Constraint Coefficient Tuning in Local Search Optimization
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Solution Overview
Problem
Conventional methods for adaptively adjusting the constraint coefficient in combinatorial optimization problems face inefficiencies as the solution is not updated based on problem-specific conditions, leading to potential constraint violations or difficulty in escaping local solutions.
Innovation Solution
A computer program and data processing apparatus that dynamically adjusts the constraint coefficient by changing its value in the direction of approaching a target value, using a look-up-table (LUT) to optimize the search for a solution candidate, thereby enhancing the efficiency of local search methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a value of the constraint coefficient is too small, then the possibility of obtaining a constraint violation solution increases, but the search efficiency may decline
Solution Approach 1:
The patent implements dynamic adjustment of the constraint coefficient γ throughout the search process. The coefficient is increased in stages as the search progresses, transforming the static coefficient approach into a dynamic one. This allows the system to initially explore the solution space with smaller γ values (allowing constraint violations) and then progressively enforce constraints more strictly, thereby maintaining both search efficiency and constraint satisfaction reliability
Solution Approach 2:
The patent changes the parameter γ (constraint coefficient) from a fixed value to a dynamically adjusted value that evolves during the search process. By modifying this key parameter based on search progress and solution quality, the system optimizes the balance between exploration (allowing constraint violations) and exploitation (enforcing constraints), resolving the contradiction between search efficiency and constraint satisfaction
2Reliability
If a value of the constraint coefficient is too large, then the value of the evaluation function of a constraint violation solution becomes too large, but it becomes difficult to escape from a local solution
Solution Approach 1:
The patent employs dynamic adjustment of the constraint coefficient γ, starting with smaller values that allow the search to escape local solutions by tolerating constraint violations. As the search progresses and better solutions are found, γ is progressively increased to enforce constraints more strictly. This dynamic approach prevents the system from being trapped in local optima while ultimately achieving constraint satisfaction
Solution Approach 2:
The patent applies preliminary action by initially using smaller constraint coefficient values before the search begins or early in the search process. This allows the algorithm to freely explore the solution space and escape local optima without being constrained by strict penalty enforcement. The constraint coefficient is then gradually increased as the search progresses, ensuring the system has already explored diverse regions of the solution space
3Device complexity
If an appropriate value of the constraint coefficient is fixed, then the adjustment process is simple, but the solution is not updated depending on problems even if a search is repeated
Solution Approach 1:
The patent transforms the static fixed coefficient approach into a dynamic adjustment mechanism where γ is automatically modified during the search process based on solution quality and constraint violation levels. This dynamic system adapts to different problems and search states, ensuring continuous improvement of search efficiency without requiring complex manual intervention or problem-specific tuning
Solution Approach 2:
The patent implements self-service by enabling the constraint coefficient adjustment mechanism to automatically adapt to different problems and search states without external intervention. The system monitors solution quality and constraint satisfaction levels, then autonomously adjusts γ to optimize search performance, eliminating the need for manual parameter tuning while maintaining high search efficiency across diverse problems
Data Source
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AI summary
A storage unit stores evaluation function information of an evaluation function of a combinatorial optimization problem including a sum of an objective function and one or more constraint functions including a first constraint function weighted by a first coefficient (γt) representing a weight of a first constraint condition. When repeatedly executing a local search for searching for a solution candidate (x*) of the combinatorial optimization problem using the evaluation function information while changing a value of γt, a processing unit changes the value of γt in a direction in which a value (V(x*)) of the first constraint function corresponding to x* obtained by the local search using each value of γt approaches a target value (Vtarget) that is a positive value.