Automatic generation of algorithms for the binary knapsack problem

Abstract

Because it is classified as NP-hard, the binary knapsack problem is a good example of a combinatorial optimization problem that still presents increased difficulty when attempting to determine the optimal solution for any instance. Although exact and heuristic methods have been developed in an attempt to solve the problem, such methods have been unable to solve even small instances of the problem. In this paper, new algorithms for this problem are automatically generated by means of genetic programming from sets of training instances of different sizes and are then evaluated against other larger sized sets of instances, thereby detecting the robustness of the algorithms for larger instances. Overall, the produced algorithms are able to identify up to 52% of the optimal solutions for the biggest instances used.

Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem

“…The different algorithms generated during the evolutionary process can be decoded manually from their tree structure to obtain their corresponding pseudocode. An illustrative case is presented in Algorithm 1 that builds a solution in 6 Scientific Programming Input: Graph Output: Generalized minimum spanning tree (1) repeat (2) condition-repeat1 ← false (3) condition-repeat2 ← false (4) if least-cluster-initial-connection () or tree-leaf-connection-improvement () (5) condition-repeat1 ← true (6) else (7) while1 [condition-repeat1 ← connect-cluster-with-fewer-vertices ()] = true do (8) tree-leaf-connection-improvement () (9) end while1 (10) end if (11) if condition-repeat1 = true (12) repeat (13) flag ← connection-cluster-improvement () (14) if internal-edge-connection-improvement () (15) while1 [flag2 ← subtree-4-cluster-connection-improvement ()] = true do (16) connect-smallest-edge-with-the-tree () (17) end while1 (18) else (19) flag2 ← false (20) end if (21) if flag = flag2 (22) condition-repeat2 ← true (23) while1 connect-cluster-with-fewer-vertices() do (24) connect-cluster-with-fewer-vertices () (25) end while1 (26) end if (27) until condition-repeat2 (28) end if (29) until condition-repeat1 (30) return GMSTP Algorithm 1: Pseudocode of GMSTP2. two stages.…”

“…Some of the most widely used approaches to generating hyperheuristics are genetic programming [19,20], genetic algorithms [21], and learning systems [22]. The hyperheuristic approach has been used to approach various optimization problems, such as packing [23], timetabling [24], scheduling [25], MAX-SAT [26], vertex coloring problems [27], and binary knapsack problem [28,29].…”

Optimal deterministic algorithm generation

“…Automatic algorithm generation for retrieval, classification and other data manipulation has been proposed by [23] based on statistical data analysis and other methods. For instance, in [33] algorithms for the well-known knapsack problem are automatically generated by genetic algorithms. Algorithms are first generated for small knapsack instances and then compared to algorithms computed on larger test sets.…”