce the fuel consumption and emission has become a hot topic. This paper proposes a two-phase optimization method to handle the vehicle routing problem, considering the customer demands and time windows coupled with multivehicles. The first phase of the optimization method provides a fuzzy hierarchical clustering method for customer grouping. The second phase formulates the optimization en-group vehicle routing problem model and a genetic algorithm to account for vehicle routing optimization within each group so that fuel consumption and emissions are minimized. Finally, we provide some numerical examples. Results show that the two-phase optimization method and the designed algorithm are efficient.

Movable Unmanned Aerial System: Optimization of System, Resource Design and Drone Routing

One of the strengths of drone is the mobility. Drone can fly without avoiding obstacles and provide services in a timely manner. However ironically, the mobility of drone cannot last for long duration due to the low battery capacity and limited loadable products. As a consequence, the use of drones may be extremely limited in a wide field of operation. One of the solutions for complementing such weaknesses of drone is the use of movable stations. Stations move across a wide field of operation and replenish consumables for drones, such as battery and service product. By visiting movable stations and replenishing consumables, drones can provide persistent service in a wide range of operation area. In this study, design and operation issues of movable unmanned aerial system (MUAS) are address for long term and persistent drone service. A two-phase optimization approach is developed to efficiently handle the system complexity. In the phase I, locations of movable stations and allocation of tasks are identified for multi-period of service duration. In the phase II, number of drones for each station and their routings are optimized based on the result of phase I. Mathematical models are proposed and verified with a case study.

Border-search and jump reduction method for size optimization of spatial truss structures

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.

A Multi-Objective Optimization Approach for Corrective Switching of Transmission Systems in Emergency Scenarios

The large capacity transmission of power over long distance and the rapid development of renewable energy increase the probability of unexpected emergencies such as overload and under-voltage. To tackle these emergencies and defend future disturbances, the corrective switching is implemented as an online control and a multi-objective scheme-making approach is proposed. A multi-objective 0-1 integer optimization model is established to cover a set of contradictory objectives from the aspects of economics, security and reliability. A two-phase optimization approach is proposed to ensure computation efficiency and coordinate the trade-off between these objectives: in the first phase, a feasible set silting method is utilized to quickly search for a set of candidate corrective switching schemes; in the second phase, the technique for order preference by similarity to an ideal solution (TOPSIS) method is applied to the candidate set to coordinate the contradictory objectives and determine the ultimate engineering scheme. Two case studies are conducted to verify the proposed approach in overload and under-voltage scenarios. The results are discussed to show the strengths when the performance indices of economics, security and reliability are considered.

A Two-Phase Optimization Method for Solving the Multi-Type Maximal Covering Location Problem in Emergency Service Networks

This study introduces the Multi-Type Maximal Covering Location Problem (MTMCLP) that arises from the design of emergency service networks, and represents a generalization of the well-known Maximal Covering Location Problem (MCLP). Differently from the basic MCLP, several types of incidents and emergency units are considered and hierarchy of emergency units of different types is assumed in the MTMCLP. The numbers of available emergency units of each type are limited to some constants. The objective of the MTMCLP is to choose locations for establishing emergency units of each type, such that the total number of covered incidents is maximized. In order to provide a decision maker with optimal solutions in an efficient manner, a two-phase optimization approach to the MTMCLP is designed. In the first phase, a variant of Reduced Variable Neighborhood Search (RVNS) is applied to quickly find a high-quality solution. The obtained RVNS solution is used as a good starting point for the Linear Programming method in the second phase, which returns the optimal solution to the MTMCLP. All constructive elements of the proposed two-phase method, denoted as RVNS-LP, are adapted to the characteristics of the considered problem. The RVNS-LP approach is evaluated on real-life instances obtained from two networks of police units in Montenegro and Serbia, and randomly generated test instances of larger dimensions. Experimental evaluation shows that the proposed RVNS-LP reached all optimal solutions on all real-life test instances in very short CPU time. On generated test instances, the RVNS-LP also returned optimal solutions in all cases, within short running times and significant time savings compared to CPLEX solver. The mathematical model and the proposed two-phase optimization method may be applicable in the design and management of various emergency-service networks.DOI: http://dx.doi.org/10.5755/j01.itc.46.1.13853

