Combinatorial Exchange Bid Allocation via Minimax Regret Optimization
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Solution Overview
Problem
Current methods for determining optimal allocations in combinatorial exchanges, such as auctions, fail to efficiently explore tradeoff spaces between costs and non-price attributes, leading to suboptimal choices due to manual navigation processes that do not guarantee sufficient or efficient exploration of allocation options.
Innovation Solution
A method involving the calculation of minimax regret and maximum regret values to iteratively refine candidate allocations, using equations EQ1 and EQ2 to determine desirable allocations within a predetermined range of optimality, incorporating utility values and constraints to ensure efficient exploration of tradeoff spaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If manual scenario navigation is used to explore allocations, then users can examine specific allocation options, but the exploration process is inefficient and does not guarantee sufficient coverage of tradeoff space
Solution Approach 1:
The system automatically performs scenario navigation and allocation exploration without requiring manual user intervention. The automated algorithm generates and evaluates multiple allocation scenarios, selecting those that satisfy user-defined constraints and exploring tradeoff spaces efficiently, thereby eliminating the inefficiencies of manual navigation while maintaining ease of use through automated decision support
Solution Approach 2:
The system implements iterative feedback loops where allocation evaluations are continuously refined based on user preferences and constraints. The algorithm receives feedback about user priorities and dynamically adjusts the exploration strategy, generating new allocation scenarios and refining existing ones to ensure comprehensive coverage of relevant tradeoff spaces while maintaining computational efficiency
2Adaptability or versatility
If tradeoff weights are made explicit and incorporated into the objective function, then algorithms can deal with non-price attributes, but most bid takers are unable or unwilling to articulate precise tradeoffs
Solution Approach 1:
The system introduces an intermediary layer between the user's qualitative preferences and the quantitative optimization algorithm. Instead of requiring users to directly specify tradeoff weights, the system translates user-defined constraints and preferences into mathematical formulations that the algorithm can process, effectively mediating between human judgment and computational optimization
Solution Approach 2:
The system dynamically adjusts optimization parameters and objective function formulations based on user preferences and problem characteristics. Rather than requiring fixed explicit tradeoff weights, the algorithm adapts its parameters iteratively to capture the essence of user preferences, enabling versatile handling of non-price attributes without requiring precise quantitative articulation from users
3Measurement precision
If multiple allocations are generated by imposing constraints, then users can examine implications on optimal allocation, but the process does not ensure sufficient or efficient exploration of allocations
Solution Approach 1:
The system performs preliminary actions by pre-computing and pre-evaluating multiple allocation scenarios before the user needs to make decisions. The algorithm proactively generates a diverse set of allocations that satisfy various constraints and explores their implications in advance, providing the user with ready-to-examine options that save time and ensure comprehensive coverage of tradeoff spaces
Solution Approach 2:
The system generates and evaluates more allocation scenarios than would be practical to examine manually, using computational power to explore extensive portions of the allocation space. By performing excessive action in the computational domain, the system provides sufficient exploration coverage while the user only needs to review the most relevant outcomes, effectively trading computational exhaustiveness for user-time efficiency
Data Source
AI summary
A desirable allocation of bids in a combinatorial exchange can be selected by determining a first candidate allocation of the bids and a first value of a minimax regret, related to the difference in utility between the adversarial allocation and the candidate allocation, as a function of a first adversarial allocation of the bids. Based on the first candidate allocation, a second adversarial allocation of the bids and a first value of a maximum regret related to the difference in utility between the new adversarial allocation and the utility of the candidate allocation can be determined. When the value of the maximum regret is greater than the value of the minimax regret, the candidate allocation can be designated as the desirable allocation.