Commercial Optimization Research Articles

Automatic source code generation for deterministic global optimization with parallel architectures

Trends over the past two decades indicate that much of the performance gains of commercial optimization solvers is due to improvements in x86 hardware. To continue making progress, it is critical to consider alternative/specialized massively parallel computing architectures. In this work, we detail the development of an open-source source code transformation approach built using Symbolics.jl to construct McCormick-based relaxations of functions that enables their effective parallelized evaluation. We then apply this approach in a novel parallelized branch-and-bound routine that offloads lower- and upper-bounding problems to a GPU. The effectiveness of this new approach is demonstrated on three nonconvex problems of interest, where it yields convergence time improvements of 22–118x compared to an equivalent serial CPU implementation and in two cases outperforms vanilla branch-and-bound versions of existing state-of-the-art solvers that use tighter bounding techniques. This work exemplifies how deterministic global optimizers using alternative hardware architectures can compete with—or eventually outclass—even the most powerful serial CPU implementations, and to the best of the authors' knowledge, represents the first successful demonstration of deterministic global optimization using a GPU.

A practical vehicle routing problem in small and medium cities for fuel consumption minimization

Today, reducing fossil fuel consumption in the transport sector is one of the important requirements to preserve the ecological environment. In this paper, we investigated a logistics problem in small and medium cities. We proposes the time-dependent vehicle routing problem model in small and medium cities considering heterogeneous fleets, time windows, multi-trip, time dependency, and road network. We conducted a numerical analysis on fuel consumption minimizing path selection between two customer nodes and found that the path selection is independent of the payload in most cases. The model is formulated as a mathematical integer linear programming model, and small problems are solved using a commercial optimization solver. For large-scale instances, we proposed a heuristic algorithm based on the variable neighborhood search and evaluated its performance. The proposed algorithm can decrease fuel consumption by 25 % compared to manual routing and scheduling. Furthermore, for provide useful managerial insights, sensitivity analyses were performed considering different vehicle capacities.

Energy Transition: The Impact of Increasing Energy Production from Renewable Sources on the Commercial Optimization Process of Conventional Power Generation Assets

Abstract Changing the way electricity is produced, as part of the energy transition process, brings new challenges to the energy industry and in particular to the power generation practices. The switch from energy systems based on fossil fuels to generation technologies based on renewable sources is proving to be much more complex than expected. Multiple recent studies have shown that the intermittency in renewable production processes is putting pressure on the system and increasing balancing and maintenance costs of the grid, calling for an efficient management of the electricity produced. Therefore, a complete phase-out of conventional power generation units (e.g. coal, gas and nuclear) is still difficult to imagine in practice, mainly because of their role in balancing the system during the hours when renewables are not available (e.g. no wind, no sun or reduced hydraulicity). From the perspective of technical and commercial management aspects, the operation of conventional assets involves the consideration of multiple constraints (such as a longer operating time before they are shut down, or a longer preparation time before they can be restarted) in order to avoid financial loss and further damages. Therefore, the aim of this is to: 1. study the impact brought by the large installed capacity of renewable assets on the energy system; 2. analyse the options for gradual phase-out of conventional assets, from the perspective of system stability; 3. draw conclusions on how the commercial optimization of the production assets should develop as the energy transition advances. The novelty of this paper lies in the fact that it makes a business study of this transition process, which does not really exist yet, and case and simulation studies, along with statistical and time series analysis were used as a methodological approach for the research.

A multi-level capacitated arc routing problem with intermediate facilities in waste collection

This study investigates a multi-level capacitated arc routing problem for waste collection with two levels of intermediate facilities: huts and transfer stations. The problem aims to implement integrated optimisation of the intermediate facilities and find optimal routes for a fleet consisting of manually operated vehicles and vehicles with compressors. We first build an integer linear programming model to address this problem. Then, we propose an extended adaptive large neighbourhood search (E-ALNS) approach, including a tailored Shake procedure inspired by variable neighbourhood search to effectively solve this problem. Computational experiments were conducted on 264 instances generated using existing benchmarks. Compared to commercial optimisation software and other algorithms, our extended algorithm exhibits superior performance for this problem. The results also demonstrate that the integrated optimisation of intermediate facilities significantly decreases the total cost compared to separate optimisations.

