Qie He

An effective co-evolutionary particle swarm optimization for constrained engineering design problems

Many engineering design problems can be formulated as constrained optimization problems. So far, penalty function methods have been the most popular methods for constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanism. By employing the notion of co-evolution to adapt penalty factors, this paper proposes a co-evolutionary particle swarm optimization approach (CPSO) for constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. The proposed CPSO is population based and easy to implement in parallel. Especially, penalty factors also evolve using PSO in a self-tuning way. Simulation results based on well-known constrained engineering design problems demonstrate the effectiveness, efficiency and robustness on initial populations of the proposed method. Moreover, the CPSO obtains some solutions better than those previously reported in the literature.

A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization

During the past decade, hybrid algorithms combining evolutionary computation and constraint-handling techniques have shown to be effective to solve constrained optimization problems. For constrained optimization, the penalty function method has been regarded as one of the most popular constraint-handling technique so far, whereas its drawback lies in the determination of suitable penalty factors, which greatly weakens the efficiency of the method. As a novel population-based algorithm, particle swarm optimization (PSO) has gained wide applications in a variety of fields, especially for unconstrained optimization problems. In this paper, a hybrid PSO (HPSO) with a feasibility-based rule is proposed to solve constrained optimization problems. In contrast to the penalty function method, the rule requires no additional parameters and can guide the swarm to the feasible region quickly. In addition, to avoid the premature convergence, simulated annealing (SA) is applied to the best solution of the swarm to help the algorithm escape from local optima. Simulation and comparisons based on several well-studied benchmarks demonstrate the effectiveness, efficiency and robustness of the proposed HPSO. Moreover, the effects of several crucial parameters on the performance of the HPSO are studied as well.

An effective co-evolutionary differential evolution for constrained optimization

Many practical problems can be formulated as constrained optimization problems. Due to the simple concept and easy implementation, the penalty function method has been one of the most common techniques to handle constraints. However, the performance of this technique greatly relies on the setting of penalty factors, which are usually determined by manual trial and error, and the suitable penalty factors are often problem-dependent and difficult to set. In this paper, a differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems. First, a special penalty function is designed to handle the constraints. Second, a co-evolution model is presented and differential evolution (DE) is employed to perform evolutionary search in spaces of both solutions and penalty factors. Thus, the solutions and penalty factors evolve interactively and self-adaptively, and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously. Simulation results based on several benchmark functions and three well-known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method.

A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem

We study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed-integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-routes with additional constraints. A family of cycle elimination constraints are derived for the arc-load formulation. We then compare the linear programming LP relaxations of these formulations with the two-index one-commodity flow formulation proposed in the literature. In particular, we show that the arc-load formulation with the new cycle elimination constraints gives the same LP bound as the set partitioning formulation based on 2-cycle-free q-routes, which is stronger than the LP bound given by the two-index one-commodity flow formulation. We propose a branch-and-cut algorithm for the arc-load formulation, and a branch-cut-and-price algorithm for the set partitioning formulation strengthened by additional constraints. Computational results on instances from the literature demonstrate that a significant improvement can be achieved by the branch-cut-and-price algorithm over other methods.

A hybrid Differential Evolution with double populations for constrained optimization

How to balance the objective and constraints is always the key point of solving constrained optimization problems. This paper proposes a hybrid differential evolution with double populations (HDEDP) to handle it. HDEDP uses a two-population mechanism to decouple constraints from objective function: one population evolves by differential evolution only according to either objective function or constraint, while the other stores feasible solutions which are used to repair some infeasible solutions in the former population. Thus, this technique allows objective function and constraints to be treated separately with little costs involved in the maintenance of the double population. In addition, to enhance the exploitation ability, simplex method (SM) is applied as a local search method to the best feasible solution of the first population. Simulation results based on three well-known engineering design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method.

A probabilistic comparison of split and type 1 triangle cuts for two-row mixed-integer programs

We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables in terms of cut coefficients and volume cutoff. Under a specific probabilistic model of the problem parameters, we show that for the above measure, the probability that a split cut is better than a type 1 triangle cut is higher than the probability that a type 1 triangle cut is better than a split cut.

Nonlinear constrained optimization by enhanced co-evolutionary PSO

Penalty function methods have been the most popular methods for nonlinear constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanisms. By employing the notion of co-evolution to adapt penalty factors, we present a co-evolutionary particle swarm optimization approach (CPSO) for nonlinear constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. To enhance the performance of our proposed algorithm, three improvement strategies are proposed. The proposed algorithm is population-based and easy to implement in parallel, in which the penalty factors to evolve in a self-tuning way. Simulation results based on three famous engineering constrained optimization problems demonstrate the effectiveness, efficiency and robustness of the proposed enhanced CPSO (ECPSO).

Optimized Treatment Schedules for Chronic Myeloid Leukemia

Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substantial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies. However, the design of such combination therapies (timing, sequence, etc.) remains an open challenge. In this work we mathematically model the dynamics of CML response to combination therapy and analyze the impact of combination treatment schedules on treatment efficacy in patients with preexisting resistance. We then propose an optimization problem to find the best schedule of multiple therapies based on the evolution of CML according to our ordinary differential equation model. This resulting optimization problem is nontrivial due to the presence of ordinary different equation constraints and integer variables. Our model also incorporates drug toxicity constraints by tracking the dynamics of patient neutrophil counts in response to therapy. We determine optimal combination strategies that maximize time until treatment failure on hypothetical patients, using parameters estimated from clinical data in the literature.

On the Computational Complexity of Minimum-Concave-Cost Flow in a Two-Dimensional Grid

We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs, and the location of sources and sinks. The concave cost over each arc is assumed to be evaluated through an oracle machine, i.e., the oracle machine returns the cost over an arc in a single computational step, given the flow value and the arc index. We propose an algorithm whose running time is polynomial in the number of columns of the grid, for the following cases: (1) the grid has a constant number of rows, a constant number of different capacities over all arcs, and sources and sinks in at most two rows; (2) the grid has two rows and a constant number of different capacities over all arcs connecting rows; (3) the grid has a constant number of rows and all sources in one row, with infinite capacity over each arc. These are presumably the most general polynomially solvable cases, since we show the problem becomes NP-hard when any condition in these cases is removed. Our results apply to abundant variants and generalizations of the dynamic lot sizing model, and answer several questions raised in serial supply chain optimization.

Sell or Hold: A simple two-stage stochastic combinatorial optimization problem

Abstract The sell or hold problem (SHP) is to sell k out of n indivisible assets over two stages, with known first-stage prices and random second-stage prices, to maximize the total expected revenue. We show that SHP is NP-hard when the second-stage prices are realized as a finite set of scenarios. We show that SHP is polynomially solvable when the number of scenarios in the second stage is constant. A max { 1 / 2 , k / n } -approximation algorithm is presented for the scenario-based SHP.