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

Pei Cao Graduate Research Assistant and Ph.D. Candidate Department of Mechanical Engineering University of Connecticut Storrs, CT 06269, USA

Zhaoyan Fan Assistant Professor
Department of Mechanical, Industrial and Manufacturing Engineering
Oregon State University Corvallis, OR 97331, USA

Robert X. Gao Cady Staley Professor of Engineering Department of Mechanical and Aerospace Engineering Case Western Reserve University Cleveland, OH 44106, USA

Jiong Tang Professor Department of Mechanical Engineering University of Connecticut Storrs, CT 06269, USA Phone: (860) 486-5911, Email: jiong.tang@uconn.edu

Submitted to: Robotics and Computer-Integrated Manufacturing

 Corresponding author

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

Pei Cao1, Zhaoyan Fan2, Robert Gao3, and J. Tang1 1: Department of Mechanical Engineering University of Connecticut Storrs, CT 06269, USA 2: Department of Mechanical, Industrial and Manufacturing Engineering Oregon State University Corvallis, OR 97331, USA 3: Department of Mechanical and Aerospace Engineering Case Western Reserve University Cleveland, OH 44106, USA

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.

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Keywords: configuration design, multi-objective optimization, Simulated Annealing, hard constraints.

1. Introduction Configuration design and optimization have been studied since the Kepler Conjecture (i.e., no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing and hexagonal close packing arrangements). In modern computer-integrated manufacturing, configuration optimizations are frequently encountered in aerospace and automotive systems [1], manufacturing facilities and plants [2-5], and 3-dimensonal laser cutting [6] etc. In general, configuration design involves a wide variety of goals and objectives rather than just optimizing the volume and weight; however, densest packing is a good example in terms of the difficulties one may encounter when dealing with such topics. In 2-dimensional scenarios, one is given a set of geometries such as rectangles, polyminos or spheres. The goal is to pack these items orthogonally into a single rectangular box of unlimited height which needs to be minimized [7], or alternatively, to pack a number of circles inside a circumcircle whose radius needs to be minimized [8]. Three-dimensional problems can be defined in a similar fashion [9], e.g., given a set of three-dimensional objects of arbitrary geometry and an available space (possibly the space of a container), find a placement for the objects within the space that achieves the design objectives, such that none of the objects interferes (i.e. occupy the same space) while optional spatial and performance constraints on the objects are satisfied. The problem of packing has shown to be NP-complete [10], i.e., no optimal algorithm is known running in polynomial time.
   Therefore, even simple design problems involving spheres, squares or rectangles are known to be difficult problems in the mathemati

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