GOSAC: global optimization with surrogate approximation of constraints

We introduce GOSAC, a global optimization algorithm for problems with computationally expensive black-box constraints and computationally cheap objective functions. The variables may be continuous, integer, or mixed-integer. GOSAC uses a two-phase optimization approach. The first phase aims at finding a feasible point by solving a multi-objective optimization problem in which the constraints are minimized simultaneously. The second phase aims at improving the feasible solution. In both phases, we use cubic radial basis function surrogate models to approximate the computationally expensive constraints. We iteratively select sample points by minimizing the computationally cheap objective function subject to the constraint function approximations. We assess GOSAC’s efficiency on computationally cheap test problems with integer, mixed-integer, and continuous variables and two environmental applications. We compare GOSAC to NOMAD and a genetic algorithm (GA). The results of the numerical experiments show that for a given budget of allowed expensive constraint evaluations, GOSAC finds better feasible solutions more efficiently than NOMAD and GA for most benchmark problems and both applications. GOSAC finds feasible solutions with a higher probability than NOMAD and GOSAC.

Resource Allocation Optimization for Users with Different Levels of Service in Multicarrier Systems

We optimize the throughput of a single cell multiuser orthogonal frequency division multiplexing system with proportional data rate fairness among the users. The concept is to support mobile users with different levels of service. The optimization problem is a mixed integer nonlinear programming problem, which is computationally very expensive. We propose a novel and efficient near-optimal solution adopting a two-phase optimization approach that separates the subcarrier and power allocation. In the first phase, we relax the strict proportional data rate requirements and employ an iterative subcarrier allocation approach that coarsely satisfies desired data rate proportionality constraints. In the second phase, we reallocate the power among the users in an iterative way to further enhance the adherence to the desired proportions by exploiting the normalized proportionality deviation measure. The simulation results show that the proposed solution exhibits very strong adherence to the desired proportional data rate fairness while achieving higher system throughput compared to the other existing solutions.

Application of Two-Phase Fuzzy Optimization Approach to Multiproduct Multistage Integrated Production Planning with Linguistic Preference under Uncertainty

This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.

Two-phase optimization approach to transit hub location – the case of Dalian

This paper proposes an approach to deal with the hub location problem in urban public transit network design, which includes two phases: to determine the candidate nodes and to optimize the distribution of transit hubs. Firstly, an indicator defined as passenger attraction is introduced to describe the attraction level of a transit node to passengers. A selection model based on passenger attraction is built to choose several candidate nodes from all the transit nodes. Secondly, a mathematical model, aiming at maximizing served populations per construction cost, is proposed to optimize multi-hub location based on the selected candidate nodes. At last, the data of Dalian city, China is used for testing the validity of the proposed approach. The results indicate that the candidate node selection model according to passenger attraction can provide an appropriate searching space for hub location optimization and the selected candidate nodes can almost cover all the passenger flow collection and distribution centers in the urban area of Dalian. Furthermore, the optimized hub location in the case study is consistent with the practice situation in Dalian. This indicates that the proposed two-phase optimization approach is a competitive method for transit hub location.

Using time-varying tolls to optimize truck arrivals at ports

An analytical point-wise stationary approximation model is proposed to analyze time-dependent truck queuing processes with stochastic service time distributions at gates and yards of a port terminal. A convex nonlinear programming model is developed which minimizes the total truck turn time and discomfort due to shifted arrival times. A two-phase optimization approach is used to first compute a system-optimal truck arrival pattern, and then find a desirable pattern of time-varying tolls that leads to the optimal arrival pattern. Numerical experiments are conducted to test the computational efficiency and accuracy of the proposed optimization models.

