Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0/1 knapsack problem.

Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach

The paradigmatic shift from a Web of manual interactions to a Web of programmatic interactions driven by Web services is creating unprecedented opportunities for the formation of online business-to-business (B2B) collaborations. In particular, the creation of value-added services by composition of existing ones is gaining a significant momentum. Since many available Web services provide overlapping or identical functionality, albeit with different quality of service (QoS), a choice needs to be made to determine which services are to participate in a given composite service. This paper presents a middleware platform which addresses the issue of selecting Web services for the purpose of their composition in a way that maximizes user satisfaction expressed as utility functions over QoS attributes, while satisfying the constraints set by the user and by the structure of the composite service. Two selection approaches are described and compared: one based on local (task-level) selection of services and the other based on global allocation of tasks to services using integer programming.

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QoS-aware middleware for Web services composition

Since 1985 various evolutionary approaches to multiobjective optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of different methods available to date are mostly qualitative and restricted to two approaches. In this paper an extensive, quantitative comparison is presented, applying four multiobjective evolutionary algorithms to an extended 0/1 knapsack problem.

Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study

Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

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Greedy Randomized Adaptive Search Procedures

The clonal selection principle is used to explain the basic features of an adaptive immune response to an antigenic stimulus. It establishes the idea that only those cells that recognize the antigens (Ag's) are selected to proliferate. The selected cells are subject to an affinity maturation process, which improves their affinity to the selective Ag's. This paper proposes a computational implementation of the clonal selection principle that explicitly takes into account the affinity maturation of the immune response. The general algorithm, named CLONALG, is derived primarily to perform machine learning and pattern recognition tasks, and then it is adapted to solve optimization problems, emphasizing multimodal and combinatorial optimization. Two versions of the algorithm are derived, their computational cost per iteration is presented, and a sensitivity analysis in relation to the user-defined parameters is given. CLONALG is also contrasted with evolutionary algorithms. Several benchmark problems are considered to evaluate the performance of CLONALG and it is also compared to a niching method for multimodal function optimization.

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Learning and optimization using the clonal selection principle

We consider the problem of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of three-dimensional rectangular bins. The problem is NP-hard in the strong sense and extremely difficult to solve in practice. We characterize relevant subclasses of packing and present an algorithm which is able to solve moderately large instances to optimality. Extensive computational experiments compare the algorithm for the three-dimensional bin packing when solving general orthogonal packings and when restricted to robot packings.

Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem

We present a computer code that implements a general Tabu Search technique for the solution of two- and three-dimensional bin packing problems, as well as virtually any of their variants requiring the minimization of the number of bins. The user is only requested to provide a procedure that gives an approximate solution to the actual variant to be solved.

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TSpack: A Unified Tabu Search Code for Multi-Dimensional Bin Packing Problems

The k -cardinality assignment problem

Vorhanden ist eine Menge von Gegenstanden mit gegebenem Gewicht und gegebenem Wert, ferner eine Menge von Rucksacken mit gegebener Tragfahigkeit. Die Gegenstande sollen so in die Rucksacke gepackt werden, das die Tragfahigkeit der einzelnen Rucksacke nicht uberschritten wird und der Gesamtwert der verwendeten Gegenstande moglichst gros ist. Die besten bekannten Algorithmen liefern mit vertretbarem Rechenaufwand, Losungen fur hochstens 200 Gegenstande und 4 Rucksacke. Aber praktische, Anwendungen wie z. B. Teilungs-, Lagerhaltungs- und Ladeaufgaben benotigen oft eine grosere Zahl von Variablen und verlangen, daher die Verwendung von Heuristik. Der vorliegende Artikel erlautert Methoden, mit deren Hilfe sich suboptimale Losungen des Mehr-Rucksack-Problems finden lassen. Numerische Experimente mit Problemen verschiedener, Grose zeigen, das sich die verschiedenen Algorithmen zufriedenstellend verhalten, sowohl hinsichtlich der Laufzeiten als auch bezuglich der Gute der gefundenen Losungen. Eine RORTRAN-IV-Version der Algorithmen ist beigefugt.

Heuristic algorithms for the multiple knapsack problem

Crew and vehicle scheduling are fundamental issues in public transit management. Informally, they can be described as the problem of determining the optimal duties for a set of crews e.g., bus drivers or vehicles e.g., buses so as to cover a given set of timetabled trips, satisfying a number of constraints laid down by the union contract and company regulations. We consider the simplified but still NP-hard case in which several depots are specified, and limits on both the total time between the start and the end of any duty spread time and the total duty operational time working time are imposed. We give a 0-1 linear programming formulation based on binary variables associated with trip transitions, which applies to both crew and vehicle scheduling. The model is enhanced by means of new families of valid inequalities, for which exact and heuristic separation procedures are proposed. These techniques are embedded into an exact branch-and-cut algorithm, which also incorporates heuristic procedures. The performance of two implementations of the method for vehicle scheduling and crew scheduling, respectively are evaluated through computational testing on both random and real-world test problems from the literature.

Silvano Martello

Papers

Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem

TSpack: A Unified Tabu Search Code for Multi-Dimensional Bin Packing Problems

The k -cardinality assignment problem

Heuristic algorithms for the multiple knapsack problem

A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems