A Weight-coded Evolutionary Algorithm for the Multidimensional Knapsack Problem

A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.Comment: Submitted to Applied Mathematics and Computation on April 8, 201

A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. We tackle the problem using duality concept, differently from traditional approaches. Our method is based on Lagrangian relaxation. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Through empirical investigation of Lagrangian space, we can see the potentiality of using a memetic algorithm. So we use a memetic algorithm to find the optimal Lagrange multipliers. We show the efficiency of the proposed method by the experiments on well-known benchmark data

Empirical Analysis of Various Multi-Dimensional Knapsack Heuristics

Since the multidimensional knapsack problems are NP-hard problems, the exact solutions of knapsack problems often need excessive computing time and storage space. Thus, heuristic approaches are more practical for multidimensional knapsack problems as problems get large. This thesis presents the results of an empirical study of the performance of heuristic solution procedures based on the coefficients correlation structures and constraint slackness settings. In this thesis, the three representative greedy heuristics, Toyoda, Senju and Toyoda, and Loulou and Michaelides’ methods, are studied. The purpose of this research is to explore which heuristic of the three representative greedy heuristics performs best under certain combinations of conditions between constraint slackness and correlation structures. This thesis examines three heuristics over 1120 problems which are all the two-dimensional knapsack problems (2KPs) with 100 variables created by four constraint slackness settings and 45 feasible correlation structures. Then we analyze why the best heuristic behaves as it does as a function of problem characteristics. Finally we present two new heuristics using knowledge gained in the study. When these new heuristics are competitively tested against the three representative greedy heuristics, the results show the new heuristics perform better

Developing New Multidimensional Knapsack Heuristics Based on Empirical Analysis of Legacy Heuristics

The multidimensional knapsack problem (MKP) has been used to model a variety of practical optimization and decision-making applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. While there have been a variety of heuristics proposed for the MKP, and a plethora of empirical studies comparing the performance of these heuristics, little has been done to garner a deeper understanding of heuristic performance as a function of problem structure. This dissertation presents a research methodology, empirical and theoretical results explicitly aimed at gaining a deeper understanding of heuristic procedural performance as a function of test problem characteristics. This work first employs an available, robust set of two-dimensional knapsack problems in an empirical study to garner performance insights. These performance insights are tested against a larger set of problems, five-dimensional knapsack problems specifically generated for empirical testing purposes. The performance insights are found to hold in the higher dimensions. These insights are used to formulate and test a suite of three new greedy heuristics for the MKP, each improving upon its successor. These heuristics are found to outperform available legacy heuristics across a complete spectrum of test problems. Problem reduction heuristics are examined and the subsequent performance insights garnered are used to derive a new problem reduction heuristic, which is then further extended to employ a local improvement phase. These problem reduction heuristics are also found to outperform currently available approaches. Available problem test sets are shown lacking along multiple dimensions of importance for viable empirical testing. A new problem generation methodology is developed and shown to overcome the current limitations in available problem test sets. This problem generation methodology is used to generate a new set of empirical test problems specifically designed for competitive computational tests. This new test set is shown to stress existing heuristics; not only does the computational time required by these legacy heuristics increase with problem size, but solution quality is found to decrease with problem size. However, the solution quality obtained by the suite of heuristics developed in this dissertation are shown to be unaffected by problem size thereby providing a level of robust solution quality not previously seen in heuristic development for the MKP. This research demonstrates that the test problems can have a profound, and sometimes misleading, impact on the general insights gained via empirical testing, provides six new quality heuristics, and two new robust sets of test problems, one focused on empirical testing, the other focused on competitive testing

A case study of controlling crossover in a selection hyper-heuristic framework using the multidimensional knapsack problem

Hyper-heuristics are high-level methodologies for solving complex problems that operate on a search space of heuristics. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. The use of crossover low-level heuristics is possible in an increasing number of general-purpose hyper-heuristic tools such as HyFlex and Hyperion. However, little work has been undertaken to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution, and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. First, crossover is controlled at the hyper-heuristic level where no problem-specific information is required. Second, it is controlled at the problem domain level where problem-specific information is used to produce good-quality solutions to use in crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem: the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain. © 2016 Massachusetts Institute of Technolog

An Improved Surrogate Constraints Method for Separable Nonlinear Integer Programming

An improved surrogate constraints method for solving separable nonlinear integer programming problems with multiple constraints is presented. The surrogate constraints method is very effective in solving problems with multiple constraints. The method solves a succession of surrogate constraints problems having a single constraint instead of the original multiple constraint problem. A surrogate problem with an optimal multiplier vector solves the original problem exactly if there is no duality gap. However, the surrogate constraints method often has a duality gap, that is it fails to find an exact solution to the original problem. The modification proposed closes the surrogate duality gap. The modification solves a succession of target problems that enumerates all solutions hitting a particular target. The target problems are produced by using an optimal surrogate multiplier vector. The computational results show that the modification is very effective at closing the surrogate gap of multiple constraint problems

A decomposition approach for multidimensional knapsacks with family-split penalties

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant of the more classical Multidimensional Knapsack and Multi-Knapsack problems. This problem deals with a set of items partitioned in families, and when a single item is picked to maximize the utility, then all items in its family must be picked. Items from the same family can be assigned to different knapsacks, and in this situation split penalties are paid. This problem arises in real applications in various fields. This paper proposes a new exact and fast algorithm based on a specific Combinatorial Benders Cuts scheme. An extensive experimental campaign computationally shows the validity of the proposed method and its superior performance compared to both commercial solvers and state-of-the-art approaches. The paper also addresses algorithmic flexibility and scalability issues, investigates challenging cases, and analyzes the impact of problem parameters on the algorithm behavior. Moreover, it shows the applicability of the proposed approach to a wider class of realistic problems, including fixed costs related to each knapsack utilization. Finally, further possible research directions are considered

Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”

This paper reviews existing literatures on the analysis of performance appraisal (PA) paying special attention to those which try to take into account the “social context” of appraisal systems and processes. The special place of political action within these processes is underlined and the different levels at which politics need to be considered in research are outlined. Research on politics is considered and shown to lack an adequate consideration of the social relations involved in the reciprocal interactions between PA tools and processes and users interpretation and manipulation of them.Performance appraisal; Social context; Politics