Production planning optimization framework for integrated refinery, ethylene and aromatics industrial chains considering environmental performance

Nonlinear modeling for the processing units and enterprise-wide optimization are essential to improve the overall profitability of production planning in the petrochemical enterprise. This study proposed a novel data-driven modeling approach for the ethylene plant and enterprise-wide production planning optimization framework for integrated the refinery, the ethylene plant and the aromatics complex considering environmental impact. The data-driven model was developed for different feedstocks in the ethylene plant to better predict product yield. The integrated model increased potential profitability of the petrochemical enterprise through considering the material balances of the intermediate products between the refinery, the ethylene plant and the aromatics complex. The integrated model planned utilization of dry gas resources, which reduced the waste of C2 and C3 resources and increased the production of olefin products. The enterprise-wide multi-period production planning model was constructed to optimize the planning operation of the refinery, the ethylene plant and the aromatics complex simultaneously, which was solved with the commercial optimization solver SBB. An industrial scenario was investigated to demonstrate the performance of the proposed model. Computational results for several cases indicated that integrated approach achieves a significant improvement in overall profit and provide valuable guidance for emission reduction.

A benchmark of optimization solvers for genome-scale metabolic modeling of organisms and communities.

Genome-scale metabolic modeling is a powerful framework for predicting metabolic phenotypes of any organism with an annotated genome. For two decades, this framework has been used for the rational design of microbial cell factories. In the last decade, the range of applications has exploded, and new frontiers have emerged, including the study of the gut microbiome and its health implications and the role of microbial communities in global ecosystems. However, all the critical steps in this framework, from model construction to simulation, require the use of powerful linear optimization solvers, with the choice often relying on commercial solvers for their well-known computational efficiency. In this work, I benchmark a total of six solvers (two commercial and four open source) and measure their performance to solve linear and mixed-integer linear problems of increasing complexity. Although commercial solvers are still the fastest, at least two open-source solvers show comparable performance. These results show that genome-scale metabolic modeling does not need to be hindered by commercial licensing schemes and can become a truly open science framework for solving urgent societal challenges.IMPORTANCEModeling the metabolism of organisms and communities allows for computational exploration of their metabolic capabilities and testing their response to genetic and environmental perturbations. This holds the potential to address multiple societal issues related to human health and the environment. One of the current limitations is the use of commercial optimization solvers with restrictive licenses for academic and non-academic use. This work compares the performance of several commercial and open-source solvers to solve some of the most complex problems in the field. Benchmarking results show that, although commercial solvers are indeed faster, some of the open-source options can also efficiently tackle the hardest problems, showing great promise for the development of open science applications.

A hybrid genetic algorithm based on reinforcement learning for the energy-aware production scheduling in the photovoltaic glass industry

Recently, the growing solar energy capacity has played a significant role in developing a clean energy supply system in China. However, the resulting rapid expansion of photovoltaic component (e.g., glass) manufacturing intensifies the energy demand in the locality of the plant. Therefore, this paper considers the energy-aware production scheduling of a deep-processing line in the photovoltaic glass plant, whose layout is a hybrid flow shop with batch and non-batch machines. Firstly, we establish a mixed integer programming model with the minimization of the energy consumption and the penalty for excess of the due date. Then, we propose a hybrid genetic algorithm (GA) based on reinforcement learning to solve the problem. Specifically, the expected Sarsa is used to extract critical knowledge about algorithmic parameters during the population evolution to guide the exploration of the GA. Finally, we conduct extensive numerical experiments to validate the effectiveness of the proposed algorithm by comparing it with a commercial optimization solver and other metaheuristics. The numerical results show that the average gap between the solver and the proposed algorithm is around 4% in small-sized instances. Compared with the heuristic used in the plant, the improvements of this paper are about 16%∼18% and 17%∼21% in practical-sized instances for the delay penalty and energy consumption objectives, respectively. In addition, the computational results provide managerial insights for managers in further pursuing energy efficiency from higher-level decision-making, e.g., planning over multiple periods from a tactical perspective, and changing production line configurations and introducing new processing techniques from a strategic perspective.

