Recently, the cedar solver Copt ushered in the latest 5Version 0 has been upgraded, the speed of integer programming MIP solving has been greatly improved, and the semi-definite programming SDP module has been added and rushed to the top of the public beta list, and the domestic solver has once again achieved a new leap. Since its release in 2019, COPT has gone from 1Version 0 upgraded to 5Version 0 not only continues to make breakthroughs in solution performance, but also continues to penetrate into various fields at the application level, from infrastructure construction, industrial manufacturing to retail consumption, Shanshu solver COPT is escorting the digital and intelligent transformation of Chinese enterprises.
The solver is known as the "computational chip", which can quickly find the optimal solution to a large-scale real-world problem, given the model and data. In China, more than 10,000 flights take off and land every day, more than 10,000 subway trains run every day in Beijing alone, hundreds of millions of parcels are transported every day in the logistics field, and the country's power generation capacity exceeded 8 trillion kilowatt hours in 2021. In such extremely complex operational scenarios, there is a leading computing "chip" behind it to solve a myriad of scheduling optimization problems, which is the solver. Today, we will take a look at how the "black box" of the solver empowers all walks of life from the practical application of the cedar solver copt.
Energy and power, aerospace, rail transit and other infrastructure fields.
In the fields of energy and power, aerospace, rail transit and other infrastructure fields, the optimization solver is one of the important basic tools. In the face of the changeable market economic environment and huge pressure on operation and control, each operating organization must not only ensure the safe and stable operation of the system, but also balance supply and demand to achieve the optimal cost, efficiency and effectiveness.
For a large-scale power system, the safety constraint unit combination needs to consider the constraints such as power balance constraints, network security constraints, unit capacity constraints, unit operation standby constraints, unit climbing and descending speeds, etc., which is a large-scale mixed integer programming problem (MIP) mathematically, with complex models and large computational costs. In the optimization problem of Sichuan hydrothermal power combined safety constraint unit combination, the State Grid hopes to meet the needs of system load and auxiliary services (frequency modulation, rotary standby, non-rotating standby) under the premise of considering the safety constraints of the ground state power grid and the operation constraints of generator sets (hydrothermal power), so as to improve operational efficiency and minimize power generation costs. Through the optimization model and solver Copt built by Shanshu Technology, the State Grid optimizes the start-stop and power generation plan and auxiliary service plan of the generator set according to the cost curve of the generator set, which effectively reduces the unit power generation cost and significantly improves the stability and reliability of the whole set of solution schemes. In addition, the cedar solver COPT can also be widely used in typical energy and power optimization scenarios such as reactive power scheduling optimization, power market pricing, and power market clearing.
Another example is the aviation field, in scenarios such as crew scheduling, aircraft maintenance, aviation network planning, airport location selection, flight scheduling, and emergency flight recovery, there are many data dimensions and large volumes, and the accuracy requirements are relatively high, and the support of the solver will effectively improve operational efficiency. For example, for the aero engine maintenance module, the current civil aviation company mainly relies on manual experience to arrange the maintenance plan, when the amount of maintenance tasks increases, the number of engines to be inspected increases, etc., there will be high maintenance costs, insufficient maintenance and excessive maintenance problems. In the engine intelligent management decision-making system built by China Southern Airlines, Shanshu Technology designed and constructed an engine replacement model based on the engine implementation parameters, performance monitoring, inspection records and other information, combined with the time of hole exploration, maintenance cost and cycle, and the model built a mixed integer programming model based on the COPT solver, formulated short-term, medium- and long-term replacement plans, and opened up the whole life cycle management of the engine and the operation and management of the fleet. It has achieved a plan accuracy improvement of up to 12%, a reduction in total operating costs of nearly 100 million yuan, and at the same time ensured flight safety and improved aircraft utilization.
In the field of urban rail transit, complex problems such as train maintenance, train scheduling, schedule compilation, crew scheduling, and energy management can all be optimized with the help of the solver. For example, when the subway crew is scheduled, it is usually according to the current operation chart that the corresponding rotation table is manually discharged, and then the corresponding shift parent table is discharged considering the specific personnel situation, the whole process takes several weeks, and the experience dependence on the planner is strong, and because it is difficult to consider all the factors manually, the result of the discharge may lead to a large number of crew members, unbalanced tasks, etc. Shanshu Technology selected one of the busiest subway lines in Beijing as a pilot to build an intelligent crew scheduling model, and used COPT to solve the problem under the condition of comprehensively considering the scheduling constraints such as attendance time, number of retirees, mileage working hours, and station transfer, which effectively reduced the number of passengers on the main line and improved the satisfaction of the crew. Taking a typical subway line as an example, the compilation of the line timetable involves 54 trains and 38 stations with 1200 minutes of two-way transportation conditions, including nearly 10 million decision-making variables, and it is very difficult to compile manually. Based on the operation of the line, Shanshu Technology has configured an intelligent operation diagram compilation model for it, comprehensively considering the constraints such as full load rate, minimum departure interval, minimum travel distance, line capacity resources, as well as signal system and train operation rules, and solving the model through the solver COPT, helping operators search for the optimal operation plan in a large number of feasible solutions, maximize the operation potential, and reduce operating costs.
