A distributed constraint optimization problem (DCOP) is a formalism that captures the rewards and costs of local interactions within a team of agents. Because complete algorithms to solve DCOPs are unsuitable for some dynamic or anytime domains, researchers have explored incomplete DCOP algorithms that result in locally optimal solutions. One type of categorization of such algorithms, and the solutions they produce, is k-optimality; a k-optimal solution is one that cannot be improved by any deviation by k or fewer agents. This paper presents the first known guarantees on solution quality for k-optimal solutions. The guarantees are independent of the costs and rewards in the DCOP, and once computed can be used for any DCOP of a given constraint graph structure. 1

Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We say that P admits an Asymptotic Domination Ratio One (ADRO) algorithm if there is a polynomial time approximation algorithm A for P such that lims→ ∞ domr(A, s) = 1. Alon, Gutin and Krivelevich (J. Algorithms 50 (2004), 118–131) proved that the partition problem admits an ADRO algorithm. We extend their result to the minimum multiprocessor scheduling problem.

Abstract Memetic Algorithms have become one of the key methodologies behind solvers that are capable of tackling very large, real-world, optimisation problems. They are being actively investigated in research institutions as well as broadly applied in industry. In this chapter we provide a pragmatic guide on the key design issues underpinning Memetic Algorithms (MA) engineering. We begin with a brief contextual introduction to Memetic Algorithms and then move on to define a Pattern Language for MAs. For each pattern, an associated design issue is tackled and illustrated with examples from the literature. In the last section of this chapter we “fast forward ” to the future and mention what, in our mind, are the key challenges that scientistis and practitioner will need to face if Memetic Algorithms are to remain a relevant technology in the next 20 years. 1

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Abstract. Optimization heuristics are often compared with each other to determine which one performs best by means of worst-case performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the Max-Regret heuristic introduced by Balas and Saltzman finds the unique worst possible solution for some instances of the s-dimensional (s ≥ 3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s = 3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the s-dimensional (s ≥ 3) assignment problem. 1