A new evolutionary approach to cutting stock problems with and without contiguity

Abstract

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two di!erent types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the e!ectiveness of the EP algorithm. They show that EP can provide a simple yet more e!ective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are signi"cantly better (in most cases) than or comparable to those found by GAs. Scope and purposeThe one-dimensional cutting stock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially "nished items (pattern sequencing or contiguity problem). Although some traditional OR techniques (e.g., programming based approaches) can "nd the global optimum for small CSPs, they are impractical to "nd the exact global optimum for large problems due to combinatorial explosion. Heuristic techniques (such as various hill-climbing algorithms) need to be used for large CSPs. One of the heuristic algorithms which have been applied to CSPs recently with success is the genetic algorithm (GA). This paper proposes a much simpler evolutionary algorithm than the GA, based on evolutionary programming (EP). The EP algorithm has been shown to perform signi"cantly better than the GA for most benchmark problems we used and to be comparable to the GA for other problems.

An investigation into two bin packing problems with ordering and orientation implications

“…For our experiments, we took the well-known one-dimensional SCP instance "10a" from the work of Liang et al (2002), which involves n = 600 items of 36 types with ∑ j∈I A(j) = 25, 790. This is seen to be a difficult problem and, by default, uses W = 120 and H = 1 resulting in approx.…”

“…of many different sizes), whereas in the SCP items are only weakly heterogeneous (that is, many items have the same size). Though rather subjective, this difference is important to note as, historically, it has brought about quite different solution approaches for the two problems (Falkenauer, 1998;Haessler and Sweeny, 1991;Liang et al, 2002;Martello and Toth, 1990b;Lewis, 2009).…”

Mathematical models and decomposition algorithms for cutting and packing problems

“…Liang et al [188] proposed an evolutionary programming algorithm for the CSP and some of its variants.…”

Computing Minimum Cuts by Randomized Search Heuristics

“…Examples are the maximum cut problem or the minimum multicut problem [11]. Evolutionary algorithms have produced good results for various kinds of difficult cutting problems [5,14,20].…”