HEURISTICS FOR COMBINATORIAL OPTIMIZATION Lecture 3 Metaheuristics for Construction Heuristics

Task: Pack all the items into a minimum number of unit-capacity bins An algorithm A is said to be a δ-approximation algorithm if it runs in polynomial time and for every problem instance π with optimal solution value OP T (π) minimization: A(π) OP T (π) ≤ δ δ ≥ 1 maximization: A(π) OP T (π) ≥ δ δ ≤ 1 A family of approximation algorithms for a problem Π, {A } , is called a polynomial approximation scheme (PAS), if algorithm A is a (1 +)-approximation algorithm and its running time is polynomial in the size of the input for a fixed A family of approximation algorithms for a problem Π, {A } , is called a fully polynomial approximation scheme (FPAS), if algorithm A is a (1 +)-approximation algorithm and its running time is polynomial in the size of the input and 1// Key idea: use greedy construction alternation of Construction and Deconstruction phases an acceptance criterion decides whether the search continues from the new or from the old solution.