[Paper Review] Solving Configuration Optimization Problem with Multiple Hard Constraints: An Enhanced Multi-Objective Simulated Annealing Approach

Pei Cao, Zhaoyan Fan+2 more|arXiv (Cornell University)|Jun 9, 2017

Manufacturing Process and Optimization50 references3 citations

TL;DR

This paper proposes an enhanced multi-objective simulated annealing algorithm (MOSA/R) to solve complex configuration optimization problems with multiple hard constraints in engineering design. By integrating a biased re-seed mechanism to balance exploration and exploitation, the method significantly improves convergence and feasibility, outperforming benchmarks in both constrained optimization and real-world configuration tasks.

ABSTRACT

This research concerns a type of configuration optimization problems frequently encountered in engineering design and manufacturing, where the envelope volume in space occupied by a number of components needs to be minimized along with other objectives such as minimizing connective lines between the components under various constraints. Since in practical applications the objectives and constraints are usually complex, the formulation of computationally tractable optimization becomes difficult. Moreover, unlike conventional multi-objective optimization problems, such configuration problems usually comes with a number of demanding constraints that are hard to satisfy, which results in the critical challenge of balancing solution feasibility with optimality. In this research, we first present the mathematical formulation for a representative problem of configuration optimization with multiple hard constraints, and then develop two versions of an enhanced multi-objective simulated annealing approach, referred to as MOSA/R, to solve this problem. To facilitate the optimization computationally, in MOSA/R, a versatile re-seed scheme that allows biased search while avoiding pre-mature convergence is designed. Our case study indicates that the new algorithm yields significantly improved performance towards both constrained benchmark tests and constrained configuration optimization problem. The configuration optimization framework developed can benefit both existing design/manufacturing practices and future additive manufacturing.

Motivation & Objective

• Address the challenge of balancing solution feasibility and optimality in configuration optimization with multiple hard constraints.
• Formulate a computationally tractable mathematical model for a representative configuration optimization problem in engineering design.
• Develop an improved metaheuristic algorithm capable of handling complex, real-world constraints while maintaining convergence and diversity.
• Facilitate practical application in design and manufacturing, especially in emerging additive manufacturing contexts.
• Overcome limitations of conventional multi-objective optimization by incorporating constraint handling mechanisms that prevent premature convergence.

Proposed method

• Propose a mathematical formulation for a configuration optimization problem involving minimization of envelope volume and connective line length under multiple hard constraints.
• Design a re-seed mechanism that enables biased search to explore promising regions without falling into premature convergence.
• Implement two versions of the enhanced multi-objective simulated annealing (MOSA/R) algorithm to improve solution diversity and convergence speed.
• Integrate dynamic temperature scheduling and neighborhood search strategies to maintain balance between exploration and exploitation.
• Use constraint-handling techniques that prioritize feasibility while optimizing multiple objectives simultaneously.
• Validate the algorithm on both benchmark problems and a real-world configuration optimization case study.

Experimental results

Research questions

• RQ1 How can a multi-objective optimization algorithm effectively handle multiple hard constraints in engineering configuration problems?
• RQ2 What mechanisms can improve convergence and prevent premature convergence in simulated annealing for constrained multi-objective problems?
• RQ3 To what extent does the proposed re-seed scheme enhance solution diversity and feasibility in complex configuration tasks?
• RQ4 How does the MOSA/R algorithm compare to standard multi-objective optimization methods in terms of convergence and constraint satisfaction?
• RQ5 Can the proposed framework be effectively applied to real-world engineering design and manufacturing scenarios, including additive manufacturing?

Key findings

• The MOSA/R algorithm achieves significantly improved performance on constrained benchmark problems compared to conventional multi-objective optimization methods.
• The re-seed mechanism effectively enhances search diversity and avoids premature convergence, leading to better convergence to the true Pareto front.
• The algorithm successfully satisfies all hard constraints across all test cases, demonstrating strong feasibility preservation.
• In the case study, MOSA/R outperformed baseline methods in minimizing both envelope volume and connective line length under complex spatial and connectivity constraints.
• The framework is adaptable to real-world engineering applications and shows strong potential for integration into design and additive manufacturing workflows.
• The proposed method maintains a good balance between convergence speed and solution quality, even under high-complexity constraint environments.