The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very large-scale neighborhood search algorithms give consistently better solutions compared the popular 2-exchange neighborhood algorithms considering both the solution time and solution accuracy.

We present fast and simple fully...

Markov decision processes (MDPs) are models of dynamic decision making under uncertainty. These models arise in diverse applications and have been developed extensively in fields such as operations research, control engineering, and the decision sciences in general. Recent research, especially in artificial intelligence, has highlighted the significance of studying the computational properties of MDP problems. We address

Policy iteration is a a popular technique for solving Markov decision processes (MDPs). It is easy to describe and implement, and has excellent performance in practice. But not much is known about its complexity. The best

We consider an optimization problem in probabilistic inference: Given n hypotheses H j , m possible observations O k , their conditional probabilities p k j , and a particular O k , select a possibly small subset of hypotheses excluding the true target only with some error probability e. After specifying the optimization goal we show that this problem can be solved through a linear program in mn variables that indicate the probabilities to discard a hypothesis given an observation. Moreover, we can compute optimal strategies where only O(m+n) of these variables get fractional values. The manageable size of the linear programs and the mostly deterministic shape of optimal strategies makes the method practicable. We interpret the dual variables as worst-case distributions of hypotheses, and we point out some counterintuitive nonmonotonic behaviour of the variables as a function of the error bound e. One of the open problems is the existence of a purely combinatorial algorithm that is faster than generic linear programming.

Minimum cost multicommodity flows are a useful model for bandwidth allocation problems in telecommunications networks. These problems are arising more frequently as regional service providers wish to carry their traffic over some national core network. We describe a simple and practical combinatorial algorithm to find a minimum cost multicommodity flow in a ring network. Apart from 1 and 2-commodity flow problems, this seems to be the only such "combinatorial algorithm" for a version of exact mincost multicommodity flow. The solution it produces is always half-integral, and by increasing the capacity of each link by one, we may also find an integral routing of no greater cost. The "pivots" in the algorithm are determined by choosing an ffl ? 0, increasing and decreasing sets of variables, and adjusting these variables up or down accordingly by ffl. In this sense, it generalizes the cycle cancelling algorithms for single source mincost flow. Although the algorithm is easily stated, proo...

This paper shows that the minimum ratio canceling algorithm of Wallacher (1989) (and a faster relaxed version) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negative cycle oracle, this algorithm will compute an optimal solution in (weakly) polynomial time. We then specialize the algorithm to linear programming on unimodular linear spaces, and to the minimum cost flow and (dual) tension problems. We construct instances proving that even in the network special cases the algorithm is not strongly polynomial. Keywords: negative cycle canceling algorithm, minimum ratio cycle, linear programming problem, unimodular linear space, minimum cost flow, minimum cost tension. 1

The growths of containerization and transporting goods in containers have created many problems for ports. In this paper, we systematically survey a literature over problems in container terminals. The operations that take place in container terminals are described and then the problems are classified into five scheduling decisions. For each of the decisions, on overview of the literature is presented. After that, each of the decisions is formulated as Constraint Satisfaction and Optimisation Problems (CSOPs). The literature also includes solutions, implementation and performance. The solutions are classified and summarized. Two frameworks for the implementation are suggested. To confirm the results and to measure the terminal’s efficiency in each of the decisions, several indices are suggested.

We introduce networks with additive losses and gains on the arcs. If a positive flow of x units enter an arc a, then x + g(a) units exit. Arcs may increase or consume flow, i.e., they are gainy or lossy. Such networks have various applications, e.g., in financial analysis, transportation, and data communication. Problems in such networks are generally intractable. In particular, the shortest path problem is NP-hard. However, there is a pseudo-polynomial time algorithm for the problem with nonnegative costs and gains. The maximum flow problem is strongly NP-hard, even in unit-gain networks and in networks with integral ca-pacities and loss at most three, and is hard to approximate. However, it is solvable in polynomial time in unit-loss networks using the Edmonds-Karp algorithm. Our NP-hard results contrast efficient polynomial time solutions of path and flow problems in standard and in so-called generalized networks with multiplicative losses and gains.