In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach. Computational results show that the genetic algorithm heuristic is capable of obtaining high-quality solutions for problems of various characteristics, whilst requiring only a modest amount of computational effort. Computational results also show that the genetic algorithm heuristic gives superior quality solutions to a number of other heuristics.

A Genetic Algorithm for the Multidimensional Knapsack Problem

Multiobjective programming in optimization of the interval objective function

Research in metaheuristics for combinatorial optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for optimization. At the same time, the focus of research has changed from being rather algorithm-oriented to being more problem-oriented. Nowadays the focus is on solving the problem at hand in the best way possible, rather than promoting a certain metaheuristic. This has led to an enormously fruitful cross-fertilization of different areas of optimization. This cross-fertilization is documented by a multitude of powerful hybrid algorithms that were obtained by combining components from several different optimization techniques. Hereby, hybridization is not restricted to the combination of different metaheuristics but includes, for example, the combination of exact algorithms and metaheuristics. In this work we provide a survey of some of the most important lines of hybridization. The literature review is accompanied by the presentation of illustrative examples.

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Hybrid metaheuristics in combinatorial optimization: A survey

Fuzzy goal programming- an additive model

The multidimensional 0–1 knapsack problem: An overview

In this paper, we formally establish connections between two standard approaches proposed for resolving multi-objective programs, namely, the nonpreemptive and the preemptive methods. We demonstrate in the linear case that, if the preemptive problem has an optimal solution, then there exists a set of weights for the nonpreemptive problem, such that any optimal solution to the nonpreemptive problem is optimal to the preemptive problem. Conversely, and more importantly, any optimal solution to the preemptive problem is optimal to the nonpreemptive problem. A similar result is established for arbitrary multi-objective functions being optimized over a finite discrete set. Thus, the preemptive problem is subsumed within the nonpreemptive problem in these cases. Although we actually construct a set of equivalent weights, we do not advocate our technique as a computational device for solving the preemptive problem. However, a previous attempt (Ref. 1), which does prescribe a set of equivalent weights to solve a preemptive problem as a linear program, is shown to be erroneous. Moreover, our constructive proof exhibits the features of the problem which govern the determination of such equivalent weights.

Preemptive and nonpreemptive multi-objective programming: Relationship and counterexamples

Zero-one programming with many variables and few constraints

An inventory model is developed for a finite horizon and price changes. The structure and form of the optimal policy is determined along with sensitivity analysis with respect to the length of the horizon. This is a prelude to considering an infinite horizon problem in which at some a priori known time the purchase price of the item will increase. In this paper appropriate ordering policies are determined with respect to known information about an ensuing price rise.

An Inventory Model with Finite Horizon and Price Changes

Inexact linear programming with generalized resource sets

The classical Economic Order Quantity Model requires the parameters of the model to be constant. Some EOQ models allow a single parameter to change with time. We consider EOQ systems in which one or more of the cost or demand parameters will change at some time in the future. The system we examine has two distinct advantages over previous models. One obvious advantage is that a change in any of the costs is likely to affect the demand rate and we allow for this. The second advantage is that often, the times that prices will rise are fairly well known by announcement or previous experience. We present the optimal ordering policy for these inventory systems with anticipated changes and a simple method for computing the optimal policy. For cases where the changes are in the distant future we present a myopic policy that yields costs which are near-optimal. In cases where the changes will occur in the relatively near future the optimal policy is significantly better than the myopic policy.

A. L. Soyster

Papers

Preemptive and nonpreemptive multi-objective programming: Relationship and counterexamples

Zero-one programming with many variables and few constraints

An Inventory Model with Finite Horizon and Price Changes

Inexact linear programming with generalized resource sets

Optimal ordering policies when anticipating parameter changes in EOQ systems