Constraint Handling in Genetic Algorithms: The Set Partitioning Problem

In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem (SPP). The SPP is an important combinatorial optimisation problem used by many airlines as a mathematical model for flight crew scheduling.A key feature of the SPP is that it is a highly constrained problem, all constraints being equalities. New genetic algorithm (GA) components: separate fitness and unfitness scores, adaptive mutation, matching selection and ranking replacement, are introduced to enable a GA to effectively handle such constraints. These components are generalisable to any GA for constrained problems.We present a steady-state GA in conjunction with a specialised heuristic improvement operator for solving the SPP. The performance of our algorithm is evaluated on a large set of real-world problems. Computational results show that the genetic algorithm-based heuristic is capable of producing high-quality solutions.     

Scatter Search for the 0–1 Multidimensional Knapsack Problem

The evolutionary metaheuristic called scatter search has been applied successfully to optimization problems for several years. In this paper, we apply the scatter search technique to the well-known 0–1 multidimensional knapsack problem. We propose a new relaxation-based diversification generator, which produces an initial population with elite solutions. The computational results obtained for a set of classic and correlated instances clearly show that (1) this generator can also be used as a heuristic for solving the multidimensional knapsack problem; (2) using the population produced by our generator as a starting point for the scatter search algorithm leads to better performance. We also enhance the scatter search algorithm by integrating memory and by using adapted intensification phases. Overall, the results are interesting and competitive compared to other population-based algorithms, such as genetic algorithms.      

Convex optimization under combinatorial sparsity constraints

We present a heuristic approach for convex optimization problems containing different types of sparsity constraints. Whenever the support is required to belong to a matroid, we propose an exchange heuristic adapting the support in every iteration. The entering non-zero is determined by considering the dual multipliers of the bounds on variables being fixed to zero. While this algorithm is purely heuristic, we show experimentally that it often finds near-optimal solutions for cardinality-constrained knapsack problems and for sparse regression problems.     

A beam search implementation for the irregular shape packing problem

This paper investigates the irregular shape packing problem. We represent the problem as an ordered list of pieces to be packed where the order is decoded by a placement heuristic. A placement heuristic from the literature is presented and modified with a more powerful nofit polygon generator and new evaluation criteria. We implement a beam search algorithm to search over the packing order. Using this approach many parallel partial solutions can be generated and compared. Computational results for benchmark problems show that the algorithm generates highly competitive solutions in significantly less time than the best results currently in the literature.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

An Efficient Genetic Algorithm for the p-Median Problem

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.     

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

The unconstrained binary quadratic programming problem (BQP) is known to be NP-hard and has many practical applications. This paper presents a simulated annealing (SA)-based heuristic for the BQP. The new SA heuristic for the BQP is based on a simple (1-opt) local search heuristic and designed with a simple cooling schedule, but the multiple annealing processes are adopted. To show practical performances of the SA, we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi-start local search, the previous SA, tabu search, and genetic algorithm incorporating the 1-opt local search. Computational results indicate that our SA leads to high-quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set. Furthermore, the values of new best-known solutions found by the SA for several large instances are also reported.     

物流服务供应链订单分配优化及其遗传算法

针对物流服务供应链订单分配问题中,物流服务集成商通常会按照所分配的订单价值向分包商收取一定比例交易费用的特点,设定交易费用为交易额的线性函数,构建了新的物流服务供应链订单分配优化混合整数规划模型,其优化目标为最小化交易费用、采购费用、短缺服务与延迟供给的物流能力数量。鉴于问题的NP-hard特性,设计了相应的遗传算法,并结合基于优先权的启发式规则避免了大量非法初始解的出现。实验算例表明所建立的模型能够反映物流服务供应链订单分配过程中的线性交易费用因素,其所设计的算法能够在可接受的时间内获得质量较高的满意解,并且对于大规模订单分配优化问题,遗传算法的求解时间与求解结果要优于LINGO软件。     

Smart greedy procedure for solving a nOnlinear knapsack class of reliability optimization problems

A new heuristic procedure, which is called Smart Greedy, is proposed for solving a kind of general reliability optimization problems (non-DGR type knapsack problems). Smart Greedy uses Recursive Greedy with multiple greedy functions designated by balance coefficients, generates several solutions and then determines the best solution among them as the smart greedy solution. Recursive Greedy first checks the feasibility of sets of items for a given problem and removes infeasible items from the item sets. Second, the procedure checks the gain ratio of increments of objective function to constraint function and reduces the problem to DGR type problem by invoking LP dominance. Third, the procedure continues to allocate the increments for current items until the constraint is violated. With the current solution, the procedure then repeats the greedy procedure for current items that are added to the items removed by the LP dominance in the previous step.Computational results show that the Smart Greedy is more effective than the previously reported methods.