Unconstrained Binary Optimization for Pooling Problem
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The pooling problem in petrochemical engineering, wastewater treatment, and mining lacks an efficient method to optimize the transportation of ingredients from sources to terminals through pools, leading to suboptimal solutions and high costs due to the complexity of constraints and variables.
Innovation Solution
A computer-based method transforms the pooling problem into an unconstrained binary optimization problem by discretizing variables and constraints, creating a binary cost function that can be solved using quantum or classical computers, approximating the optimal solution within a specified error margin.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional optimization methods are used to solve the pooling problem, then the solution accuracy can be maintained, but the computational complexity and resource requirements become excessively high
Solution Approach 1:
The patent transforms the continuous optimization variables of the pooling problem into binary variables (0 or 1), fundamentally changing the parameter space. This discretization allows the problem to be reformulated as a binary optimization problem that can be solved more efficiently using specialized algorithms and hardware, reducing computational complexity while maintaining solution accuracy through the binary representation of flow decisions
Solution Approach 2:
The patent replaces traditional continuous optimization mechanics with binary optimization mechanics. By substituting the continuous variable space with discrete binary variable space, the problem can be solved using binary optimization algorithms and quantum computing approaches, which offer reduced computational complexity compared to traditional continuous optimization methods
2Reliability
If traditional optimization methods are used to solve the pooling problem, then the solution quality can be maintained, but the resource requirements and computational time increase significantly
Solution Approach 1:
The transformation of continuous parameters to binary parameters enables the use of efficient binary optimization solvers and quantum algorithms that can find high-quality solutions faster than traditional continuous optimization methods, thereby reducing computational time while maintaining solution quality
Solution Approach 2:
The patent segments the continuous variable space into discrete binary states, allowing the optimization problem to be broken down into discrete decision units. This segmentation enables parallel processing and more efficient search algorithms, reducing the time required to find high-quality solutions
3Measurement precision
If the pooling problem is solved using exact methods, then the global optimum can be found, but the computational resources required become prohibitively large
Solution Approach 1:
By changing the parameter representation from continuous to binary, the patent enables the use of binary optimization techniques that require fewer computational resources. The binary formulation allows specialized hardware and algorithms to solve the problem efficiently, finding the global optimum with reduced memory and processing requirements compared to traditional exact methods
Data Source
AI summary
A computer optimizes transport of a set of ingredients between a plurality of sources, at least one terminal, and a plurality of pools, described by an objective function, a set of variables, and a set of constraints, by: (A) transforming the objective function, variables, and constraints into a binary cost function, including: discretizing the set of variables into a set of a binary variables; transforming the objective function into a binary cost function of the set of binary variables; and adding, for each constraint in the set of constraints, one or more terms to the binary cost function, to create a completed cost function; and (B) providing the completed cost function to a solver to obtain a solution or approximate solution representing a flow of the set of ingredients between the plurality of sources, the plurality of pools, and the at least one terminal.