Modèles d'optimisation pour la conception des chaînes logistiques internationales

This paper presents a two-phase optimization approach for the design of global supply chains. The first phase is concerned with the strategic planning level while the second phase deals with the tactical level. We consider several international factors such as transfer prices of tangible and intangible activities. To model the transfer price, we adopt a realistic profit-based approach. The proposed model is finally illustrated by a case study.

Graph theory-based approach to optimize single-product flow-line configurations of RMS

Generating economical and distinctive configurations for a given demand period is an important optimization problem for reconfigurable manufacturing systems (RMS) at both initial design and reconfiguration stages. This paper presents a graph model to optimize capital cost of singe-product flow-line (SPFL) configurations of RMS. The parameters of the SPFL configuration include number of workstations, number and type of machines and assigned operations for each workstation. The full topological sorting and graph augmentation procedures are developed to derive a combined machine graph from the operation precedence graph of a specific product. Then a two-phase optimization approach is proposed. In the first phase, the optimal and K-1 suboptimal configurations are generated by solving a constrained K-shortest paths problem on the machine graph. In the second phase, a dissimilarity index is introduced to measure the dissimilarity between every pair of found configurations. Subsequently p distinctive ones out of K configurations are obtained using the algorithms for p-dispersion problem. Case studies illustrate the effectiveness of our approach and show some superiority of our approach compared to existing approaches. Computational experience shows that the approach is fit for small-to-medium size problems of configuration generation. The approach is also applied to optimizing SPFL in mechanical production.

Value chain management for commodities: a case study from the chemical industry

We present a planning model for chemical commodities related to an industry case. Commodities are standard chemicals characterized by sales and supply volatility in volume and value. Increasing and volatile prices of crude oil-dependent raw materials require coordination of sales and supply decisions by volume and value throughout the value chain to ensure profitability. Contract and spot demand differentiation with volatile and uncertain spot prices, spot sales quantity flexibility, spot sales priceȁ3quantity functions and variable raw material consumption rates in production are problem specifics to be considered. Existing chemical industry planning models are limited to production and distribution decisions to minimize costs or makespan. Demand-oriented models focus on uncertainty in demand quantities not in prices.We develop an integrated model to optimize profit by coordinating sales quantity, price and supply decisions throughout the value chain. A two-phase optimization approach supports robust planning ensuring minimum profitability even in case of worst-case spot sales price scenarios. Model evaluations with industry case data demonstrate the impact of elasticities, variable raw material consumption rates and price uncertainties on planned profit and volumes.

Extracting the autonomic nerve wreath of iris based on an improved snake approach

The autonomic nerve wreath (ANW) is a major landmark feature of iris topography in iridology. Finding the edge of the ANW is of great importance to an automated iris diagnosis system. Based on a two-phase greedy optimization approach, this paper presents an improved snake model for extracting the edge of ANW, which solves the problem that the traditional snake initial contour should be close to the true boundary of interested object in an image. Experimental results show the validity of this approach.

A Compact Design of W-Band High-Pass Waveguide Filter Using Genetic Algorithms and Full-Wave Finite Element Analysis

This paper proposes an efficient two-phase optimization approach for a compact W-band double-plane stepped rectangular waveguide filter design, which combines genetic algorithms (GAS) with the simplified transmission-line model and full-wave analysis. Being niotc effcient and robust than the gradient-based method, the approach can lead to a compact waveguide filter design. Numerical results shod that the resultant waveguide filter design with 4 sections (total length 19.6 mm) is sufficient to meet the design goal and provides comparable performance to that with 8 sections (total length 35.6mm) by the Chebyshev synthesis approach. Based on the present approach, nineteen compact high-pass waveguide filters have been implemented and measured at the W-band with satisfactory performance.