Fast,effective heuristics for the 0–1 multi-dimensional knapsack problem

The objective of the multi-dimensional knapsack problem (MKP) is to find a subset of items with maximum value that satisfies a number of knapsack constraints. Solution methods for MKP, both heuristic and exact, have been researched for several decades. This paper introduces several fast and effective heuristics for MKP that are based on solving the LP relaxation of the problem. Improving procedures are proposed to strengthen the results of these heuristics. Additionally, the heuristics are run with appropriate deterministic or randomly generated constraints imposed on the linear relaxation that allow generating a number of good solutions. All algorithms are tested experimentally on a widely used set of benchmark problem instances to show that they compare favourably with the best-performing heuristics available in the literature.     

Immune-based algorithms for dynamic optimization

The main problem with biologically inspired algorithms (like evolutionary algorithms or particle swarm optimization) when applied to dynamic optimization is to force their readiness for continuous search for new optima occurring in changing locations. Immune-based algorithm, being an instance of an algorithm that adapt by innovation seem to be a perfect candidate for continuous exploration of a search space. In this paper we describe various implementations of the immune principles and we compare these instantiations on complex environments.     

Speeding up global optimization with the help of intelligent supervisors

It is shown in the paper that Developmental Genetic Programming is an efficient tool for evolutionary development of intelligent supervisors that solve an extension of Resource-Constrained Project Scheduling Problem. The extension assumes that resources are only partially available. It also assumes that renewable resources affect the project cost. The cost should be as low as possible and a deadline of the project must be met. This is apparent with regard to software houses and building enterprises. Computational experiments showed that supervisors find solutions of the problem much faster than other genetic approaches. A specific property of the supervisor is that it has various strategies of allocating the resources to the tasks. The supervisor uses the strategies in order to develop a procedure for producing the best schedule for the whole project. The analysis of the evolutionary process was performed and experimental results were compared with the optimal ones obtained by means of the exhaustive search method.     

The shape of feature code: an analysis of twenty C-preprocessor-based systems

Feature annotations (e.g., code fragments guarded by #ifdef C-preprocessor directives) control code extensions related to features. Feature annotations have long been said to be undesirable. When maintaining features that control many annotations, there is a high risk of ripple effects. Also, excessive use of feature annotations leads to code clutter, hinder program comprehension and harden maintenance. To prevent such problems, developers should monitor the use of feature annotations, for example, by setting acceptable thresholds. Interestingly, little is known about how to extract thresholds in practice, and which values are representative for feature-related metrics. To address this issue, we analyze the statistical distribution of three feature-related metrics collected from a corpus of 20 well-known and long-lived C-preprocessor-based systems from different domains. We consider three metrics: scattering degree of feature constants, tangling degree of feature expressions, and nesting depth of preprocessor annotations. Our findings show that feature scattering is highly skewed; in 14 systems (70 %), the scattering distributions match a power law, making averages and standard deviations unreliable limits. Regarding tangling and nesting, the values tend to follow a uniform distribution; although outliers exist, they have little impact on the mean, suggesting that central statistics measures are reliable thresholds for tangling and nesting. Following our findings, we then propose thresholds from our benchmark data, as a basis for further investigations.     

Constrained motion planning of nonholonomic systems

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts.     

Consensus models: Computational complexity aspects in modern approaches to the list coloring problem

In the paper we study new approaches to the problem of list coloring of graphs. In the problem we are given a simple graph G=(V,E) and, for every v∈V, a nonempty set of integers S(v); we ask if there is a coloring c of G such that c(v)∈S(v) for every v∈V. Modern approaches, connected with applications, change the question—we now ask if S can be changed, using only some elementary transformations, to ensure that there is such a coloring and, if the answer is yes, what is the minimal number of changes. In the paper for studying the adding, the trading and the exchange models of list coloring, we use the following transformations:

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adding of colors (the adding model): select two vertices u, v and a color c∈S(u); add c to S(v), i.e. set S(v):=S(v)∪{c};

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trading of colors (the trading model): select two vertices u, v and a color c∈S(u); move c from S(u) to S(v), i.e. set S(u):=S(u)?{c} and S(v):=S(v)∪{c};

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exchange of colors (the exchange model): select two vertices u, v and two colors c∈S(u), d∈S(v); exchange c with d, i.e. set S(u):=(S(u)?{c})∪{d} and S(v):=(S(v)?{d})∪{c}.

Our study focuses on computational complexity of the above models and their edge versions. We consider these problems on complete graphs, graphs with bounded cyclicity and partial k-trees, receiving in all cases polynomial algorithms or proofs of NP-hardness.     

A multicriteria approach to two-level hierarchy scheduling in grids

In this paper we address a multicriteria scheduling problem for computational Grid systems. We focus on the two-level hierarchical Grid scheduling problem, in which at the first level (the Grid level) a Grid broker makes scheduling decisions and allocates jobs to Grid nodes. Jobs are then sent to the Grid nodes, where local schedulers generate local schedules for each node accordingly. A general approach is presented taking into account preferences of all the stakeholders of Grid scheduling (end-users, Grid administrators, and local resource providers) and assuming a lack of knowledge about job time characteristics. A single-stakeholder, single-criterion version of the approach has been compared experimentally with the existing approaches.     

Leftist Grammars and the Chomsky Hierarchy

Leftist grammars are characterized in terms of rules of the form a → ba and cd → d, without distinction between terminals and nonterminals. They were introduced by Motwani et al. [13], where the accessibility problem for some general protection system was related to these grammars. This protection system was originally proposed in [4] and [15] in the context of Java virtual worlds. The accessibility problem is formulated in the form "Can object p gain (illegal) access to object q by a series of legal moves (as prescribed by the policy)?" The membership problem for leftist grammar is decidable [13], which implies decidability of the accessibility problem for the appropriate protection system. We study relationships between language classes defined by various types of leftist grammars and classes of the Chomsky hierarchy. We show that general leftist grammars can define languages which arenot context free, answering in the negative a question from [13]. Moreover, we study some restricted variants of leftist grammars and relate them to regular, deterministic context-free, and context-free languages.     

Gauss-Hermite approximation formula

A multidimensional function defined by a sample of points is approximated by a differentiable function . The problem is solved by using the Gauss-Hermite folding method developed in the nuclear shell correction method by Strutinsky.