自适应人工蜂群算法：连续优化的双重策略
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"这篇研究论文探讨了一种高效自适应人工蜂群算法，通过结合两种策略来优化连续函数。该算法旨在解决人工蜂群(ABC)算法在进化过程中如何动态平衡探索与开发的问题。"
正文:
在优化问题领域，人工蜂群(ABC)算法作为一种基于群体智能的优化方法，已经在解决复杂优化问题上展现出潜力。然而，ABC算法的一个主要挑战是如何在搜索过程中灵活地调整探索和开发的平衡，以避免早熟收敛或陷入局部最优。论文"A high-efficiency adaptive artificial bee colony algorithm using two strategies for continuous optimization"提出了一种新的变体，通过引入两种策略实现这一目标，从而提高了算法的效率。
1. 策略一：动态搜索策略适应
这种策略关注于如何根据算法的当前状态动态改变搜索策略。在传统的ABC算法中，工蜂通常按照固定的方式搜索解决方案空间。新的算法中，工蜂的搜索行为将根据其所在环境的特性进行调整，例如，当遇到复杂的优化区域时，可能会增加探索性；而在接近潜在最优解的地方，则增加开发性，以深化对这些区域的挖掘。
2. 策略二：选择概率和成功率的自适应调整
算法还引入了对选择概率的自适应调整，以影响蜜蜂的决策过程。工蜂选择下一个解决方案的概率不再是一成不变的，而是根据其过去的成功率动态变化。这意味着，成功的工蜂更有可能被选中进行进一步的优化，而失败的工蜂则有更大的概率被替换，从而促进整体种群的进化。
这两种策略的结合使得算法能够更好地适应不断变化的优化环境，同时平衡全局搜索和局部搜索的能力，从而在解决连续优化问题时提高收敛速度和解决方案的质量。
此外，论文还可能包含了以下内容：
- 实验设计：可能对比了新算法与标准ABC算法以及其他优化算法（如遗传算法、粒子群优化等）的性能，通过一系列基准测试函数来验证新算法的优越性。
- 性能指标：可能使用了如收敛速度、最优解精度、稳定性等指标来评估算法的性能。
- 参数分析：可能对算法中的关键参数进行了敏感性分析，以确定最佳参数设置。
- 结果讨论：可能深入探讨了新算法在不同问题上的表现，以及策略适应如何影响优化过程。
这篇研究论文提出了一种创新的方法，通过结合两种策略的自适应机制来改进人工蜂群算法，以更有效地处理连续优化问题，这对优化算法的理论研究和实际应用具有重要意义。
X. Song et al. Swarm and Evolutionary Computation 50 (2019) 100549
search process, so as to balance exploration and exploitation, and thus
the search efficiency of the algorithm is improved.
3.1.1. CABC (and CABC_Elite)
To ensure the exploration ability of the algorithm, we employed
the search strategy which used random solution as the starting point
of search. Inspired by the crosser operator in genetic algorithms,
Literature [39] proposed a similar search strategy named CABC as
follows:
v
i,j
= x
r1,j
+ 𝜙
i,j
(x
r1,j
− x
r2,j
) (1)
where
𝜙
i,j
is a uniform random number on [−1, 1]; r1, r2andj are ran-
domly selected and r1
, r2 ∈{1, 2, SN}, j ∈{1, 2, D}, r1 ≠ r2 ≠ i.
In Eq. (1), the individuals are randomly selected from the population
with high randomness, thus the equation has strong exploration ability
and it has no preference to any search direction. So it can ensure the
exploration and maintain population diversity by adopting CABC in the
employed bee phase.
However, as a result, the exploitation is poor. Inspired by the natural
phenomenon that excellent individuals always have excellent genes, we
improved CABC as follows:
v
i,j
= x
pbest,j
+ 𝜙
i,j
(x
pbest,j
− x
r2,j
) (2)
In Eq. (2), pbest is an elite individual in the population. Obviously, Eq.
(2) can greatly increase the opportunity to improve around the elite
solutions, and effectively enhance the exploitation ability. This search
strategy is named CABC_Elite. It can be seen from the above equations
that CABC_Elite just limits the selection range of the first random solu-
tion in CABC to the elite solutions of the population, so as to enhance
exploitability. So CABC_Elite can be regarded as a special case of
CABC.
3.1.2. M2ABC
Although the above equation improves the exploitation ability to a
certain extent, but the exploitation ability needs to be further enhanced
because of the poor exploitation of ABC. For this purpose, a novel search
strategy named M2ABC is designed, which uses the best-so-far solution
information and searches with the mean of two random solutions as the
starting point, as shown in (3):
v
i,j
=(x
r1,j
+ x
r2,j
)∕2 + 𝜙
i,j
(x
r1,j
− x
r2,j
)+𝜙
i,j
(x
best,j
− x
r1,j
) (3)
where r1andr2 are different integers selected in
[1, SN] uniformly, and
they are different from best as well;
𝜙
i,j
is a random number generated
uniformly between
[−1, 1] and 𝜙
i,j
is also a random number generated
uniformly in the range
[0, 1]; x
best,j
is the jth element of the best-so-far
solution.
The first item of M2ABC is the midpoint of two random selected
solutions, which has certain randomness and is beneficial to maintain
exploration; the second item offers some information about direction,
which can improve the population diversity; the third item makes the
search move towards the best-so-far solution to increase the exploita-
tion ability.
To further discuss the exploration and exploitation of Eqs. (1) and
(3). We introduce the definition of exploration and exploitation in
Ref. [70], where, Crepinsek et al. proposed a more detailed definition.
Specifically, supposing that v is a candidate solution, the process of
exploration and exploitation is defined as follows:
Min
{v − x
i
2
x
i
∈ P} >𝜍 (4)
Min
{v − x
i
2
x
i
∈ P} ≤ 𝜍 (5)
where P denotes the current population, x
i
is the ith individual,
and
𝜍 is the threshold to define the nearest neighbourhood bound-
ary and depends on the problem. Eq. (4) represents exploration, and
Eq. (5) represents exploitation. In other words, the exploration pro-
cess visits areas outside the current nearest neighbourhood, while
the exploitation process searches areas within the current nearest
neighbourhood.
To prove the effectiveness of TSaABC, first of all, it should be noted
that any equation has the abilities to explore and to exploit. That
is, CABC and M2ABC not only focus on exploration or exploitation.
However, how to coordinate the proportion between exploration and
exploitation is very important to make full use of the advantages for
each equation. In the early evolution stage, the whole population con-
centrates on exploration. At this time, because of the strong randomness
of CABC, individuals in the population can search more areas, which
makes it possible to find better solutions. Later, with the population
evolution, CABC_Elite can accelerate convergence by effectively utiliz-
ing the information of high-quality solutions in the current population.
At the later evolution stage, the whole population tends to converge. At
this time, M2ABC can provide a large step due to its trinomial. This
increases the possibility of jumping out of the local optimum when
the population falls into the local optimum, and achieves the balance
between exploration and exploitation.
But, it is unknown when the population will shift from exploration
to exploitation, which is related to the specific problem. Therefore, in
order to take full advantage of each equation, this paper uses an adap-
tive mechanism to combine CABC and M2ABC. By dynamically choos-
ing different search equations in the evolution process, the population
can realize the fast optimizing behavior. The principle of the adaptive
mechanism is that if the success rate of a certain equation is higher in
the previous generation, more choices should be allocated to it in the
next generation to facilitate further search.
3.2. Adaptive mechanism
Inspired by the pheromone updating scheme [58] of ant colony algo-
rithm, the pf is updated as follows:
pf
G+1
= 𝛼 ∗ pf
G
+(1 − 𝛼)∗P
G
(6)
P
G
= S
G
1∕(S
G
1 + S
G
2) (7)
where SGk represents the success rate of candidate solutions generated
by strategy k in the previous generation. To ensure that the select proba-
bilities of the strategies are always summed to 1, we further divide S
G
k
by
(S
G
1 + S
G
2) to calculate PG. Obviously, the strategy with higher
success rate will have a higher probability to be selected to generate
candidate solution. A real number
𝛼 ∈[0, 1], is used to control the
proportion of historical experience.
In fact, the algorithm focuses more on historical experience when
𝛼
takes a larger value, while more on recent experience when 𝛼 takes a
smaller value. It can be seen from Table 1 that when
𝛼 = 0.95, the effect
of pf is only 35.85% and 12.85% respectively after the evolution of 10
and 20 generations (each generation employed bees and onlooker bees
modify pf only one time respectively). When
𝛼 = 0.9, after the evolution
of 10 and 20 generations, the original influence of pf only accounts
for 12.16% and 1.48% respectively. Thus considering the randomness
assigned to each individual by each strategy, a larger value of
𝛼 can
reduce the impact of randomness. Therefore, in this paper, the value of
𝛼 is 0.95.
3.3. TSaABC algorithm
In TSaABC, the exploration ability of the algorithm is ensured by uti-
lizing the characteristic of CABC that randomly selects individuals from
the population and does not bias in any direction. At the same time,
M2ABC can use the information of the best-so-far solution to enhance
the exploitation ability; moreover, it can provide more combinations
of search directions and step sizes because its search equation contains
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