Some versions of the maximum common subgraph problem are studied and approximation algorithms are given. The maximum bounded common induced subgraph problem is shown to be Max SNP-hard and the maximum unbounded common induced subgraph problem is shown to be as hard to approximate as the maximum independent set problem. The maximum common induced connected subgraph problem is still harder to app...

In this chapter we are going to study metaheuristics based on the Automata Theory for the Multi-objective Optimization of Combinatorial Problems. As well known, Combinatorial Optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best possible solution(Yong-Fa ...

The vertex cover problem Find a set of vertices that cover the graph LP rounding is a 4 step scheme to approximate combinatorial problems with theoretical guarantees on solution quality. Several problems in machine learning, computer vision and data analysis can be formulated using NP-­‐hard combinatorial optimization problems. In many of these applications, approximate solutions for these NP-­...

Total weighted tardiness is a measure of customer satisfaction. Minimizing it represents satisfying the general requirement of on-time delivery. In this research, we consider an ant colony optimization (ACO) algorithm to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense. Computational results show that th...

despite the growing use of evolutionary multi-objective optimization algorithms in different categories of science, these algorithms as a powerful tool in portfolio optimization and specially solving multi-objective portfolio optimization problem is still in its early stages. in this paper, moeas have been used for solving multi-objective portfolio optimization problem in tehran stock market. f...

Many problems that we face nowadays can be expressed as optimization problems. Finding the best solution for real-world instances of such problems is hard or even infeasible. Metaheuristic algorithms have been used for decades to guide the search for satisfactory solutions in hard optimization problems at an affordable cost. However, despite its many benefits, the application of metaheuristics ...

Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more fine-tuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to exi...

The theory of NP-completeness, as developed by Cook, Levin, and Karp, states that any language, L in NP is reducible to the Boolean satisfiability problem, 3SAT. By this, we mean that for every instance, x of the language L, we can obtain a satisfiability instance, φ such that x ∈ L if and only if φ is satisfiable. Thus, 3SAT is at least as hard as any other problem in NP. Karp further showed t...