Designing robust green sustainable supply chain network by bi-objective optimization method

Designing a green supply chain is becoming popular in the context of sustainable development. To address this academic concern, this paper designs a multi-product, multi-echelon green supply chain network (GSCN) from economic and environmental aspects. During the modeling process, the main challenge is to access the accurate probability distributions of uncertain parameters from limited historical data. To overcome this difficulty, this paper develops a distributionally robust design framework for bi-objective GSCN, where the distribution information of uncertain parameter is partially available and characterized by ambiguity sets. For the tractability, this paper discusses robust counterpart reformulation under Wasserstein-distance-based ambiguity sets. Finally, the obtained mixed integer programming model is resolved via commercial optimization software. To validate the proposed optimization framework, we design a meat supply chain network for a Chinese realistic food enterprise. The computational results demonstrate that the proposed distributionally robust model can provide reliable solutions compared with stochastic optimization method.

Research on CCHP Design and Optimal Scheduling Based on Concentrating Solar Power, Compressed Air Energy Storage, and Absorption Refrigeration.

In response to the country's "carbon neutrality, peak carbon dioxide emissions" task, this paper constructs an integrated energy system based on clean energy. The system consists of three subsystems: concentrating solar power (CSP), compressed air energy storage (CAES), and absorption refrigeration (AR). Among them, thermal energy storage equipment in the photothermal power generation system can alleviate the fluctuation of solar energy and provide a stable power supply for the system. The compression heat generated during the compression process of the CAES system can be recovered through heat transfer oil to provide a heat load. The compressed air in the air accumulator (ACC) expands in the air turbine to provide an electric load. The low-temperature exhaust gas discharged from the turbine can provide cool load. First, a multienergy system that includes CSP, CAES, and AR is built. Then, the system takes the lowest economic cost as the objective function and constructs the system day-ahead scheduling model. Finally, for data obtained from scene reduction, the commercial optimization software Gurobi is invoked through YALMIP to solve the model. The results show that the three subsystems achieve multienergy complementarity; system operating costs are reduced by 59.94% and fully absorb wind and solar energies by the system.

A demand‐responsive feeder service with a maximum headway at mandatory stops

AbstractPublic transportation out of suburban or rural areas is crucial. Feeder transportation services offer a solution by transporting passengers to areas where more options for public transport are available. On one hand, fully flexible demand‐responsive feeder services (DRFSs) efficiently tailor their service to the needs of the passengers. On the other hand, traditional feeder services provide predictability and easier cost control. In this article, a semi‐flexible DRFS is considered, which combines positive characteristics of both traditional services as well as fully flexible services. This feeder service has two types of bus stops: mandatory bus stops and optional bus stops. Mandatory bus stops are guaranteed to be visited by a bus within a certain time interval. Optional stops are only visited when there is demand for transportation nearby. The performance of this feeder service is optimized with the use of a new type of metaheuristic framework, which we denote as parameter space search. Experimental results on small benchmark instances indicate that the heuristic performs on average 12.42% better than LocalSolver, a commercial optimization solver, with an average runtime of 2.1 s. Larger instances can also be solved, typically within 2 min.

