The two-dimensional cutting problem requires maximising the sum of the profits of small rectangular pieces, each of which has its own profit and size, obtained from a large rectangular plate. In this paper, a best-first branch-and-bound algorithm is proposed for the unconstrained problem, which has no limit on the number of pieces cut. Each small piece can have its own profit or can use the area of the piece instead of the profit. The proposed algorithm extends the concept of dominated patterns to remove the dominated patterns efficiently. Our proposed algorithm can also remove duplicate patterns and reduce the search space. The existing upper bound is revised and a new bounding strategy that can prune several nodes simultaneously is proposed. Additionally, new data structures are introduced to improve the performance of the algorithm. Computational results using the proposed algorithm on some benchmark examples were compared to the performance of previous algorithms to show the efficiency of the new algorithm. The proposed algorithm reduced the average computational time by up to 93% for 48 sample problems, excluding those problems that required almost no time using existing algorithms. Additionally, a large-scale problem that could not be solved in a reasonable time by the existing exact algorithms was solved successfully using the proposed algorithm.
Thermal
management problems in high-power flexible electronics are exacerbated
by the design complexity and requirement of stringent temperature
control to prevent skin burns. Thus, effective heat dissipation methods
applicable to flexible electronics on polymer substrates are an essential
device design component. Accordingly, this study investigates the
pool boiling heat transfer characteristics and potential enhancements,
enabled by laser-induced graphene (LIG), which is both highly porous
and bendable. Patterned LIG with a mesh spacing of 200 μm was
formed on flexible polyimide substrates by laser direct writing, and
the resulting surfaces exhibited enhanced heat transfer characteristics.
Pool boiling experiments were conducted with an FC-72 working fluid
to investigate the heat removal capability of LIG, and its performance
was further improved by separating the liquid supply passages from
the vapor escape routes. Overall, the inclusion of LIG resulted in
a 2- to 3-fold increase in both the critical heat flux (33.6 W/cm2) and heat transfer coefficient (7.6 kW/(m2·K)),
compared to pristine polyimide films.
The constrained two-dimensional cutting problem involves maximising the sum of the profits obtained from small rectangular pieces cut from a large rectangular plate where the number of each type of cut piece cannot exceed a prescribed quantity. This paper proposes a best-first branch-and-bound algorithm to find the optimal solution to the problem. The proposed algorithm uses an efficient method to remove the duplicate patterns, and it improves the existing upper bounds. It also prevents the construction of dominated patterns and introduces a new bounding strategy that can prune more than one node at a time. Computational results are compared with a well-known exact algorithm to demonstrate the efficiency of the proposed algorithm. The proposed algorithm is as fast as or faster than the existing algorithm and reduces the average computing time by up to 99% for benchmark problems. For some problems, it can also find optimal solutions that existing algorithms are not able to find.
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