Industrial manufacturing field.
Production scheduling, production and marketing coordination and energy consumption control in the industrial field are thorny problems faced by many enterprises, due to the complexity of the first chain and the rapid change of customer demand, enterprises must quickly respond to market changes, and make optimal decisions on demand, procurement, production, transportation, etc., which is a very complex mathematical optimization problem.
For example, an ICT giant has hundreds of processing plants, tens of thousands of high-quality suppliers and raw materials, and in the production scheduling scenario, the constraints under the complete model reach the level of 100 million, and the amount of computing has exceeded the scope of manual calculation. If multiple factories can produce the same product, which factory should be assigned to produce in the face of temporary order demand to ensure the highest efficiency and the lowest cost? How to coordinate the planning between each process? How are raw materials distributed? Based on the cedar solver COPT, the company built a multi-factory coordinated scheduling engine, comprehensively considered the differentiated attributes, material constraints, and capacity constraints of multiple factories to achieve intelligent collaborative production of multiple factories and multiple production lines, and used the scheduling model and solver to quickly calculate and make decisions to achieve the optimal multi-cycle production scheduling plan in the day and week dimensions, and finally increased the order satisfaction rate by 20% and reduced the capacity loss rate by 30%, which flexibly and efficiently met customer needs.
In order to coordinate procurement and sales, reduce costs and increase efficiency, a steel company hopes to optimize the ratio of raw fuel with the help of digital technology. However, the steel smelting process is complex, from sintering pellets, blast furnace ironmaking to converter steelmaking, involving hundreds of raw fuels, under the condition of meeting the process requirements, it is necessary to comprehensively consider multiple constraints such as sinter composition, pellet composition, comprehensive ore, coke, scrap steel, oxygen enrichment, output, etc., and relying on manual calculation and decision-making has been unable to meet the demand. The intelligent decision-making platform for procurement and marketing built by the company realizes rapid solution based on the cedar number solver COPT, obtains the optimal raw fuel ratio scheme, provides guidance for production and procurement, effectively improves the efficiency of production and operation, and reduces production costs.
Retail consumer sector.
In the field of retail consumption, there are more and more product types, logistics and distribution are getting faster and faster, even in special periods such as festivals and Double 11, online and offline non-closing is already the norm. Behind this, enterprises need to make appropriate arrangements and arrangements for the first chain, including marketing strategy, product selection, pricing, distribution, site selection, etc., and a problem in one link may affect the entire consumption chain. For example, a live broadcast down the sales volume of hundreds of millions of yuan, the goods may be snatched up, but the effect is not good, but it may not be sold, resulting in a backlog of goods, how to divide the goods and fulfill the contract to comprehensively consider the factory capacity, upstream inventory, storage capacity, transportation capacity, product characteristics, regional characteristics and other constraints, relying on manual decision-making is difficult to do. For companies with hundreds or thousands of SKU categories, the computation is exponentially harder.
With the help of the solver, these problems can be effectively solved. For example, with the expansion of Xiaomi's business, the number of SKUs, total volumes, and stores continues to increase, and it is difficult to meet business needs with a simple distribution logic. Shanshu Technology has built an end-to-end intelligent distribution platform for Xiaomi, according to the constraints of total volume, first-class results, arrival time rules, distribution preference rules and other constraints, establish a global perspective of operation research optimization model, and use the solver CPU to solve the daily distribution results, increasing the spot rate by an average of 8% and reducing the number of times by an average of 015 times, the turnover days were reduced by an average of 10 days, which effectively improved the consumer experience while reducing costs and improving efficiency.
At present, the commercial implementation of domestic solvers is still in the early stage, but from the successful application of solver CPU in various fields, the solution effect and commercial value are very bright. This time, Opt5The new semi-fixed planning module in version 0 will further broaden its application scope. After continuous testing and polishing in the market, while continuously improving the solution performance, the CST solver also has stronger technical feasibility, which can be better combined with application scenarios, and can provide standardized products, and can also be customized algorithm development for customers' special problems, bringing safe and reliable localized solutions for large-scale solving optimization problems.