Location-pricing decisions with carbon emission considerations: A behavioral game-theoretic approach

The location-pricing problem aims to solve pricing and facility location problems at the same time. While the demand of customers is known in the classical facility location problem, it is a function of price in the location-pricing problem. Moreover, some other factors, such as production, transportation and inventory costs, and competition, can affect the final price of products, making the location-pricing problem more complicated. Considering the necessity of incorporating environmental aspects into supply chain design and the importance of considering the behavioral characteristics of decision-makers, this study addresses the location-pricing problem based on these two significant perspectives. In this paper, there is a lead company responsible for locating and planning a set of manufacturers in the first echelon. On the other hand, the focal manager controls the total emissions and sets the wholesale price. In the second echelon, there are two retailers that base their pricing strategies on social preferences in order to gain a larger market share. The competition between the retailers determines the demands of the customers. The modeling approach is based on the Stackelberg-behavioral Nash game and is formulated as a bi-level mixed-integer nonlinear programming model. The problem is solved using a combination of an analytical solution method and the utilization of a commercial optimization solver. The proposed model is assessed using a real case study in the energy sector. The results indicate that deviating from purely selfish behavior in the pursuit of profit can lead to beneficial outcomes. Generally speaking, price competition between status-seeking retailers results in lower prices for the leader and followers compared to the standard game theory approach. This leads to an increase in average demand in the market, which results in increased profit for members and consequently improves the performance of the whole system. Also, it is worth mentioning that the status-seeking behavior of retailers results in a decrease in retail prices, which improves social welfare.

Integrated production and transportation scheduling problem under nonlinear cost structures

We consider an integrated production and transportation scheduling problem arising in several make-to-order settings, where customer orders have release times and pre-specified delivery time windows. These orders are first processed in a plant and, thereafter, delivered to their customer sites by transporters (e.g., freight trains, ships, or air flights) with fixed departure times and nonlinear transportation cost functions. If the processing of an order is completed but not immediately delivered, it will be stored temporarily, incurring inventory holding costs. The objective is finding an integrated schedule for production and transportation such that the total cost of inventory holding and transportation is minimized. In this study, we consider the following two cases: one where partial delivery is not allowed, and the other where partial delivery is allowed. For each case, we propose an exact algorithm to find optimal solutions for small-scale instances, and a heuristic algorithm to find near-optimal solutions for large-scale instances. For the randomly generated test instances, the computational results reveal that the exact algorithms significantly outperform a commercial optimization solver in terms of the computational times and the number of instances solved within a specified time limit, and the heuristic algorithms are capable of generating near-optimal solutions within a reasonable computational time. Finally, we incorporate considerations of sequence-dependent setup time into the problem and apply the approaches for designing the algorithms to address the more general problem.

Collaborative passenger flow control optimization of urban rail transit network based on sliding window mechanism

In order to enhance the operational performance of urban rail transit networks under overloaded conditions, this study proposes a novel network-level collaborative passenger flow strategy based on a sliding window mechanism. The main idea is to categorize arriving passengers at stations into different groups using variable-length windows and allocate them to specific trains. With the aim of minimizing the total passenger extra waiting time under cost budget, we establish a mixed integer programming model with sliding window constraints, flow distribution constraints, and node flow constraints to build the optimal matching relation between passenger flow demands and transportation resources. Specifically, the model incorporates precise quantity constraints related to transfers, facilitating the accurate quantification of both internal and external demands of network passenger flow. Then we use logical constraint transformation and linearization techniques to enable the model to be solved directly by commercial optimization solvers. For large-scale problems, we adopt a rolling horizon approach to improve computing efficiency. To validate the effectiveness of the sliding-window based passenger control method, we conduct case studies including a small designed example and real-world research on the Beijing Subway network. The experimental results demonstrate that our proposed model assists managers in developing flexible and accurate network-level collaborative passenger flow control schemes.

A linear optimization model for high dose rate brachytherapy using a novel distance metric.

Purpose.We propose a linear network-based optimization model (LNBM) for high dose rate brachytherapy (HDR-BT) that uses a novel distance metric to measure the discrepancy between the dose delivered and the prescription. Unlike models in the literature, LNBM takes advantage of the adjacency structure of the patients' voxels by formalizing them into a network.Methods.We apply LNBM to a set of 7 cervical cancer cases treated with HDR-BT. State-of-the-art commercial optimization software solves LNBM to global optimality. The results of LNBM are compared with those of inverse planning by simulated annealing (IPSA) based on tumor coverage, dosimetric indices for the critical organs at risk (OARs), isodose contour plots, and two metrics of homogeneity new to this work (hot-spots volumes and diameters).Results.LNBM produces plans with improved tumor coverage and with improved isodose contour plots and dosimetric indices for OARs that receive highest dose (bladder and rectum in this study) when compared with IPSA. Using new metrics of homogeneity, we also demonstrate that LNBM produces more homogeneous plans on these cases. An analysis of the solutions of LNBM shows that they use a significant part of the voxel network structure, providing evidence that the plans produced are different from those created using traditional penalty approaches and are more directly guided by the geometry of the patients' anatomy.Conclusions.The proposed linear network-based optimization model efficiently generates more homogeneous high quality treatment plans for HDR-BT.

Search for the Optimal Design of a Supercritical-CO2 Brayton Power Cycle from a Superstructure-Based Approach Implemented in a Commercial Simulation Software

Improving the efficiency and flexibility of fossil-fired power plants remains a current and challenging issue. In that regard, supercritical CO2 Brayton cycles offer promising potential. This paper aims to apply a process synthesis approach to the design of a closed Brayton cycle using supercritical CO2 as a working fluid with a coal furnace as a heat source. The general methodology presented here for designing closed power cycles includes the construction of a superstructure containing all relevant possible cycle layouts, the formulation of the cycle-synthesis problem as a mathematical optimization problem, and its solution using an appropriate algorithm. This study was conducted with the help of a process simulation commercial software (PROSIM) and using the Mixed-Integer Distributed Ant Colony Optimization (MIDACO) as a commercial optimization algorithm. This work highlights the limits of a purely technical optimization approach that would ignore the economical layer. The optimal structure obtained regarding Levelized Cost Of Electricity (LCOE) minimization is a configuration with one reheat of the supercritical CO2 in the boiler, two recuperators, and one recompression loop around the low-temperature recuperator; it is associated with a cycle efficiency of 49.35 % and a 10% reduction in the LCOE in comparison to the optimal case found through energy optimization under typical design heuristics constraints.

A Memetic Algorithm for the multi-product Production Routing Problem

This article addresses the Production Routing Problem (PRP), which consists of determining, in an integrated way, production and inventory planning, and vehicle routing to minimize the costs involved. In the problem, a plant is responsible for producing several types of products to meet the known demand of a set of customers using a homogeneous fleet of vehicles over the planning horizon. In the literature, evolutionary approaches have not been explored in depth for the PRP, specifically for the problem with multiple products. Thus, this work mitigates this gap, presenting a novel Memetic Algorithm and testing its effectiveness on randomly generated sets of instances, comparing the results obtained with a commercial optimization solver. In our solution approach, several classic operators from the literature were implemented. Furthermore, we propose four novel genetic operators. In addition, we evaluated the proposed method’s performance in classical instances of literature considering a single item. The computational experiments were carried out to assess the impact of the numerous parameter combinations involving the metaheuristic, and, from statistical analyses, we evidence the proposed technique’s robustness. Computational experiments showed that our proposed method outperforms the commercial solver Gurobi in determining feasibly high-quality solutions, mainly on large instances for the PRP with multiple items.

Shipment Consolidation with Multiple Shipping Methods Under Nonlinear Cost Structures

We study a shipment consolidation problem commonly faced by companies that outsource logistics operations and operate in a commit-to-delivery mode. It involves delivering a given set of orders to their destinations by their committed due times using multiple shipping methods at the minimum total shipping and inventory cost. The shipping cost is generally nonlinear in shipping quantity and can be represented by a subadditive piecewise linear function. We investigate two shipping scenarios, one involving long-haul shipping only and the other involving joint long-haul and short-haul shipping. We develop analytical results and solution algorithms for the shipment consolidation problem under each shipping scenario. The problem under the first shipping scenario is shown to be strongly [Formula: see text]-hard. We find that a simple policy, called the First-Due-First-Delivered (FDFD) policy, which assigns orders with earlier delivery due times to shipping methods with earlier destination arrival times, is very effective. This policy enables us to develop a polynomial time algorithm, which not only solves the problem under the concave shipping cost structure optimally but also achieves a performance guarantee of 2 for the problem under the general subadditive shipping cost structure. For the problem under the second shipping scenario, we extend the FDFD policy for long-haul shipping and derive another policy, called the No-Wait policy, for short-haul shipping. We use these policies to develop a polynomial time algorithm and analyze its performance guarantee. Our computational experiments show that the algorithm significantly outperforms a commercial optimization solver, and its performance is robust across different parameter settings that reflect various practical situations. This paper was accepted by Jeannette Song, operations management. Supplemental Material: The data and e-companion are available at https://doi.org/10.1287/mnsc.2023.4835 .

Multiplant Location Involving Resource Allocation

Recently, a multisource, raw material allocation form of Weber's classic single‐facility location problem was rediscovered and recognized for its significance in contemporary planning and decision‐making. This variation of the Weber problem investigates the location of a production plant while permitting the selection of each required raw material source. This article reviews the Weber problem with an emphasis on its extension to incorporate multiple facilities. The only formulated multiplant Weber problem involving resource allocation remains unsolved due to its complexity. An effective approach integrating GIS processing (i.e., the Voronoi diagram and vector‐based overlay) with the classic optimization algorithm (i.e., the Weiszfeld algorithm) is developed to address raw material sourcing in the process of siting facilities. The implementation relies entirely on open‐source Python packages, making the work reproducible, replicable, and expandable. Application findings demonstrate that the utility and computational efficiency of the proposed method to tackle this challenging problem are superior to those of the most advanced commercial optimization software.

An Approximation Algorithm for k-Depot Split Delivery Vehicle Routing Problem

A multidepot capacitated vehicle routing problem aims to serve customers’ demands using a fleet of capacitated vehicles located in multiple depots, such that the total travel cost of the vehicles is minimized. We study a variant of this problem, the k-depot split delivery vehicle routing problem (or k-DSDVRP in short), for the situation where each customer’s demand can be served by more than one vehicle, and the total number of depots, denoted by [Formula: see text], is a fixed constant. This is a challenging problem with broad applications in the logistics industry, for which no constant ratio approximation algorithm is known. We develop a new approximation algorithm for the k-DSDVRP, ensuring an approximation ratio of [Formula: see text] and a polynomial running time for any fixed constant [Formula: see text]. To achieve this, we propose a novel solution framework based on a new relaxation of the problem, a cycle splitting procedure, and a vehicle assignment procedure. To further enhance its efficiency for practical usage, we adapt the newly developed approximation algorithm to a heuristic, which runs in polynomial time even when k is arbitrarily large. Experimental results show that this heuristic outperforms a commercial optimization solver and a standard vehicle routing heuristic. Moreover, our newly proposed solution framework can be applied to developing new constant ratio approximation algorithms for several other variants of the k-DSDVRP with [Formula: see text] being a fixed constant. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 71971177, 71725001, U1811462], Research Grants Council of Hong Kong SAR, China [Grant 15221619], and Guangdong Basic and Applied Basic Research Foundation [Grant 2023A1515030260]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2021.0193 . The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0193 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0193 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Discrete Whale Optimization Algorithm for Disassembly Line Balancing With Carbon Emission Constraint

With the advancement of science and technology in recent years, the rate of product upgrading by end users has increased, resulting in a high number of End-Of-Life (EOL) products. For environmental protection and economic benefits, disassembly lines are set up to recycle them. A disassembly line balancing problem arises and has attracted widespread attention. In this paper, we design a model to address a class of disassembly line balancing problems in which the main optimization objective is to maximize profits, while keeping carbon emission in a tolerable range. A discrete whale optimization algorithm is proposed to search their high-quality solutions. Its efficiency is verified by comparing its solutions with their analytic solutions obtained from a commercial optimization solver and other swarm intelligence algorithms. Experimental results show that it is significantly faster than CPLEX and other swarm intelligence algorithms in solving large-scale optimization problems while guaranteeing its solutions quality.